Current proof boundary

Current findings and proof limits

Correction, not an earned milestone · 2026-09-30

Why a complete local search can still miss a global improvement

The project has verified a limit of the implemented circuit search: no fixed cap on the number of gates checked together makes it a complete test for global minimality. For every such cap, a circuit can be made smaller even though the complete bounded search finds no accepted improvement. Every proper selected part, including disconnected selections, is already minimal when its boundary inputs are treated as independent.

The result rules out using this fixed-size local search alone to certify that an entire circuit is minimal. It does not settle P versus NP or rule out growing windows or transformations that use the surrounding circuit. A corrected route must still prove global coverage and polynomial runtime for the complete construction. This correction does not earn a positive milestone or increase the proof-completion estimate.

This correction adds no earned positive publication row or fixed checkpoint credit. Read the verified correction and its limits.

Correction, not an earned milestone · 2026-09-24

A verified limit on replacing parts of a circuit

The project has verified a counterexample to an unrestricted reading of the original report's replacement claim. The checked example has a smaller replacement for one part, but inserting it would create a circular dependency; the whole circuit was already minimal.

This does not invalidate the checked replacement results that enforce the necessary restrictions, and it does not settle P versus NP. It identifies a central obligation for the next research: derive the admissible replacements and show that the general method can use them without losing the required saving.

This correction adds no earned positive publication row or fixed checkpoint credit. Read the verified correction and its limits.

Latest earned milestone: M280.

Proving cost comparisons for nested completed supports

This establishes the enlargement step for already-completed supports. It does not show that every raw local witness can be completed without losing its saving, and the complete admissibility and global routing arguments remain open.

This is not a globally successful rewrite strategy or a theorem of total polynomial runtime.

M230 and M231 retain the complete Cook-Levin builder and concrete CNF-SAT NP-completeness; a polynomial-time SAT decision algorithm remains open.

Risk-weighted proof completion estimate: 40%, with uncertainty 20% to 40%. Formal artefact coverage: 256 of 258 current scoped publication rows earned. Global gates closed: 0 of 5. Project-specific axioms remaining: 0. The eligible root theorem PNP.Main.p_eq_np remains absent and the publication gate is false.

P = NP is not established.

Read the source-bound milestone and limitations

Formal status · 2026-09-20

The project has verified parts of the construction, not P = NP.

256 of 258 scoped milestone rows are earned. This is formal artefact coverage, not proof completion. For nested supports that have already been completed by the existing construction, the project now builds the comparison circuits needed to prove cost and positive-saving bounds. The bounds follow from those physical constructions instead of being assumptions.

Read the latest earned update Open technical status Open current report

Fixed-weight model v0

Risk-weighted proof completion estimate

40%

Current uncertainty range: 20% to 40%

A conservative estimate of how much of the complete formal proof burden has been retired. This is not confidence that P=NP is true, a probability of success, or a time estimate.

40%

Risk-weighted proof completion estimate 40 percent, with uncertainty from 20 to 40 percent

Five-track breakdown

Formal foundations and proof infrastructure13 / 15
Concrete reductions and locked-NAND route20 / 20
Unconditional residual core and ZeroSlack2 / 35
Exact PCCMin algorithm, complexity and bounds1 / 20
Root theorem and project-axiom elimination4 / 10

Separate evidence metric

Formal artefact coverage

256 of 258

99.2% of the current evidence ledger.

This measures coverage of the current scoped publication ledger. It is not proof completion, and the denominator can grow as new formal dependencies are discovered.

Load-bearing obligations

Global proof gates

0 of 5 closed

Concrete SATOpen
Residual-band minimiserOpen
Unconditional ZeroSlackOpen
Polynomial runtime and certificate boundsOpen
Root theorem and axiom auditOpen

Project-specific axioms remaining: 0
Root theorem PNP.Main.p_eq_np: absent
Publication gate: false

Current values are generated from the byte-mirrored PNPProofProgress0 ledger and checked against the formal reconstruction status and compiled theorem inventory.

The milestone ledger below preserves recorded scopes and boundaries. Later results may close obligations described as open in older rows. The tracker above and current proof boundary describe today's project status.

Plain-language snapshot

Verified, next, and still missing

These cards are orientation. The compiled inventory and exact theorem records remain the technical authority below.

Verified now

For nested supports that have already been completed by the existing construction, the project now builds the comparison circuits needed to prove cost and positive-saving bounds. The bounds follow from those physical constructions instead of being assumptions. M230 and M231 retain the complete Cook-Levin builder and concrete CNF-SAT NP-completeness; a polynomial-time SAT decision algorithm remains open.

Next construction work

Derive the admissible replacements and prove that the general method reaches a valid improving step without losing the required saving. The unrestricted replacement claim has a checked counterexample. The highest-impact next obligation is complete source-derived admissibility and global routing, not another finite example.

Still missing globally

A deterministic polynomial-time SAT algorithm, unconditional residual minimization and global ZeroSlack, complete PCCMin runtime and certificate bounds, and the eligible root theorem remain open. The report-facing compatibility alias and conditional report bridge are not a proof. All five global gates remain open.

Exact theorem and gate fieldsnot established

leanResidualTerminalProfileDependencySemanticsFormalized = true
leanResidualTerminalProfileDependencySemanticsAxiomAuditPassed = true
leanResidualTerminalProfileDependencySemanticsAuditedDeclarationCount = 4
leanResidualTerminalProfileDependencyNoninterferenceTheorem = "PNP.DirectWire.terminalCandidateSaturate_profile_noninterference"
leanResidualTerminalProfileDependencySemanticsScope = "all-finite-candidates-executable-models-computed-profile-influence-role-labelled-edges-and-computed-saturation-noninterference-in-canonical-contexts-only"
leanResidualTerminalProfileLocalityFormalized = true
leanResidualTerminalProfileLocalityAxiomAuditPassed = true
leanResidualTerminalProfileLocalityAuditedDeclarationCount = 5
leanResidualTerminalProfileLocalityTheorem = "PNP.DirectWire.terminalCandidateSaturate_profile_locality"
leanResidualTerminalProfilePreservationTheorem = "PNP.DirectWire.terminalCandidateSaturate_profile_preserved"
leanResidualTerminalProfileLocalityScope = "all-finite-candidates-executable-models-arbitrary-primitive-record-supports-computed-saturation-retained-ambient-profile-locality-and-preservation-only"
leanResidualTerminalSaturationTraceFidelityFormalized = true
leanResidualTerminalSaturationTraceFidelityAxiomAuditPassed = true
leanResidualTerminalSaturationTraceFidelityAuditedDeclarationCount = 5
leanResidualTerminalSaturationReplayTheorem = "PNP.DirectWire.terminalSaturateTrace_replayRecords_iff"
leanResidualTerminalSaturationEventValidityTheorem = "PNP.DirectWire.terminalSaturateTrace_event_valid"
leanResidualTerminalSaturationMetadataTransparencyTheorem = "PNP.DirectWire.terminalCandidateSaturateTrace_metadata_transparent"
leanResidualTerminalSaturationTraceFidelityScope = "all-finite-systems-candidates-executable-models-seeds-generated-events-actual-replay-ambient-endpoint-cost-snapshot-and-metadata-transparency-only"
leanResidualTerminalPhysicalSaturationAccountingFormalized = true
leanResidualTerminalPhysicalSaturationAccountingAxiomAuditPassed = true
leanResidualTerminalPhysicalSaturationAccountingAuditedDeclarationCount = 5
leanResidualTerminalSaturationEventContextTheorem = "PNP.DirectWire.terminalSaturateTrace_event_context"
leanResidualTerminalPhysicalSaturationSupportCostTheorem = "PNP.DirectWire.terminalCandidateSaturateTrace_supportCostBalanced"
leanResidualTerminalPhysicalSaturationActiveOwnerTheorem = "PNP.DirectWire.terminalCandidateSaturateTrace_event_owner"
leanResidualTerminalPhysicalSaturationObstructionTheorem = "PNP.DirectWire.terminalCandidateSaturateTrace_physicalObstruction"
leanResidualTerminalPhysicalSaturationBalanceOrObstructionTheorem = "PNP.DirectWire.terminalCandidateSaturateTrace_balance_or_physicalObstruction"
leanResidualTerminalPhysicalSaturationAccountingScope = "all-finite-systems-candidates-executable-models-seeds-generated-events-fresh-context-unit-physical-support-cost-active-owner-and-canonical-endpoint-first-obstruction-only"
leanResidualTerminalPhysicalChargeLedgerFormalized = true
leanResidualTerminalPhysicalChargeLedgerAxiomAuditPassed = true
leanResidualTerminalPhysicalChargeLedgerAuditedDeclarationCount = 5
leanResidualTerminalPhysicalChargeLedgerNodupTheorem = "PNP.DirectWire.terminalSaturatePhysicalCharges_nodup"
leanResidualTerminalPhysicalChargeLedgerCompletenessTheorem = "PNP.DirectWire.terminalSaturatePhysicalCharges_complete"
leanResidualTerminalPhysicalChargeLedgerProvenanceTheorem = "PNP.DirectWire.terminalSaturatePhysicalCharges_provenance"
leanResidualTerminalPhysicalChargeLedgerLookupTheorem = "PNP.DirectWire.terminalSaturatePhysicalChargeProvenance?_iff"
leanResidualTerminalPhysicalChargeLedgerSizeTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalCharges_size"
leanResidualTerminalPhysicalChargeLedgerScope = "all-finite-systems-candidates-executable-models-seeds-computed-physical-nand-charge-partition-nodup-completeness-introduction-provenance-lookup-and-total-support-size-only"
leanResidualTerminalSaturatedSupportContextFormalized = true
leanResidualTerminalSaturatedSupportContextAxiomAuditPassed = true
leanResidualTerminalSaturatedSupportContextAuditedDeclarationCount = 5
leanResidualTerminalSaturatedSupportContextBoundaryTheorem = "PNP.DirectWire.terminalCandidateSaturate_boundary_isInput"
leanResidualTerminalSaturatedSupportContextSizeTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_size"
leanResidualTerminalSaturatedSupportContextReconstructionTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_equivalent"
leanResidualTerminalSaturatedSupportContextReplacementTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_replace_equivalent"
leanResidualTerminalSaturatedSupportContextSlackTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalSupport_slack_le"
leanResidualTerminalSaturatedSupportContextScope = "all-finite-candidates-executable-models-seeds-production-saturated-supports-computed-physical-complement-context-primary-input-boundary-exact-gate-partition-whole-boolean-reconstruction-equivalent-replacement-and-physical-slack-only"
leanResidualTerminalPhysicalGainFormalized = true
leanResidualTerminalPhysicalGainAxiomAuditPassed = true
leanResidualTerminalPhysicalGainAuditedDeclarationCount = 5
leanResidualTerminalPhysicalGainEquivalenceTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_equivalent"
leanResidualTerminalPhysicalGainSizeTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_size_gain"
leanResidualTerminalPhysicalGainSlackTheorem = "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_slack_gain"
leanResidualTerminalPhysicalGainSearchSoundnessTheorem = "PNP.DirectWire.findTerminalCandidatePhysicalGain_sound"
leanResidualTerminalPhysicalGainSearchFailureTheorem = "PNP.DirectWire.findTerminalCandidatePhysicalGain_eq_none_iff"
leanResidualTerminalPhysicalGainScope = "all-finite-candidates-executable-models-production-saturated-supports-computed-reference-minimum-replacements-exact-physical-size-and-slack-descent-and-complete-proper-positive-search-only"
leanResidualTerminalGainProfileFirewallFormalized = true
leanResidualTerminalGainProfileFirewallAxiomAuditPassed = true
leanResidualTerminalGainProfileFirewallAuditedDeclarationCount = 7
leanResidualTerminalGainProfileFirewallProfileScanTheorem = "PNP.DirectWire.firstTerminalGainProfileMismatch_eq_none_iff"
leanResidualTerminalGainProfileFirewallFirstMismatchTheorem = "PNP.DirectWire.firstTerminalGainProfileMismatch_spec"
leanResidualTerminalGainProfileFirewallFullMinimumTheorem = "PNP.DirectWire.terminalFullProfileMinimum_eq_of_fullRealization"
leanResidualTerminalGainProfileFirewallAcceptanceTheorem = "PNP.DirectWire.classifyTerminalCandidateGainProfile_accepted_iff"
leanResidualTerminalGainProfileFirewallSearchFailureTheorem = "PNP.DirectWire.classifyTerminalCandidateGainProfile_noGain_iff"
leanResidualTerminalGainProfileFirewallRejectionTheorem = "PNP.DirectWire.classifyTerminalCandidateGainProfile_mismatch_iff"
leanResidualTerminalGainProfileFirewallFullSlackTheorem = "PNP.DirectWire.TerminalCandidateFullProfileGain.fullSlack_gain"
leanResidualTerminalGainProfileFirewallScope = "all-finite-candidates-supplied-executable-profile-models-computed-physical-gain-full-coordinate-first-mismatch-acceptance-and-exact-accepted-full-profile-slack-descent-only"
leanResidualIndependentMaterializerCostFormalized = true
leanResidualIndependentMaterializerCostAxiomAuditPassed = true
leanResidualIndependentMaterializerCostAuditedDeclarationCount = 7
leanResidualIndependentMaterializerCostSizeTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_size"
leanResidualIndependentMaterializerCostOriginalOutputsTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_original"
leanResidualIndependentMaterializerCostFreshOutputsTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_materializer"
leanResidualIndependentMaterializerCostLowerBoundTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_lower_bound"
leanResidualIndependentMaterializerCostEquivalenceTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_equivalent"
leanResidualIndependentMaterializerCostMinimumTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_referenceMinimum"
leanResidualIndependentMaterializerCostSlackTheorem = "PNP.DirectWire.appendIndependentNandMaterializers_residualSlack"
leanResidualIndependentMaterializerCostScope = "all-finite-original-candidates-and-bank-sizes-disjoint-fresh-input-nand-materializers-computed-erasure-unrestricted-competitors-exact-reference-minimum-additivity-and-physical-slack-preservation-only"
leanResidualTerminalPhysicalOwnershipFormalized = true
leanResidualTerminalPhysicalOwnershipAxiomAuditPassed = true
leanResidualTerminalPhysicalOwnershipAuditedDeclarationCount = 10
leanResidualTerminalPhysicalOwnershipUnrequestedTheorem = "PNP.DirectWire.terminalPhysicalOwner_none_iff"
leanResidualTerminalPhysicalOwnershipFirstOwnerTheorem = "PNP.DirectWire.terminalPhysicalOwner_first"
leanResidualTerminalPhysicalOwnershipPartitionTheorem = "PNP.DirectWire.terminalOwnedPhysicalGates_partition"
leanResidualTerminalPhysicalOwnershipDisjointTheorem = "PNP.DirectWire.terminalOwnedPhysicalGates_disjoint"
leanResidualTerminalPhysicalOwnershipRestrictionTheorem = "PNP.DirectWire.terminalOwnedPhysicalGates_restrict"
leanResidualTerminalPhysicalOwnershipGateCountTheorem = "PNP.DirectWire.terminalOwnedPhysicalMaterializer_gateCount"
leanResidualTerminalPhysicalOwnershipChargeIdentityTheorem = "PNP.DirectWire.terminalOwnedPhysicalMaterializer_chargeIdentity"
leanResidualTerminalPhysicalOwnershipOpenSemanticsTheorem = "PNP.DirectWire.terminalOwnedPhysicalMaterializer_semantics"
leanResidualTerminalPhysicalOwnershipInducedSemanticsTheorem = "PNP.DirectWire.terminalOwnedPhysicalMaterializer_induced"
leanResidualTerminalPhysicalOwnershipWholeChargeTheorem = "PNP.DirectWire.terminalOwnedPhysicalMaterializer_wholeCharge"
leanResidualTerminalPhysicalOwnershipScope = "all-finite-candidates-raw-request-families-and-supports-first-requester-ambient-ownership-fixed-remainder-disjoint-stable-physical-pieces-actual-extracted-nand-counts-open-semantics-and-exact-charge-total-only"
leanPCCMinConstructiveNANDSharingFormalized = true
leanPCCMinConstructiveNANDSharingAxiomAuditPassed = true
leanPCCMinConstructiveNANDSharingAuditedDeclarationCount = 9
leanPCCMinConstructiveNANDSharingAliasSemanticsTheorem = "PNP.DirectWire.compileNANDSharing_alias_semantics"
leanPCCMinConstructiveNANDSharingGateAccountingTheorem = "PNP.DirectWire.compileNANDSharing_exact_accounting"
leanPCCMinConstructiveNANDSharingEquivalenceTheorem = "PNP.DirectWire.sharingImplementation_equivalent"
leanPCCMinConstructiveNANDSharingGateCountTheorem = "PNP.DirectWire.sharingImplementation_gateCount_le"
leanPCCMinConstructiveNANDSharingReferenceMinimumTheorem = "PNP.DirectWire.sharingImplementation_referenceMinimum"
leanPCCMinConstructiveNANDSharingResidualSlackTheorem = "PNP.DirectWire.sharingImplementation_residualSlack"
leanPCCMinConstructiveNANDSharingStrictGainTheorem = "PNP.DirectWire.sharingImplementation_strictGain_iff"
leanPCCMinConstructiveNANDSharingStrictResidualDescentTheorem = "PNP.DirectWire.sharingImplementation_strictResidualDescent"
leanPCCMinConstructiveNANDSharingNormalizerTheorem = "PNP.DirectWire.nandSharingNormalizer_checked"
leanPCCMinConstructiveNANDSharingScope = "all-finite-nand-programs-and-ordered-outputs-computed-structural-and-commuted-reuse-alias-semantics-exact-fold-accounting-invariant-reference-minimum-residual-descent-and-concrete-normalizer-stage-only"
leanConcreteFinalReportBridgeFormalized = true
leanConcreteFinalReportBridgeAxiomAuditPassed = true
leanConcreteFinalReportBridgeAuditedDeclarationCount = 4
leanConcreteFinalReportBridgeSATHardnessTheorem = "PNP.sat_np_hard_checked"
leanConcreteFinalReportBridgeSATCompletenessTheorem = "PNP.sat_np_complete_checked"
leanConcreteFinalReportBridgePackageConsequenceTheorem = "PNP.accepted_generated_package_implies_p_eq_np"
leanConcreteFinalReportBridgeFinalReportTheorem = "PNP.final_report_bridge"
leanConcreteFinalReportBridgeRequiresSuppliedSATHardness = false
leanConcreteFinalReportBridgeLoopCertificateExistenceDischarged = false
leanConcreteFinalReportBridgeScope = "checked-all-input-concrete-cook-levin-hardness-consumed-by-the-active-conditional-final-report-bridge-explicit-proof-bearing-pccmin-loop-existence-still-required"
leanPCCMinOutputConePruningFormalized = true
leanPCCMinOutputConePruningAxiomAuditPassed = true
leanPCCMinOutputConePruningAuditedDeclarationCount = 11
leanPCCMinOutputConePruningOutputCoverageTheorem = "PNP.DirectWire.outputConeRecords_output"
leanPCCMinOutputConePruningPredecessorClosureTheorem = "PNP.DirectWire.outputConeRecords_closed"
leanPCCMinOutputConePruningLeastConeTheorem = "PNP.DirectWire.outputConeRecords_least"
leanPCCMinOutputConePruningNoExternalGateTheorem = "PNP.DirectWire.outputConeRecords_noExternalGate"
leanPCCMinOutputConePruningEquivalenceTheorem = "PNP.DirectWire.outputConeImplementation_equivalent"
leanPCCMinOutputConePruningGateCountTheorem = "PNP.DirectWire.outputConeImplementation_gateCount_le"
leanPCCMinOutputConePruningGateAccountingTheorem = "PNP.DirectWire.outputConeImplementation_exact_accounting"
leanPCCMinOutputConePruningReferenceMinimumTheorem = "PNP.DirectWire.outputConeImplementation_referenceMinimum"
leanPCCMinOutputConePruningResidualSlackTheorem = "PNP.DirectWire.outputConeImplementation_residualSlack"
leanPCCMinOutputConePruningStrictGainTheorem = "PNP.DirectWire.outputConeImplementation_strictGain_iff"
leanPCCMinOutputConePruningNormalizerTheorem = "PNP.DirectWire.outputConeNormalizer_checked"
leanPCCMinOutputConePruningFullProfilePreservationProved = false
leanPCCMinOutputConePruningPolynomialRuntimeProved = false
leanPCCMinOutputConePruningScope = "all-finite-nand-candidates-derived-least-physical-output-predecessor-cone-checked-support-extraction-original-io-semantics-exact-deletion-accounting-and-physical-normalizer-stage-only"
leanPCCMinDeadSupportContextFormalized = true
leanPCCMinDeadSupportContextAxiomAuditPassed = true
leanPCCMinDeadSupportContextAuditedDeclarationCount = 20
leanPCCMinDeadSupportContextFrontierSemanticsTheorem = "PNP.DirectWire.outputConeFrontierCandidate_semantics"
leanPCCMinDeadSupportContextEmptyInterfaceTheorem = "PNP.DirectWire.deadSupport_interface_empty"
leanPCCMinDeadSupportContextGatePartitionTheorem = "PNP.DirectWire.deadSupportGateCount_partition"
leanPCCMinDeadSupportContextDeletedCountTheorem = "PNP.DirectWire.deadSupportGateCount_eq_deleted"
leanPCCMinDeadSupportContextBoundaryValuesTheorem = "PNP.DirectWire.deadSupportEnvironment_boundary"
leanPCCMinDeadSupportContextBypassOutputsTheorem = "PNP.DirectWire.deadSupportEnvironment_bypass"
leanPCCMinDeadSupportContextActualExtractionTheorem = "PNP.DirectWire.deadSupportCandidate_extracted"
leanPCCMinDeadSupportContextExtractedProgramTheorem = "PNP.DirectWire.deadSupportCandidate_program"
leanPCCMinDeadSupportContextLocalEquivalenceTheorem = "PNP.DirectWire.deadSupportEmptyReplacement_equivalent"
leanPCCMinDeadSupportContextFramedEquivalenceTheorem = "PNP.DirectWire.deadSupportContext_plug_equivalent"
leanPCCMinDeadSupportContextOriginalFrameSizeTheorem = "PNP.DirectWire.deadSupportContext_original_size"
leanPCCMinDeadSupportContextReplacementGateCountTheorem = "PNP.DirectWire.deadSupportReplacement_gateCount"
leanPCCMinDeadSupportContextReplacementEquivalenceTheorem = "PNP.DirectWire.deadSupportReplacement_equivalent"
leanPCCMinDeadSupportContextReplacementAccountingTheorem = "PNP.DirectWire.deadSupportReplacement_accounting"
leanPCCMinDeadSupportContextResidualSlackTheorem = "PNP.DirectWire.deadSupportReplacement_residualSlack"
leanPCCMinDeadSupportContextStrictGainTheorem = "PNP.DirectWire.deadSupportReplacement_strictGain_iff"
leanPCCMinDeadSupportContextProperAcceptanceTheorem = "PNP.DirectWire.deadSupportProperGain_isSome_iff"
leanPCCMinDeadSupportContextProperGainSoundnessTheorem = "PNP.DirectWire.deadSupportProperGain_sound"
leanPCCMinDeadSupportContextAllDeadRejectionTheorem = "PNP.DirectWire.deadSupportProperGain_none_of_all_dead"
leanPCCMinDeadSupportContextNoDeadRejectionTheorem = "PNP.DirectWire.deadSupportProperGain_none_of_no_dead"
leanPCCMinDeadSupportContextFullProfileAdmissibilityProved = false
leanPCCMinDeadSupportContextCompletePackageEVerifierProved = false
leanPCCMinDeadSupportContextPolynomialRuntimeProved = false
leanPCCMinDeadSupportContextScope = "all-finite-nand-implementations-computed-dead-gate-complement-empty-interface-exact-extracted-support-live-frontier-environment-framed-replacement-and-nonempty-proper-physical-gain-only"
leanPCCMinDeadSupportFullModeFormalized = true
leanPCCMinDeadSupportFullModeAxiomAuditPassed = true
leanPCCMinDeadSupportFullModeAuditedDeclarationCount = 8
leanPCCMinDeadSupportFullModeObligationScanTheorem = "PNP.DirectWire.firstTerminalOpenObligation_eq_none_iff"
leanPCCMinDeadSupportFullModeFirstOpenObligationTheorem = "PNP.DirectWire.firstTerminalOpenObligation_spec"
leanPCCMinDeadSupportFullModeCurrentObligationsTheorem = "PNP.DirectWire.DeadSupportFullModeGain.currentObligationsDischarged"
leanPCCMinDeadSupportFullModeAcceptanceTheorem = "PNP.DirectWire.classifyDeadSupportFullMode_accepted_iff"
leanPCCMinDeadSupportFullModeNoProperSupportTheorem = "PNP.DirectWire.classifyDeadSupportFullMode_noProperSupport_iff"
leanPCCMinDeadSupportFullModeFullProfileMinimumTheorem = "PNP.DirectWire.DeadSupportFullModeGain.fullProfileMinimum"
leanPCCMinDeadSupportFullModeAcceptedSoundnessTheorem = "PNP.DirectWire.DeadSupportFullModeGain.checked"
leanPCCMinDeadSupportFullModeClassifierSoundnessTheorem = "PNP.DirectWire.classifyDeadSupportFullMode_checked"
leanPCCMinDeadSupportFullModeManuscriptCarrierDerived = false
leanPCCMinDeadSupportFullModeCompletePackageEVerifierProved = false
leanPCCMinDeadSupportFullModePolynomialRuntimeProved = false
leanPCCMinDeadSupportFullModeScope = "computed-proper-dead-support-complete-finite-profile-and-observed-obligation-acceptance-over-input-observation-system-no-derived-manuscript-carrier-or-discharge-ledger"
leanPCCMinConstantPropagationFormalized = true
leanPCCMinConstantPropagationAxiomAuditPassed = true
leanPCCMinConstantPropagationAuditedDeclarationCount = 10
leanPCCMinConstantPropagationConstantRuleTheorem = "PNP.DirectWire.constantGateValue_sound"
leanPCCMinConstantPropagationAliasSemanticsTheorem = "PNP.DirectWire.compileNANDConstantPropagation_alias_semantics"
leanPCCMinConstantPropagationGateAccountingTheorem = "PNP.DirectWire.compileNANDConstantPropagation_exact_accounting"
leanPCCMinConstantPropagationEquivalenceTheorem = "PNP.DirectWire.constantPropagationImplementation_equivalent"
leanPCCMinConstantPropagationGateCountTheorem = "PNP.DirectWire.constantPropagationImplementation_gateCount_le"
leanPCCMinConstantPropagationReferenceMinimumTheorem = "PNP.DirectWire.constantPropagationImplementation_referenceMinimum"
leanPCCMinConstantPropagationResidualSlackTheorem = "PNP.DirectWire.constantPropagationImplementation_residualSlack"
leanPCCMinConstantPropagationStrictGainTheorem = "PNP.DirectWire.constantPropagationImplementation_strictGain_iff"
leanPCCMinConstantPropagationResidualDescentTheorem = "PNP.DirectWire.constantPropagationImplementation_strictResidualDescent"
leanPCCMinConstantPropagationNormalizerTheorem = "PNP.DirectWire.nandConstantPropagationNormalizer_checked"
leanPCCMinConstantPropagationFullProfilePreservationProved = false
leanPCCMinConstantPropagationCompleteNormalizationProved = false
leanPCCMinConstantPropagationPolynomialRuntimeProved = false
leanPCCMinConstantPropagationScope = "all-finite-direct-wire-nand-programs-computed-literal-constant-propagation-through-source-aliases-complete-ordered-io-exact-elimination-accounting-physical-normalizer-stage-only"
leanPCCMinPhysicalNormalizationClosureFormalized = true
leanPCCMinPhysicalNormalizationClosureAxiomAuditPassed = true
leanPCCMinPhysicalNormalizationClosureAuditedDeclarationCount = 12
leanPCCMinPhysicalNormalizationClosurePassEquivalenceTheorem = "PNP.DirectWire.physicalNormalizationPass_equivalent"
leanPCCMinPhysicalNormalizationClosurePassAccountingTheorem = "PNP.DirectWire.physicalNormalizationPass_exact_accounting"
leanPCCMinPhysicalNormalizationClosureSelectedGainTheorem = "PNP.DirectWire.PhysicalNormalizationGain.checked"
leanPCCMinPhysicalNormalizationClosurePrioritySelectionTheorem = "PNP.DirectWire.nextPhysicalNormalizationStep_checked"
leanPCCMinPhysicalNormalizationClosureTraceAccountingTheorem = "PNP.DirectWire.PhysicalNormalizationTrace.checked"
leanPCCMinPhysicalNormalizationClosureComputedClosureTheorem = "PNP.DirectWire.runPhysicalNormalization_checked"
leanPCCMinPhysicalNormalizationClosureQuiescentInputTheorem = "PNP.DirectWire.runPhysicalNormalization_of_quiescent"
leanPCCMinPhysicalNormalizationClosureIdempotenceTheorem = "PNP.DirectWire.runPhysicalNormalization_idempotent"
leanPCCMinPhysicalNormalizationClosureReferenceMinimumTheorem = "PNP.DirectWire.runPhysicalNormalization_referenceMinimum"
leanPCCMinPhysicalNormalizationClosureResidualSlackTheorem = "PNP.DirectWire.runPhysicalNormalization_residualSlack"
leanPCCMinPhysicalNormalizationClosureIterationBoundTheorem = "PNP.DirectWire.runPhysicalNormalization_gainIterations_le_residualSlack"
leanPCCMinPhysicalNormalizationClosureNormalizerTheorem = "PNP.DirectWire.physicalClosureNormalizer_checked"
leanPCCMinPhysicalNormalizationClosureFullProfilePreservationProved = false
leanPCCMinPhysicalNormalizationClosureCompleteNormalizationProved = false
leanPCCMinPhysicalNormalizationClosurePolynomialRuntimeProved = false
leanPCCMinPhysicalNormalizationClosureScope = "all-finite-direct-wire-implementations-computed-priority-three-pass-physical-closure-common-quiescence-actual-strict-trace-exact-savings-idempotent-result-no-complete-manuscript-normalization-or-polynomial-runtime"
leanArbitrarySupportSpliceFormalized = true
leanArbitrarySupportSpliceAxiomAuditPassed = true
leanArbitrarySupportSpliceAuditedDeclarationCount = 24
leanArbitrarySupportSpliceCompilerSuccessTheorem = "PNP.DirectWire.compileRawNandGraph_success_iff"
leanArbitrarySupportSpliceCompilerFailureTheorem = "PNP.DirectWire.compileRawNandGraph_failure_iff"
leanArbitrarySupportSpliceRawOutputSemanticsTheorem = "PNP.DirectWire.CompiledRawNandGraph.candidate_semantics"
leanArbitrarySupportSpliceExactGateCountTheorem = "PNP.DirectWire.ArbitrarySupportSplice.result_gateCount"
leanArbitrarySupportSpliceGraphEquationsTheorem = "PNP.DirectWire.ArbitrarySupportSplice.values_solution"
leanArbitrarySupportSpliceGlobalSemanticsTheorem = "PNP.DirectWire.ArbitrarySupportSplice.result_semantics"
leanArbitrarySupportSplicePartitionTheorem = "PNP.DirectWire.ArbitrarySupportSplice.exterior_accounting"
leanArbitrarySupportSpliceExactAccountingTheorem = "PNP.DirectWire.ArbitrarySupportSplice.result_exact_accounting"
leanArbitrarySupportSpliceStrictGainTheorem = "PNP.DirectWire.ArbitrarySupportSplice.result_strict_gain"
leanArbitrarySupportSpliceProductionOrderTheorem = "PNP.DirectWire.ArbitrarySupportSplice.graph_rank_decreases"
leanArbitrarySupportSpliceProductionSuccessTheorem = "PNP.DirectWire.ArbitrarySupportSplice.production_compiles"
leanArbitrarySupportSpliceProductionAgreementTheorem = "PNP.DirectWire.ArbitrarySupportSplice.production_agreement"
leanArbitrarySupportSpliceUnrestrictedReplacementSuccessProved = false
leanArbitrarySupportSpliceFullProfilePreservationProved = false
leanArbitrarySupportSpliceCompletePackageEProved = false
leanArbitrarySupportSplicePolynomialRuntimeProved = false
leanArbitrarySupportSpliceScope = "all-finite-actual-supports-computed-literal-exterior-replacement-graph-derived-topological-order-complete-ordered-output-semantics-exact-accounting-cyclic-rejection-production-saturation-success-physical-only"
leanWireCarrierTransportFormalized = true
leanWireCarrierTransportAxiomAuditPassed = true
leanWireCarrierTransportAuditedDeclarationCount = 16
leanWireCarrierTransportPackUnpackTheorem = "PNP.DirectWire.WireCarrier.exposed_unpack"
leanWireCarrierTransportUnpackPackTheorem = "PNP.DirectWire.WireCarrier.unpack_exposed"
leanWireCarrierTransportNormalizationOutputTheorem = "PNP.DirectWire.WireCarrier.normalize_output"
leanWireCarrierTransportNormalizationFieldTheorem = "PNP.DirectWire.WireCarrier.normalize_field"
leanWireCarrierTransportNormalizationAccountingTheorem = "PNP.DirectWire.WireCarrier.normalize_exact_accounting"
leanWireCarrierTransportNormalizationQuiescenceTheorem = "PNP.DirectWire.WireCarrier.normalize_quiescent"
leanWireCarrierTransportNormalizationIdempotenceTheorem = "PNP.DirectWire.WireCarrier.normalize_idempotent"
leanWireCarrierTransportHiddenFieldInterfaceTheorem = "PNP.DirectWire.WireCarrier.field_producer_visible"
leanWireCarrierTransportSpliceOutputTheorem = "PNP.DirectWire.WireCarrier.splice_output"
leanWireCarrierTransportSpliceFieldTheorem = "PNP.DirectWire.WireCarrier.splice_field"
leanWireCarrierTransportSpliceAccountingTheorem = "PNP.DirectWire.WireCarrier.splice_exact_accounting"
leanWireCarrierTransportSpliceStrictGainTheorem = "PNP.DirectWire.WireCarrier.splice_strict_gain"
leanWireCarrierTransportSpliceExecutionTheorem = "PNP.DirectWire.WireCarrier.splice_checked"
leanWireCarrierTransportCyclicRejectionTheorem = "PNP.DirectWire.WireCarrier.splice_failure_iff"
leanWireCarrierTransportProductionBoundaryTheorem = "PNP.DirectWire.WireCarrier.production_boundary_isInput"
leanWireCarrierTransportProductionSuccessTheorem = "PNP.DirectWire.WireCarrier.production_compiles"
leanWireCarrierTransportFullManuscriptCarrierDerived = false
leanWireCarrierTransportObligationLifecycleProved = false
leanWireCarrierTransportUnrestrictedReplacementSuccessProved = false
leanWireCarrierTransportCompletePackageEProved = false
leanWireCarrierTransportPolynomialRuntimeProved = false
leanWireCarrierTransportScope = "all-finite-literal-wire-backed-computational-fields-complete-ordered-exposure-computed-normalization-and-arbitrary-support-splice-value-preservation-exact-physical-accounting-derived-production-predecessors-no-full-manuscript-carrier-or-polynomial-runtime"
leanWireObligationRestorationFormalized = true
leanWireObligationRestorationAxiomAuditPassed = true
leanWireObligationRestorationAuditedDeclarationCount = 22
leanWireObligationRestorationProjectedOutputTheorem = "PNP.DirectWire.WireObligationRestoration.projected_output"
leanWireObligationRestorationProjectedKeptFieldTheorem = "PNP.DirectWire.WireObligationRestoration.projected_kept_field"
leanWireObligationRestorationMaterializerForgottenFieldTheorem = "PNP.DirectWire.WireObligationRestoration.materializer_forgotten_field"
leanWireObligationRestorationJoinOutputTheorem = "PNP.DirectWire.WireObligationRestoration.join_output"
leanWireObligationRestorationJoinKeptFieldTheorem = "PNP.DirectWire.WireObligationRestoration.join_kept_field"
leanWireObligationRestorationJoinForgottenFieldTheorem = "PNP.DirectWire.WireObligationRestoration.join_forgotten_field"
leanWireObligationRestorationRestoredOutputTheorem = "PNP.DirectWire.WireObligationRestoration.restored_output"
leanWireObligationRestorationRestoredFieldTheorem = "PNP.DirectWire.WireObligationRestoration.restored_field"
leanWireObligationRestorationExactGateChargeTheorem = "PNP.DirectWire.WireObligationRestoration.restored_exact_gate_charge"
leanWireObligationRestorationGateBoundTheorem = "PNP.DirectWire.WireObligationRestoration.restored_gate_bound"
leanWireObligationRestorationCreatedCoordinatesTheorem = "PNP.DirectWire.WireObligationRestoration.created_exact"
leanWireObligationRestorationDischargedCoordinatesTheorem = "PNP.DirectWire.WireObligationRestoration.discharged_exact"
leanWireObligationRestorationForgottenMaskTheorem = "PNP.DirectWire.WireObligationRestoration.mem_forgottenCoordinates_iff"
leanWireObligationRestorationCreationMembershipTheorem = "PNP.DirectWire.WireObligationRestoration.creation_iff"
leanWireObligationRestorationDischargeMembershipTheorem = "PNP.DirectWire.WireObligationRestoration.discharge_iff"
leanWireObligationRestorationClosedReplayTheorem = "PNP.DirectWire.WireObligationRestoration.replay_closed"
leanWireObligationRestorationFullDischargeValueTheorem = "PNP.DirectWire.WireObligationRestoration.dischargeR8_full_value"
leanWireObligationRestorationGainIffTheorem = "PNP.DirectWire.WireObligationRestoration.gain?_isSome_iff"
leanWireObligationRestorationCheckedGainTheorem = "PNP.DirectWire.WireObligationRestoration.gain_checked"
leanWireObligationRestorationCreationUniquenessTheorem = "PNP.DirectWire.WireObligationRestoration.created_nodup"
leanWireObligationRestorationDischargeUniquenessTheorem = "PNP.DirectWire.WireObligationRestoration.discharged_nodup"
leanWireObligationRestorationDuplicateIdentityRejectionTheorem = "PNP.DirectWire.WireObligationRestoration.replay_rejects_duplicate_ids"
leanWireObligationRestorationFullManuscriptCarrierDerived = false
leanWireObligationRestorationCompleteObligationCalculusProved = false
leanWireObligationRestorationGeneralDependencyDAGProved = false
leanWireObligationRestorationCompletePackageEProved = false
leanWireObligationRestorationPolynomialRuntimeProved = false
leanWireObligationRestorationScope = "all-finite-computational-wire-fields-actual-quotient-projection-shared-materializer-full-value-restoration-exact-gate-charge-derived-r5-full-r8-coordinate-ledger-whole-trace-unique-identities-no-full-manuscript-calculus-or-polynomial-runtime"
leanWireQuotientLiftFormalized = true
leanWireQuotientLiftAxiomAuditPassed = true
leanWireQuotientLiftAuditedDeclarationCount = 17
leanWireQuotientLiftExpandedReferenceTheorem = "PNP.DirectWire.WireQuotientLift.expanded_reference"
leanWireQuotientLiftReferenceChargeTheorem = "PNP.DirectWire.WireQuotientLift.referenceLift_charge"
leanWireQuotientLiftExpandedChargeTheorem = "PNP.DirectWire.WireQuotientLift.expanded_charge"
leanWireQuotientLiftReferenceChargeDifferenceTheorem = "PNP.DirectWire.WireQuotientLift.referenceLift_charge_difference"
leanWireQuotientLiftExpandedChargeDifferenceTheorem = "PNP.DirectWire.WireQuotientLift.expanded_charge_difference"
leanWireQuotientLiftMatchedMaterializerChargeTheorem = "PNP.DirectWire.WireQuotientLift.matched_materializer_charge"
leanWireQuotientLiftRelativeSavingIffTheorem = "PNP.DirectWire.WireQuotientLift.relative_saving_iff"
leanWireQuotientLiftOriginalGainIffTheorem = "PNP.DirectWire.WireQuotientLift.original_gain_iff"
leanWireQuotientLiftExpandedOutputTheorem = "PNP.DirectWire.WireQuotientLift.expanded_output"
leanWireQuotientLiftExpandedKeptFieldTheorem = "PNP.DirectWire.WireQuotientLift.expanded_kept_field"
leanWireQuotientLiftExpandedForgottenFieldTheorem = "PNP.DirectWire.WireQuotientLift.expanded_forgotten_field"
leanWireQuotientLiftExpandedFieldTheorem = "PNP.DirectWire.WireQuotientLift.expanded_field"
leanWireQuotientLiftExpandedEquivalenceTheorem = "PNP.DirectWire.WireQuotientLift.expanded_equivalent"
leanWireQuotientLiftDischargeSourceExactTheorem = "PNP.DirectWire.WireQuotientLift.discharge_source_exact"
leanWireQuotientLiftDischargeFullValueTheorem = "PNP.DirectWire.WireQuotientLift.discharge_full_value"
leanWireQuotientLiftGainIffTheorem = "PNP.DirectWire.WireQuotientLift.checkedGain_isSome_iff"
leanWireQuotientLiftCheckedGainTheorem = "PNP.DirectWire.WireQuotientLift.CheckedGain.checked"
leanWireQuotientLiftFullManuscriptPullExpandProved = false
leanWireQuotientLiftReferenceLiftIdentifiedWithOriginal = false
leanWireQuotientLiftAutomaticQuotientAgreementDerived = false
leanWireQuotientLiftCompleteObligationCalculusProved = false
leanWireQuotientLiftCompletePackageEProved = false
leanWireQuotientLiftPolynomialRuntimeProved = false
leanWireQuotientLiftScope = "all-finite-computational-wire-quotient-compatible-replacements-literal-shared-materializer-full-value-lift-exact-matched-integer-charges-original-cost-gain-test-expanded-source-bound-discharge-no-arbitrary-support-embedding-or-polynomial-runtime"
leanWireFrontierLiftFormalized = true
leanWireFrontierLiftAxiomAuditPassed = true
leanWireFrontierLiftAuditedDeclarationCount = 18
leanWireFrontierLiftOrdinaryOutputSelectedTheorem = "PNP.DirectWire.WireFrontierLift.ordinary_output_selected"
leanWireFrontierLiftKeptFieldSelectedTheorem = "PNP.DirectWire.WireFrontierLift.kept_field_selected"
leanWireFrontierLiftPredecessorClosureTheorem = "PNP.DirectWire.WireFrontierLift.records_predecessor_closed"
leanWireFrontierLiftSelectedFieldFrontierTheorem = "PNP.DirectWire.WireFrontierLift.selected_field_in_frontier"
leanWireFrontierLiftPrimaryBoundaryTheorem = "PNP.DirectWire.WireFrontierLift.primary_boundary"
leanWireFrontierLiftOriginalChargeTheorem = "PNP.DirectWire.WireFrontierLift.original_charge"
leanWireFrontierLiftCompileIsSomeTheorem = "PNP.DirectWire.WireFrontierLift.compile_isSome"
leanWireFrontierLiftExpandedChargeTheorem = "PNP.DirectWire.WireFrontierLift.expanded_charge"
leanWireFrontierLiftMatchedOriginalChargeTheorem = "PNP.DirectWire.WireFrontierLift.matched_original_charge"
leanWireFrontierLiftOriginalGainIffTheorem = "PNP.DirectWire.WireFrontierLift.original_gain_iff"
leanWireFrontierLiftExpandedOutputTheorem = "PNP.DirectWire.WireFrontierLift.expanded_output"
leanWireFrontierLiftExpandedFieldTheorem = "PNP.DirectWire.WireFrontierLift.expanded_field"
leanWireFrontierLiftExpandedEquivalenceTheorem = "PNP.DirectWire.WireFrontierLift.expanded_equivalent"
leanWireFrontierLiftDischargeSourceExactTheorem = "PNP.DirectWire.WireFrontierLift.discharge_source_exact"
leanWireFrontierLiftDischargeFullValueTheorem = "PNP.DirectWire.WireFrontierLift.discharge_full_value"
leanWireFrontierLiftProperIffExteriorPositiveTheorem = "PNP.DirectWire.WireFrontierLift.proper_iff_exterior_positive"
leanWireFrontierLiftProperGainIffTheorem = "PNP.DirectWire.WireFrontierLift.checkedProperGain_isSome_iff"
leanWireFrontierLiftCheckedProperGainTheorem = "PNP.DirectWire.WireFrontierLift.ProperGain.checked"
leanWireFrontierLiftEveryArbitrarySupportCovered = false
leanWireFrontierLiftAutomaticLocalAgreementDerived = false
leanWireFrontierLiftFullManuscriptPullExpandProved = false
leanWireFrontierLiftCompleteObligationCalculusProved = false
leanWireFrontierLiftCompletePackageEProved = false
leanWireFrontierLiftPolynomialRuntimeProved = false
leanWireFrontierLiftScope = "all-finite-computational-wire-input-derived-quotient-visible-cone-completed-original-frontier-primary-boundary-actual-compiler-full-local-open-agreement-original-exterior-once-exact-integer-charges-strict-proper-gain-no-full-manuscript-calculus-or-polynomial-runtime"
leanWireMatchedCancellationFormalized = true
leanWireMatchedCancellationAxiomAuditPassed = true
leanWireMatchedCancellationAuditedDeclarationCount = 26
leanWireMatchedCancellationRepresentativeAvailabilityTheorem = "PNP.DirectWire.WireMatchedCancellation.representative_isSome_iff"
leanWireMatchedCancellationRetainedObservationValueTheorem = "PNP.DirectWire.WireMatchedCancellation.observation_value"
leanWireMatchedCancellationRepresentativeFullValueTheorem = "PNP.DirectWire.WireMatchedCancellation.Representative.full_value"
leanWireMatchedCancellationAllResolvedSoundnessTheorem = "PNP.DirectWire.WireMatchedCancellation.allResolved_sound"
leanWireMatchedCancellationAllResolvedChargeTheorem = "PNP.DirectWire.WireMatchedCancellation.charge_allResolved"
leanWireMatchedCancellationUnresolvedMaterializerFieldTheorem = "PNP.DirectWire.WireMatchedCancellation.missing_unresolved_field"
leanWireMatchedCancellationMaterializerChargeBoundTheorem = "PNP.DirectWire.WireMatchedCancellation.charge_bound"
leanWireMatchedCancellationVisibleResolvedFieldTheorem = "PNP.DirectWire.WireMatchedCancellation.visible_resolved_field"
leanWireMatchedCancellationExpandedChargeTheorem = "PNP.DirectWire.WireMatchedCancellation.expanded_charge"
leanWireMatchedCancellationExpandedOutputTheorem = "PNP.DirectWire.WireMatchedCancellation.expanded_output"
leanWireMatchedCancellationExpandedFieldTheorem = "PNP.DirectWire.WireMatchedCancellation.expanded_field"
leanWireMatchedCancellationExpandedEquivalenceTheorem = "PNP.DirectWire.WireMatchedCancellation.expanded_equivalent"
leanWireMatchedCancellationDischargeWitnessFullValueTheorem = "PNP.DirectWire.WireMatchedCancellation.Discharge.full_value"
leanWireMatchedCancellationDischargeSourceExactTheorem = "PNP.DirectWire.WireMatchedCancellation.discharge_source_exact"
leanWireMatchedCancellationDischargeKindIffTheorem = "PNP.DirectWire.WireMatchedCancellation.discharge_isR6_iff"
leanWireMatchedCancellationComputedDischargeFullValueTheorem = "PNP.DirectWire.WireMatchedCancellation.discharge_full_value"
leanWireMatchedCancellationGainIffTheorem = "PNP.DirectWire.WireMatchedCancellation.checkedGain_isSome_iff"
leanWireMatchedCancellationCheckedGainTheorem = "PNP.DirectWire.WireMatchedCancellation.CheckedGain.checked"
leanWireMatchedCancellationCreatedExactTheorem = "PNP.DirectWire.WireMatchedCancellation.created_exact"
leanWireMatchedCancellationDischargedExactTheorem = "PNP.DirectWire.WireMatchedCancellation.discharged_exact"
leanWireMatchedCancellationCreationIffTheorem = "PNP.DirectWire.WireMatchedCancellation.creation_iff"
leanWireMatchedCancellationDischargeIffTheorem = "PNP.DirectWire.WireMatchedCancellation.discharge_iff"
leanWireMatchedCancellationCreatedNodupTheorem = "PNP.DirectWire.WireMatchedCancellation.created_nodup"
leanWireMatchedCancellationDischargedNodupTheorem = "PNP.DirectWire.WireMatchedCancellation.discharged_nodup"
leanWireMatchedCancellationReplayClosedTheorem = "PNP.DirectWire.WireMatchedCancellation.replay_closed"
leanWireMatchedCancellationRejectDuplicateIdsTheorem = "PNP.DirectWire.WireMatchedCancellation.replay_rejects_duplicate_ids"
leanWireMatchedCancellationAllSemanticCancellationsDerived = false
leanWireMatchedCancellationArbitraryObligationDAGsCovered = false
leanWireMatchedCancellationAutomaticLocalAgreementDerived = false
leanWireMatchedCancellationFullManuscriptCarrierProved = false
leanWireMatchedCancellationCompleteObligationCalculusProved = false
leanWireMatchedCancellationCompletePackageEProved = false
leanWireMatchedCancellationPolynomialRuntimeProved = false
leanWireMatchedCancellationScope = "all-finite-computational-wire-original-visible-source-identity-scan-local-quotient-agreement-derived-full-r6-cancellation-unresolved-shared-r8-materializer-actual-expanded-source-exact-charge-whole-trace-unique-ids-no-complete-calculus-or-polynomial-runtime"
leanWireUnaryRealizationFormalized = true
leanWireUnaryRealizationAxiomAuditPassed = true
leanWireUnaryRealizationAuditedDeclarationCount = 18
leanWireUnaryRealizationObservationValueTheorem = "PNP.DirectWire.WireUnaryRealization.observation_value"
leanWireUnaryRealizationNegationIffTheorem = "PNP.DirectWire.WireUnaryRealization.needsNegation_iff"
leanWireUnaryRealizationImplementationValueTheorem = "PNP.DirectWire.WireUnaryRealization.implementation_value"
leanWireUnaryRealizationOutputTheorem = "PNP.DirectWire.WireUnaryRealization.realize_output"
leanWireUnaryRealizationFieldTheorem = "PNP.DirectWire.WireUnaryRealization.realize_field"
leanWireUnaryRealizationEquivalenceTheorem = "PNP.DirectWire.WireUnaryRealization.realize_equivalent"
leanWireUnaryRealizationFullEquivalenceTheorem = "PNP.DirectWire.WireUnaryRealization.realize_full_equivalent"
leanWireUnaryRealizationExactGateCountTheorem = "PNP.DirectWire.WireUnaryRealization.realize_gateCount"
leanWireUnaryRealizationNegationLowerBoundTheorem = "PNP.DirectWire.WireUnaryRealization.negation_requires_gate"
leanWireUnaryRealizationFullMinimumTheorem = "PNP.DirectWire.WireUnaryRealization.realize_minimal"
leanWireUnaryRealizationNonincreaseTheorem = "PNP.DirectWire.WireUnaryRealization.realize_nonincrease"
leanWireUnaryRealizationGateBoundTheorem = "PNP.DirectWire.WireUnaryRealization.realize_gate_bound"
leanWireUnaryRealizationR7WitnessFullValueTheorem = "PNP.DirectWire.WireUnaryRealization.R7Discharge.full_value"
leanWireUnaryRealizationR7SourceExactTheorem = "PNP.DirectWire.WireUnaryRealization.dischargeR7_source_exact"
leanWireUnaryRealizationComputedR7FullValueTheorem = "PNP.DirectWire.WireUnaryRealization.dischargeR7_full_value"
leanWireUnaryRealizationGainIffTheorem = "PNP.DirectWire.WireUnaryRealization.checkedGain_isSome_iff"
leanWireUnaryRealizationGainCompletenessTheorem = "PNP.DirectWire.WireUnaryRealization.checkedGain_complete"
leanWireUnaryRealizationCheckedGainTheorem = "PNP.DirectWire.WireUnaryRealization.CheckedGain.checked"
leanWireUnaryRealizationArbitraryAmbientCutsCovered = false
leanWireUnaryRealizationAllR7CasesDerived = false
leanWireUnaryRealizationArbitraryObligationDAGsCovered = false
leanWireUnaryRealizationFullManuscriptCarrierProved = false
leanWireUnaryRealizationCompleteObligationCalculusProved = false
leanWireUnaryRealizationCompletePackageEProved = false
leanWireUnaryRealizationPolynomialRuntimeProved = false
leanWireUnaryRealizationScope = "all-unary-computational-wire-actual-two-source-valuations-arbitrary-gate-and-full-observation-counts-computed-zero-or-one-shared-not-complete-full-values-universal-full-word-minimum-source-exact-r7-discharge-complete-whole-word-gain-no-ambient-calculus-or-polynomial-runtime"
leanWireUnaryFrontierFormalized = true
leanWireUnaryFrontierAxiomAuditPassed = true
leanWireUnaryFrontierAuditedDeclarationCount = 30
leanWireUnaryFrontierConstantValueTheorem = "PNP.DirectWire.WireUnaryFrontier.constantWord_value"
leanWireUnaryFrontierConstantGateCountTheorem = "PNP.DirectWire.WireUnaryFrontier.constantWord_gateCount"
leanWireUnaryFrontierUnaryValueTheorem = "PNP.DirectWire.WireUnaryFrontier.unaryWord_value"
leanWireUnaryFrontierUnaryMinimumTheorem = "PNP.DirectWire.WireUnaryFrontier.unaryWord_minimal"
leanWireUnaryFrontierUnaryGateBoundTheorem = "PNP.DirectWire.WireUnaryFrontier.unaryWord_gate_bound"
leanWireUnaryFrontierLocalValueTheorem = "PNP.DirectWire.WireUnaryFrontier.localWord_value"
leanWireUnaryFrontierLocalMinimumTheorem = "PNP.DirectWire.WireUnaryFrontier.localWord_minimal"
leanWireUnaryFrontierLocalNonincreaseTheorem = "PNP.DirectWire.WireUnaryFrontier.localWord_nonincrease"
leanWireUnaryFrontierLocalGateBoundTheorem = "PNP.DirectWire.WireUnaryFrontier.localWord_gate_bound"
leanWireUnaryFrontierReplacementAgreementTheorem = "PNP.DirectWire.WireUnaryFrontier.replacement_agreement"
leanWireUnaryFrontierReplacementMinimumTheorem = "PNP.DirectWire.WireUnaryFrontier.replacement_minimal"
leanWireUnaryFrontierReplacementNonincreaseTheorem = "PNP.DirectWire.WireUnaryFrontier.replacement_nonincrease"
leanWireUnaryFrontierReplacementGateBoundTheorem = "PNP.DirectWire.WireUnaryFrontier.replacement_gate_bound"
leanWireUnaryFrontierZeroBoundaryGateCountTheorem = "PNP.DirectWire.WireUnaryFrontier.replacement_zero_gateCount"
leanWireUnaryFrontierOutputTheorem = "PNP.DirectWire.WireUnaryFrontier.expanded_output"
leanWireUnaryFrontierFieldTheorem = "PNP.DirectWire.WireUnaryFrontier.expanded_field"
leanWireUnaryFrontierEquivalenceTheorem = "PNP.DirectWire.WireUnaryFrontier.expanded_equivalent"
leanWireUnaryFrontierExactChargeTheorem = "PNP.DirectWire.WireUnaryFrontier.expanded_charge"
leanWireUnaryFrontierNonincreaseTheorem = "PNP.DirectWire.WireUnaryFrontier.expanded_nonincrease"
leanWireUnaryFrontierGainIffTheorem = "PNP.DirectWire.WireUnaryFrontier.expanded_gain_iff"
leanWireUnaryFrontierAttemptIffTheorem = "PNP.DirectWire.WireUnaryFrontier.attempt_isSome_iff"
leanWireUnaryFrontierAttemptOutputTheorem = "PNP.DirectWire.WireUnaryFrontier.attempt_output"
leanWireUnaryFrontierAttemptFieldTheorem = "PNP.DirectWire.WireUnaryFrontier.attempt_field"
leanWireUnaryFrontierAttemptNonincreaseTheorem = "PNP.DirectWire.WireUnaryFrontier.attempt_nonincrease"
leanWireUnaryFrontierAttemptChargeTheorem = "PNP.DirectWire.WireUnaryFrontier.attempt_charge"
leanWireUnaryFrontierR7SourceExactTheorem = "PNP.DirectWire.WireUnaryFrontier.dischargeR7_source_exact"
leanWireUnaryFrontierR7FullValueTheorem = "PNP.DirectWire.WireUnaryFrontier.dischargeR7_full_value"
leanWireUnaryFrontierProperGainIffTheorem = "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_isSome_iff"
leanWireUnaryFrontierProperGainCompletenessTheorem = "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_complete"
leanWireUnaryFrontierCheckedProperGainTheorem = "PNP.DirectWire.WireUnaryFrontier.ProperGain.checked"
leanWireUnaryFrontierArbitraryAmbientCutsCovered = false
leanWireUnaryFrontierAllR7CasesDerived = false
leanWireUnaryFrontierArbitraryObligationDAGsCovered = false
leanWireUnaryFrontierFullManuscriptCarrierProved = false
leanWireUnaryFrontierCompleteObligationCalculusProved = false
leanWireUnaryFrontierCompletePackageEProved = false
leanWireUnaryFrontierPolynomialRuntimeProved = false
leanWireUnaryFrontierScope = "all-finite-computational-wire-source-derived-visible-predecessor-cone-completed-frontier-zero-or-one-primary-boundary-computed-minimum-local-word-actual-original-exterior-once-full-field-preservation-source-exact-r7-proper-strict-gain-no-arbitrary-support-calculus-or-polynomial-runtime"
leanWireUnaryArbitrarySupportFormalized = true
leanWireUnaryArbitrarySupportAxiomAuditPassed = true
leanWireUnaryArbitrarySupportAuditedDeclarationCount = 31
leanWireUnaryArbitrarySupportPrefixCausalityTheorem = "PNP.DirectWire.terminalOpenGateEvaluation_prefix_congr"
leanWireUnaryArbitrarySupportSingleBoundaryCausalityTheorem = "PNP.DirectWire.terminalOpenGateEvaluation_single_gate_prefix"
leanWireUnaryArbitrarySupportSingleBoundaryRankTheorem = "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_singleGateBoundary"
leanWireUnaryArbitrarySupportConstantSourceTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.constantWord_source"
leanWireUnaryArbitrarySupportUnaryLiteralConstantTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.unaryWord_source_of_constant"
leanWireUnaryArbitrarySupportLocalLiteralConstantTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.localWord_source_of_constant"
leanWireUnaryArbitrarySupportReplacementAgreementTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_agreement"
leanWireUnaryArbitrarySupportReplacementGateBoundTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_gate_bound"
leanWireUnaryArbitrarySupportReplacementMinimumTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_minimal"
leanWireUnaryArbitrarySupportReplacementNonincreaseTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_nonincrease"
leanWireUnaryArbitrarySupportEarlyFrontierConstantTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_early_constant"
leanWireUnaryArbitrarySupportWellFoundedTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.graph_wellFounded"
leanWireUnaryArbitrarySupportCompilerSuccessTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.compile_isSome"
leanWireUnaryArbitrarySupportOriginalChargeTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.original_charge"
leanWireUnaryArbitrarySupportOutputTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_output"
leanWireUnaryArbitrarySupportFieldTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_field"
leanWireUnaryArbitrarySupportEquivalenceTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_equivalent"
leanWireUnaryArbitrarySupportExactChargeTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_charge"
leanWireUnaryArbitrarySupportNonincreaseTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_nonincrease"
leanWireUnaryArbitrarySupportGainIffTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_gain_iff"
leanWireUnaryArbitrarySupportProperExteriorIffTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.proper_iff_exterior_positive"
leanWireUnaryArbitrarySupportAttemptIffTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_isSome_iff"
leanWireUnaryArbitrarySupportAttemptOutputTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_output"
leanWireUnaryArbitrarySupportAttemptFieldTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_field"
leanWireUnaryArbitrarySupportAttemptNonincreaseTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_nonincrease"
leanWireUnaryArbitrarySupportAttemptChargeTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_charge"
leanWireUnaryArbitrarySupportR7SourceExactTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_source_exact"
leanWireUnaryArbitrarySupportR7FullValueTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_full_value"
leanWireUnaryArbitrarySupportProperGainIffTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_isSome_iff"
leanWireUnaryArbitrarySupportProperGainCompletenessTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_complete"
leanWireUnaryArbitrarySupportCheckedProperGainTheorem = "PNP.DirectWire.WireUnaryArbitrarySupport.ProperGain.checked"
leanWireUnaryArbitrarySupportAllBoundaryWidthsCovered = false
leanWireUnaryArbitrarySupportAllR7CasesDerived = false
leanWireUnaryArbitrarySupportArbitraryObligationDAGsCovered = false
leanWireUnaryArbitrarySupportFullManuscriptCarrierProved = false
leanWireUnaryArbitrarySupportCompleteObligationCalculusProved = false
leanWireUnaryArbitrarySupportCompletePackageEProved = false
leanWireUnaryArbitrarySupportPolynomialRuntimeProved = false
leanWireUnaryArbitrarySupportScope = "all-finite-computational-wire-arbitrary-physical-support-completed-frontier-zero-or-one-actual-boundary-including-external-gate-source-derived-prefix-causality-minimum-local-word-ranked-actual-compiler-original-exterior-once-full-fields-source-exact-r7-proper-gain-no-general-calculus-or-polynomial-runtime"
leanWireUnarySupportSearchFormalized = true
leanWireUnarySupportSearchAxiomAuditPassed = true
leanWireUnarySupportSearchAuditedDeclarationCount = 36
leanWireUnarySupportSearchMaximalAdmissibilityTheorem = "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_admissible"
leanWireUnarySupportSearchMaximalContainmentTheorem = "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_contains"
leanWireUnarySupportSearchCanonicalSelectionIffTheorem = "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected_iff"
leanWireUnarySupportSearchCanonicalSelectionTheorem = "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected"
leanWireUnarySupportSearchActualBoundaryTheorem = "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary"
leanWireUnarySupportSearchUnaryBoundaryTheorem = "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary_small"
leanWireUnarySupportSearchCandidateBoundaryTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_boundary"
leanWireUnarySupportSearchCandidatePropernessTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_proper"
leanWireUnarySupportSearchConsumedWireCountTheorem = "PNP.DirectWire.WireUnarySupportSearch.consumedWires_length"
leanWireUnarySupportSearchBoundaryEnumerationCompletenessTheorem = "PNP.DirectWire.WireUnarySupportSearch.boundary_mem_consumedWires"
leanWireUnarySupportSearchBoundaryChoiceCountTheorem = "PNP.DirectWire.WireUnarySupportSearch.boundaryChoices_length"
leanWireUnarySupportSearchCandidateFamilyCountTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_length"
leanWireUnarySupportSearchMaximalFamilyMembershipTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_maximal_mem"
leanWireUnarySupportSearchSingletonFamilyMembershipTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_singleton_mem"
leanWireUnarySupportSearchActualChoiceMembershipTheorem = "PNP.DirectWire.WireUnarySupportSearch.supportChoice_wire_mem"
leanWireUnarySupportSearchActualChoiceCompletenessTheorem = "PNP.DirectWire.WireUnarySupportSearch.supportChoice_of_mem"
leanWireUnarySupportSearchActualChoiceExteriorTheorem = "PNP.DirectWire.WireUnarySupportSearch.supportChoice_external"
leanWireUnarySupportSearchChoiceFamilyMembershipTheorem = "PNP.DirectWire.WireUnarySupportSearch.supportChoice_mem"
leanWireUnarySupportSearchGeneralSupportAdmissibilityTheorem = "PNP.DirectWire.WireUnarySupportSearch.support_admissible"
leanWireUnarySupportSearchGeneralSupportContainmentTheorem = "PNP.DirectWire.WireUnarySupportSearch.support_contained_in_candidate"
leanWireUnarySupportSearchSelectionCountMonotonicityTheorem = "PNP.DirectWire.WireUnarySupportSearch.selected_length_mono"
leanWireUnarySupportSearchSelectionCountBoundTheorem = "PNP.DirectWire.WireUnarySupportSearch.selected_length_le"
leanWireUnarySupportSearchCandidateRecordBoundTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_entry_length"
leanWireUnarySupportSearchExtractedCountMonotonicityTheorem = "PNP.DirectWire.WireUnarySupportSearch.extracted_gateCount_mono"
leanWireUnarySupportSearchSingletonCanonicalizationTheorem = "PNP.DirectWire.WireUnarySupportSearch.singleton_selection"
leanWireUnarySupportSearchGainCanonicalizationTheorem = "PNP.DirectWire.WireUnarySupportSearch.checkedGain_selection_invariant"
leanWireUnarySupportSearchCandidateFamilyCompletenessTheorem = "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_complete"
leanWireUnarySupportSearchSearchCompletenessTheorem = "PNP.DirectWire.WireUnarySupportSearch.findGain_complete"
leanWireUnarySupportSearchSearchFamilyMembershipTheorem = "PNP.DirectWire.WireUnarySupportSearch.findGain_member"
leanWireUnarySupportSearchSearchRecordBoundTheorem = "PNP.DirectWire.WireUnarySupportSearch.findGain_records_bound"
leanWireUnarySupportSearchCheckedResultTheorem = "PNP.DirectWire.WireUnarySupportSearch.GainResult.checked"
leanWireUnarySupportSearchNoResultExclusionTheorem = "PNP.DirectWire.WireUnarySupportSearch.findGain_none_excludes"
leanWireUnarySupportSearchR7SourceExactTheorem = "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_source_exact"
leanWireUnarySupportSearchR7FullValueTheorem = "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_full_value"
leanWireUnarySupportSearchReplacementRecognitionTheorem = "PNP.DirectWire.WireUnarySupportSearch.findReplacement_isSome"
leanWireUnarySupportSearchReplacementSoundnessTheorem = "PNP.DirectWire.WireUnarySupportSearch.findReplacement_sound"
leanWireUnarySupportSearchProperZeroUnaryCompletenessProved = true
leanWireUnarySupportSearchPhysicalCandidateCountBoundProved = true
leanWireUnarySupportSearchPhysicalRecordCountBoundProved = true
leanWireUnarySupportSearchCallerSuppliedFamilyRequired = false
leanWireUnarySupportSearchAllBoundaryWidthsCovered = false
leanWireUnarySupportSearchAllR7CasesDerived = false
leanWireUnarySupportSearchNoResultProvesGlobalMinimality = false
leanWireUnarySupportSearchArbitraryObligationDAGsCovered = false
leanWireUnarySupportSearchFullManuscriptCarrierProved = false
leanWireUnarySupportSearchCompleteObligationCalculusProved = false
leanWireUnarySupportSearchCompletePackageEProved = false
leanWireUnarySupportSearchPolynomialRuntimeProved = false
leanWireUnarySupportSearchScope = "all-finite-computational-wire-source-derived-proper-zero-or-one-actual-boundary-support-search-complete-maximal-and-singleton-candidates-physical-count-bounds-full-field-actual-replacement-source-exact-r7-no-global-minimum-or-total-encoded-polynomial-runtime"
leanConcreteCNFNPCompletenessFormalized = true
leanConcreteCNFNPCompletenessAxiomAuditPassed = true
leanConcreteCNFNPCompletenessAuditedDeclarationCount = 2
leanConcreteCNFNPCompletenessTheorem = "PNP.Concrete.CookLevin.cnfSAT_np_complete"
leanConcreteCNFNPCompletenessHardnessTheorem = "PNP.Concrete.CookLevin.cnfSAT_np_hard"
leanConcreteCookLevinBuilderDynamicCursorFormalized = true
leanConcreteCookLevinFormulaBuilderFormalized = true
leanConcreteCookLevinBuilderRawRefinementFormalized = true
leanConcreteCookLevinBuilderPolynomialReductionFormalized = true
status = "formal-reconstruction-in-progress"
mathematicalTheoremEstablished = false
publicTheoremEmissionAllowed = false
publicTheoremStatement = null
finalTheoremReady = false
rootLeanTheoremPresent = false
rootLeanTheoremBuilt = false
rootLeanTheoremAxiomAuditPassed = false
projectSpecificAxiomsRemaining = false
leanConcreteCNFSATMembershipFormalized = true
leanConcretePipelineStateNamespaceAxiomAuditPassed = true
leanConcretePipelineStageBridgesFormalized = true
leanConcretePipelineStageBridgesAxiomAuditPassed = true
leanConcretePipelineTerminalOutputPackingFormalized = true
leanConcretePipelineTerminalOutputPackerAxiomAuditPassed = true
leanConcretePipelineTerminalOutputPackerAuditedDeclarationCount = 69
leanConcretePipelineTerminalOutputPackerConnectedToBridgeEndpointFormalized = true
leanConcretePipelineTerminalBridgeAxiomAuditPassed = true
leanConcretePipelineTerminalBridgeAuditedDeclarationCount = 59
leanConcretePipelinePriorTraceTransportToTerminalBridgeFormalized = true
leanConcretePipelineInputFramerAxiomAuditPassed = true
leanConcretePipelineInputFramerAuditedDeclarationCount = 70
leanConcretePipelineAllInputFramingFormalized = true
leanConcretePipelinePairedCompilerAxiomAuditPassed = true
leanConcretePipelinePairedCompilerAuditedDeclarationCount = 28
leanConcretePipelineCanonicalPairCompilationFormalized = true
leanConcretePipelineCompilerAxiomAuditPassed = true
leanConcretePipelineCompilerAuditedDeclarationCount = 29
leanConcretePipelineAllInputCompilationFormalized = true
leanConcretePipelineSequentialCompilationFormalized = true
leanConcretePipelineRefinementAxiomAuditPassed = true
leanConcreteFunctionProgramRecursiveCompilationFormalized = true
leanConcreteDecisionProgramRecursiveCompilationFormalized = true
leanConcretePolynomialTimeDeciderRawCompilationFormalized = true
standardComplexityModelFormalized = true
leanConcretePipelineMalformedInputBehaviorFormalized = true
leanConcretePipelineRawRefinementFormalized = true
leanConcretePipelineExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderInputLengthFormalized = true
leanConcreteCookLevinBuilderInputLengthAxiomAuditPassed = true
leanConcreteCookLevinBuilderInputLengthCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderInputPrefixFormalized = true
leanConcreteCookLevinBuilderInputPrefixAxiomAuditPassed = true
leanConcreteCookLevinBuilderInputPrefixCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderTokenAppenderFormalized = true
leanConcreteCookLevinBuilderTokenAppenderAxiomAuditPassed = true
leanConcreteCookLevinBuilderTokenAppenderCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderTokenAppenderExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderTokenAppenderAllTokensExactFormalized = true
leanConcreteCookLevinBuilderTokenAppenderFirstFormulaBitsFormalized = true
leanConcreteCookLevinBuilderTokenAppenderMalformedPhaseTimeoutFormalized = true
leanConcreteCookLevinBuilderTokenAppenderInputPrefixComposed = true
leanConcreteCookLevinBuilderFirstTokenPrefixFormalized = true
leanConcreteCookLevinBuilderFirstTokenPrefixAxiomAuditPassed = true
leanConcreteCookLevinBuilderFirstTokenPrefixCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderFirstTokenPrefixExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderUnaryPolynomialFormalized = true
leanConcreteCookLevinBuilderUnaryPolynomialAxiomAuditPassed = true
leanConcreteCookLevinBuilderUnaryPolynomialCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderCompleteHeaderFormalized = true
leanConcreteCookLevinBuilderCompleteHeaderAxiomAuditPassed = true
leanConcreteCookLevinBuilderCompleteHeaderCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderCompleteHeaderExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderBodyStartPrefixFormalized = true
leanConcreteCookLevinBuilderBodyStartPrefixAxiomAuditPassed = true
leanConcreteCookLevinBuilderBodyStartPrefixCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderBodyStartPrefixExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderBodyStartPrefixRetainedNextTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFirstLiteralPrefixFormalized = true
leanConcreteCookLevinBuilderFirstLiteralPrefixCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderFirstLiteralPrefixExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderFirstLiteralPrefixRetainedNextTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFirstClausePrefixFormalized = true
leanConcreteCookLevinBuilderFirstClausePrefixCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderFirstClausePrefixExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderFirstClausePrefixCompleteFirstClauseFormalized = true
leanConcreteCookLevinBuilderFirstClausePrefixRetainedNextTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondClauseSecondLiteralPrefixFormalized = true
leanConcreteCookLevinBuilderSecondClauseSecondLiteralPrefixCompleteSecondNegativeLiteralFormalized = true
leanConcreteCookLevinBuilderSecondClauseSecondLiteralPrefixRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondClausePrefixFormalized = true
leanConcreteCookLevinBuilderSecondClausePrefixCompleteSecondClauseFormalized = true
leanConcreteCookLevinBuilderSecondClausePrefixRetainedFirstPaddingCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondClausePaddingRunFormalized = true
leanConcreteCookLevinBuilderSecondClausePaddingRunRemainingPaddingCountFormalized = true
leanConcreteCookLevinBuilderSecondClausePaddingRunDirectPaddingBlockFormalized = true
leanConcreteCookLevinBuilderSecondClausePaddingRunThirdClauseStartFormalized = true
leanConcreteCookLevinBuilderSecondClausePaddingRunNoEmissionSpecificationFormalized = true
leanConcreteCookLevinBuilderThirdClauseSeparatorStepFormalized = true
leanConcreteCookLevinBuilderThirdClauseSeparatorStepThirdClauseSeparatorFormalized = true
leanConcreteCookLevinBuilderThirdClauseSeparatorStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderThirdClauseSeparatorStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderThirdClauseFirstLiteralPrefixFormalized = true
leanConcreteCookLevinBuilderThirdClauseFirstLiteralPrefixCompleteFirstNegativeLiteralFormalized = true
leanConcreteCookLevinBuilderThirdClauseFirstLiteralPrefixRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderThirdClauseFirstLiteralPrefixFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderThirdClauseSecondLiteralPrefixFormalized = true
leanConcreteCookLevinBuilderThirdClauseSecondLiteralPrefixCompleteSecondNegativeLiteralFormalized = true
leanConcreteCookLevinBuilderThirdClauseSecondLiteralPrefixRetainedClauseTerminatorCoordinateFormalized = true
leanConcreteCookLevinBuilderThirdClauseSecondLiteralPrefixFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderThirdClausePrefixFormalized = true
leanConcreteCookLevinBuilderThirdClausePrefixCompleteThirdClauseFormalized = true
leanConcreteCookLevinBuilderThirdClausePrefixRetainedFirstPaddingCoordinateFormalized = true
leanConcreteCookLevinBuilderThirdClausePrefixFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderThirdClausePaddingRunFormalized = true
leanConcreteCookLevinBuilderThirdClausePaddingRunRemainingPaddingCountFormalized = true
leanConcreteCookLevinBuilderThirdClausePaddingRunFourthClauseStartFormalized = true
leanConcreteCookLevinBuilderThirdClausePaddingRunFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFourthClauseSeparatorStepFormalized = true
leanConcreteCookLevinBuilderFourthClauseSeparatorStepFourthClauseSeparatorFormalized = true
leanConcreteCookLevinBuilderFourthClauseSeparatorStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFourthClauseSeparatorStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFourthClauseFirstLiteralPrefixFormalized = true
leanConcreteCookLevinBuilderFourthClauseFirstLiteralPrefixCompleteFirstNegativeLiteralFormalized = true
leanConcreteCookLevinBuilderFourthClauseFirstLiteralPrefixRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFourthClauseFirstLiteralPrefixFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFourthClauseSecondLiteralPrefixFormalized = true
leanConcreteCookLevinBuilderFourthClauseSecondLiteralPrefixCompleteSecondNegativeLiteralFormalized = true
leanConcreteCookLevinBuilderFourthClauseSecondLiteralPrefixRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFourthClauseSecondLiteralPrefixFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFourthClausePrefixFormalized = true
leanConcreteCookLevinBuilderFourthClausePrefixCompleteFourthClauseFormalized = true
leanConcreteCookLevinBuilderFourthClausePrefixRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFourthClausePrefixFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunAxiomAuditPassed = true
leanConcreteCookLevinBuilderFourthClausePaddingRunCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunRemainingPaddingCountFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunDirectPaddingBlockFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunFifthClauseSlotStartFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunNoEmissionSpecificationFormalized = true
leanConcreteCookLevinBuilderFourthClausePaddingRunInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderFourthClausePaddingRunFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunAxiomAuditPassed = true
leanConcreteCookLevinBuilderFifthClausePaddingRunCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunPaddingCountFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunDirectPaddingBlockFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunSixthClauseSlotStartFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunNoEmissionSpecificationFormalized = true
leanConcreteCookLevinBuilderFifthClausePaddingRunInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderFifthClausePaddingRunFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunAxiomAuditPassed = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunPaddingCountFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunDirectPaddingBlockFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunSecondConstraintSeparatorFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunNoEmissionSpecificationFormalized = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderFirstConstraintPaddingRunFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepSecondConstraintSeparatorFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintSeparatorStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepSecondConstraintFirstLiteralSignFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSignStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepSecondConstraintFirstLiteralFirstUnaryUnitFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepSecondConstraintFirstLiteralSecondUnaryUnitFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepSecondConstraintFirstLiteralThirdUnaryUnitFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepSecondConstraintFirstLiteralTerminatorFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralTerminatorStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepSecondConstraintFirstLiteralSuccessorTokenFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepInputPrefixAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepPaddingOrUnaryOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFourthPaddingOrUnaryOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFifthPaddingOrTerminatorOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepInputPrefixOptionalTerminatorAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepSixthPaddingOrOpeningUnaryOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepInputPrefixOptionalAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepSeventhPaddingOrUnaryOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanLockedNANDCarrierLayoutFormalized = true
leanLockedNANDCarrierTraceAxiomAuditPassed = true
leanLockedNANDCarrierTraceAuditedDeclarationCount = 71
leanLockedNANDCarrierTraceScope = "arbitrary-finite-topological-nand-circuits-carrier-separation-and-trace-equivalence"
leanLockedNANDGlobalCandidateAssemblyFormalized = true
leanLockedNANDGlobalBaselineCandidateFormalized = true
leanLockedNANDGlobalCandidateAxiomAuditPassed = true
leanLockedNANDGlobalCandidateAuditedDeclarationCount = 71
leanLockedNANDGlobalCandidateScope = "arbitrary-finite-topological-nand-circuits-exact-baseline-and-four-gate-extension"
leanLockedNANDGlobalBaselineDistinctFormalized = true
leanLockedNANDGlobalBaselineDistinctAxiomAuditPassed = true
leanLockedNANDGlobalBaselineDistinctAuditedDeclarationCount = 5
leanLockedNANDGlobalBaselineDistinctScope = "arbitrary-finite-topological-nand-circuits-global-baseline-output-conditions-and-exact-reference-minimum"
leanLockedNANDUnsatisfiableFinalZeroFormalized = true
leanLockedNANDUnsatisfiableFinalZeroAxiomAuditPassed = true
leanLockedNANDUnsatisfiableFinalZeroAuditedDeclarationCount = 2
leanLockedNANDUnsatisfiableFinalZeroScope = "arbitrary-finite-topological-nand-circuits-whole-carrier-unsatisfiable-final-zero-and-exact-reference-minimum"
leanConcreteLockedNANDParserMachineFormalized = true
leanConcreteLockedNANDParserAxiomAuditPassed = true
leanConcreteLockedNANDParserAuditedDeclarationCount = 380
leanConcreteLockedNANDParserAllInputExactFormalized = true
leanConcreteLockedNANDParserExactOutputFormalized = true
leanConcreteLockedNANDParserCompiledNonTimeoutFormalized = true
leanConcreteLockedNANDParserPolynomialTimeMachineFormalized = true
leanConcreteLockedNANDParserPolynomialTimeFunctionFormalized = true
leanConcreteLockedNANDParserRawRefinementFormalized = true
leanConcreteLockedNANDParserScope = "literal-228-state-2052-rule-strict-version-zero-all-input-parser-byte-preserving-or-empty-with-compiled-cubic-bound"
leanConcreteLockedNANDEmitterMachineFormalized = true
leanConcreteLockedNANDEmitterAxiomAuditPassed = true
leanConcreteLockedNANDEmitterAuditedDeclarationCount = 3295
leanConcreteLockedNANDEmitterAllInputExactFormalized = true
leanConcreteLockedNANDEmitterExactTargetBytesFormalized = true
leanConcreteLockedNANDEmitterCompiledNonTimeoutFormalized = true
leanConcreteLockedNANDEmitterPolynomialTimeMachineFormalized = true
leanConcreteLockedNANDEmitterPolynomialTimeFunctionFormalized = true
leanConcreteLockedNANDEmitterRawRefinementFormalized = true
leanConcreteLockedNANDEmitterStrictParserCompositionFormalized = true
leanConcreteLockedNANDEmitterOutputSizeBoundFormalized = true
leanConcreteLockedNANDEmitterScope = "literal-1387921-rule-grammar-only-all-input-target-emitter-with-strict-parser-composition-polynomial-bounds-and-recursive-raw-refinement"
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepThirdPaddingOrUnaryOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepAxiomAuditPassed = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepSecondPaddingOrUnaryOpportunityFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed = true
leanConcreteCookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized = true
leanConcreteCNFToNANDSemanticCompilerFormalized = true
leanConcreteCNFToNANDSemanticCompilerAxiomAuditPassed = true
leanConcreteCNFToNANDSemanticCompilerAuditedDeclarationCount = 68
leanConcreteCNFToNANDExactCodecCanonicalityFormalized = true
leanConcreteCNFToNANDTypedTopologicalCompilationFormalized = true
leanConcreteCNFToNANDWellFormedOutputFormalized = true
leanConcreteCNFToNANDExactSemanticsFormalized = true
leanConcreteCNFToNANDEdgeSemanticsFormalized = true
leanConcreteCNFToNANDExactGateCountFormalized = true
leanConcreteCNFToNANDPolynomialOutputSizeBoundFormalized = true
leanConcreteCNFToNANDAllBitstringFailClosedFormalized = true
leanConcreteCNFToNANDLockedThresholdCompositionFormalized = true
leanConcreteCNFToNANDFiniteMachineFormalized = true
leanConcreteCNFToNANDPolynomialTimeFunctionFormalized = true
leanConcreteCNFToNANDPolynomialReductionFormalized = true
leanConcreteCNFToNANDPolynomialReductionAxiomAuditPassed = true
leanConcreteCNFToNANDPolynomialReductionAuditedDeclarationCount = 1316
leanConcreteCNFToNANDAllInputExactFormalized = true
leanConcreteCNFToNANDExactMachineOutputFormalized = true
leanConcreteCNFToNANDCompiledNonTimeoutFormalized = true
leanConcreteCNFToNANDRawRefinementFormalized = true
leanConcreteCNFToNANDDirectReductionFormalized = true
leanConcreteCNFToNANDLockedReductionCompositionFormalized = true
leanResidualTerminalFullBridgeFormalized = true
leanResidualTerminalFullBridgeAxiomAuditPassed = true
leanResidualTerminalQuotientCarrierFormalized = true
leanResidualTerminalModeFirewallFormalized = true
leanResidualTerminalModeFirewallAxiomAuditPassed = true
leanResidualTerminalProfileProjectionExactFormalized = true
leanResidualTerminalCheckedFullLiftFormalized = true
leanResidualTerminalQuotientEqualityNotConstructiveFormalized = true
leanResidualTerminalObligationDischargePreservedFormalized = true
leanResidualProjectionMinimumFormalized = true
leanResidualProjectionMinimumAxiomAuditPassed = true
leanResidualProjectionMinimumExecutableFullScanFormalized = true
leanResidualProjectionMinimumExecutableQuotientScanFormalized = true
leanResidualProjectionMinimumAttainmentFormalized = true
leanResidualProjectionMinimumUniversalLowerBoundsFormalized = true
leanResidualProjectionMinimumMonotonicityFormalized = true
leanResidualProjectionDefectDecompositionFormalized = true
leanResidualProjectionDefectZeroIffCheckedLiftAtMinimumFormalized = true
leanResidualProjectionTransferFormalized = true
leanResidualProjectionTransferAxiomAuditPassed = true
leanResidualProjectionTransferSignedDeltasFormalized = true
leanResidualProjectionTransferIdentityFormalized = true
leanResidualProjectionTransferConstantCutFormalized = true
leanResidualTerminalProperSupportFormalized = true
leanResidualTerminalProperSupportSearchCompleteFormalized = true
leanResidualTerminalProperSupportExactLocalGainFormalized = true
leanResidualTerminalProperSupportAxiomAuditPassed = true
leanResidualTerminalProperSupportScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-and-canonical-primitive-record-seeds-with-exhaustive-reference-minimum-local-gain"
leanResidualTerminalSupportSquareClosureFormalized = true
leanResidualTerminalSupportSquareMeetJoinExactFormalized = true
leanResidualTerminalSupportSquarePhysicalCompatibilityFormalized = true
leanResidualTerminalSupportSquareSemanticExtractionFormalized = true
leanResidualTerminalSupportSquareClosureAxiomAuditPassed = true
leanResidualTerminalSupportSquareClosureScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-and-pairs-of-finite-terminal-seeds"
leanResidualTerminalGovernedSupportCompletionFormalized = true
leanResidualTerminalGovernedProfilePartitionFormalized = true
leanResidualTerminalGovernedSupportCompletionAxiomAuditPassed = true
leanResidualTerminalGovernedSupportCompletionScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-finite-seed-lists-and-saturated-support-square-corners"
leanResidualTerminalFrontierPushoutFormalized = true
leanResidualTerminalFrontierBoundaryGlueExactFormalized = true
leanResidualTerminalFrontierInterfaceGlueExactFormalized = true
leanResidualTerminalFrontierProfileGlueExactFormalized = true
leanResidualTerminalFrontierInternalizationFormalized = true
leanResidualTerminalFrontierPushoutAxiomAuditPassed = true
leanResidualTerminalFrontierPushoutScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-and-computed-saturated-support-squares"
leanResidualTerminalSaturationFormalized = true
leanResidualTerminalSaturationAxiomAuditPassed = true
leanResidualTerminalPrimitiveUniverseFormalized = true
leanResidualTerminalSaturationExtensiveFormalized = true
leanResidualTerminalSaturationLeastFormalized = true
leanResidualTerminalSaturationMonotoneFormalized = true
leanResidualTerminalSaturationIdempotentFormalized = true
leanResidualTerminalExecutableSaturationFormalized = true
leanResidualTerminalPhysicalSupportCompletionFormalized = true
leanResidualTerminalPhysicalBoundaryFormalized = true
leanResidualTerminalPhysicalInterfaceFormalized = true
leanResidualTerminalPhysicalCompatibilityFormalized = true
leanResidualTerminalPhysicalSupportCompletionAxiomAuditPassed = true
leanResidualTerminalPhysicalSupportCompletionScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-and-finite-seed-lists"
leanResidualTerminalSupportExtractionFormalized = true
leanResidualTerminalSupportExtractionAxiomAuditPassed = true
leanResidualTerminalSupportExtractionScope = "all-finite-direct-wire-candidates-terminal-record-lists-boundary-valuations-and-interface-coordinates"
leanResidualTerminalOpenSemanticsFormalized = true
leanResidualTerminalInducedRecoveryFormalized = true
leanResidualTerminalSupportCompletionFormalized = true
leanResidualTerminalSquareLegitimacyFormalized = true
leanResidualTerminalSquareStructuralCompatibilityFormalized = true
leanResidualTerminalSquareFrontierPushoutFormalized = true
leanResidualTerminalSquareSharedQuantityCarrierFormalized = true
leanResidualTerminalSquareLocalConclusionUnderRouteSilenceFormalized = true
leanResidualTerminalSquareFailClosedRouteDichotomyFormalized = true
leanResidualTerminalSquareLegitimacyAxiomAuditPassed = true
leanResidualTerminalSquareLegitimacyScope = "all-finite-computed-terminal-support-squares-explicit-terminal-dependency-systems-direct-wire-candidates-observers-and-forgetful-projections-with-local-route-silence-or-proof-bearing-first-failure"
leanResidualTerminalComputedBCELAnchorNucleusFormalized = true
leanResidualTerminalBCELMinimumPositiveNucleusFormalized = true
leanResidualTerminalBCELAnchorAlgebraFormalized = true
leanResidualTerminalBCELCutDefectFirewallFormalized = true
leanResidualTerminalBCELCutRouteDichotomyFormalized = true
leanResidualTerminalBCELConstantCutConclusionFormalized = true
leanResidualTerminalBCELAnchorNucleusAxiomAuditPassed = true
leanResidualTerminalBCELAnchorNucleusScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-computed-governed-proper-positive-supports-forgetful-projections-executable-ambient-observers-and-positive-whole-support-projection-defect"
leanResidualTerminalSaturationPositivityFirewallFormalized = true
leanResidualTerminalSaturationPositivityFirewallAxiomAuditPassed = true
leanResidualTerminalSaturationPositivityFirewallScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-computed-governed-proper-positive-supports-forgetful-projections-and-executable-ambient-observers-total-zero-or-positive-whole-support-projection-defect-classification"
leanResidualTerminalCandidateSaturationFormalized = true
leanResidualTerminalSaturationCostBalanceFormalized = true
leanResidualTerminalFirstNontransparentStepFormalized = true
leanResidualTerminalSaturationCostBalanceAxiomAuditPassed = true
leanResidualTerminalSaturationCostBalanceScope = "all-finite-direct-wire-candidates-executable-observers-forgetful-projections-candidate-derived-dependency-system-rule-labelled-exact-cost-balance-or-first-nontransparent-step"
leanResidualTerminalInterfaceExposureRoutingFormalized = true
leanResidualTerminalFiniteInterfaceExposureRoutesToEFormalized = true
leanResidualTerminalInterfaceExposureZeroCostRetractFormalized = true
leanResidualTerminalFirstInterfaceExposureRouteFormalized = true
leanResidualTerminalInterfaceExposureRoutingAxiomAuditPassed = true
leanResidualTerminalInterfaceExposureRoutingScope = "all-finite-direct-wire-candidates-executable-observers-forgetful-projections-candidate-derived-interface-consumer-transparent-or-local-e-route-with-exact-first-failure"
leanResidualTerminalOriginKernelObligationRoutingFormalized = true
leanResidualTerminalFiniteOriginKernelObligationClosureRoutedFormalized = true
leanResidualTerminalFirstOriginKernelObligationRouteFormalized = true
leanResidualTerminalOriginKernelObligationRoutingAxiomAuditPassed = true
leanResidualTerminalOriginKernelObligationRoutingScope = "all-finite-direct-wire-candidates-executable-observers-forgetful-projections-candidate-derived-origin-kernel-obligation-closures-with-exact-safety-or-first-route"
leanResidualTerminalFiniteSaturatePositiveCompositionFormalized = true
leanResidualTerminalFiniteSaturatePositiveCompositionAxiomAuditPassed = true
leanResidualTerminalFiniteSaturatePositiveCompositionScope = "all-finite-direct-wire-candidates-executable-observers-forgetful-projections-proof-bearing-positive-full-slack-candidate-bcel-anchor-problems-total-finite-saturate-positive-composition"
leanResidualTerminalFiniteBCELReadyCompositionFormalized = true
leanResidualTerminalFiniteBCELReadyCompositionAxiomAuditPassed = true
leanResidualTerminalFiniteBCELReadyCompositionScope = "all-finite-direct-wire-candidates-executable-models-proof-bearing-positive-full-slack-anchor-problems-recomputed-finite-saturate-positive-to-computed-bcel-ready-branch"
leanResidualTerminalFiniteBCELPacketCarrierCoherenceFormalized = true
leanResidualTerminalFiniteBCELPacketCarrierCoherenceAxiomAuditPassed = true
leanResidualTerminalFiniteBCELPacketCarrierCoherenceScope = "all-arbitrary-finite-proof-bearing-same-candidate-model-bcel-ready-nuclei-bijectively-mapped-to-the-exact-packet-family-carrier"
leanResidualTerminalFiniteBCELPacketActivationObstructionFormalized = true
leanResidualTerminalFiniteBCELPacketActivationObstructionAxiomAuditPassed = true
leanResidualTerminalFiniteBCELPacketActivationObstructionScope = "all-arbitrary-finite-coherently-mapped-bcel-ready-and-packet-families-exhaustive-cut-value-and-proper-cut-activation-coherence-check-with-proof-bearing-first-obstruction"
leanConcreteLegacyLockedNANDCompatibilityFormalized = true
leanConcreteLegacyLockedNANDCompatibilityAxiomAuditPassed = true
leanConcreteLegacyLockedNANDCompatibilityEndpointProjectAssumptionFree = true
leanConcreteLegacyLockedNANDCompatibilityScope = "all-bitstring-report-facing-sat-and-locked-nand-identities-with-concrete-finite-pipeline-complexity-witnesses-and-direct-checked-reduction-reuse"
leanConcreteResidualBandCompatibilityFormalized = true
leanConcreteResidualBandCompatibilityAxiomAuditPassed = true
leanConcreteResidualBandCompatibilityAuditedDeclarationCount = 10
leanConcreteResidualBandCompatibilityEndpointProjectAssumptionFree = true
leanConcreteResidualBandCompatibilityCallerReductionRemoved = true
leanConcreteResidualBandCompatibilityScope = "all-bitstring-and-arbitrary-typed-candidate-exact-reference-minimum-threshold-semantics-with-fail-closed-decoding-and-identity-locked-to-residual-transport"
leanTypedPCCPackReflectionFormalized = true
leanTypedPCCPackReflectionAxiomAuditPassed = true
leanTypedPCCPackReflectionAuditedDeclarationCount = 15
leanTypedPCCPackReflectionEndpointProjectAssumptionFree = true
leanTypedPCCPackReflectionOpaqueDeclarationsRemoved = true
leanTypedPCCPackReflectionScope = "all-explicit-proof-bearing-pccmin-loop-certificates-with-transparent-canonical-packaging-structural-identifier-checking-exact-projection-and-mismatch-rejection"
leanPCCMinTotalOracleLoopFormalized = true
leanPCCMinTotalOracleLoopAxiomAuditPassed = true
leanPCCMinTotalOracleLoopAuditedDeclarationCount = 8
leanPCCMinTotalOracleLoopEndpointProjectAssumptionFree = true
leanPCCMinTotalOracleLoopHasUnresolvedOutcome = false
leanPCCMinTotalOracleLoopConstructsOracle = false
leanPCCMinTotalOracleLoopExactnessUnderOracleFormalized = true
leanPCCMinTotalOracleLoopGainIterationBoundFormalized = true
leanPCCMinTotalOracleLoopPolynomialRuntimeProved = false
leanPCCMinTotalOracleLoopScope = "all-finite-direct-wire-implementations-under-an-explicit-proof-bearing-total-oracle-with-strict-slack-descent-exact-terminal-evidence-and-gain-iteration-bound"
leanPCCMinNormalizeOracleCompositionFormalized = true
leanPCCMinNormalizeOracleCompositionAxiomAuditPassed = true
leanPCCMinNormalizeOracleCompositionAuditedDeclarationCount = 10
leanPCCMinNormalizeOracleCompositionEndpointProjectAssumptionFree = true
leanPCCMinNormalizeOracleCompositionHasUnresolvedOutcome = false
leanPCCMinNormalizeOracleCompositionConstructsNormalizer = false
leanPCCMinNormalizeOracleCompositionConstructsOracle = false
leanPCCMinNormalizeOracleCompositionLiftedGainFormalized = true
leanPCCMinNormalizeOracleCompositionExactEndpointTransportFormalized = true
leanPCCMinNormalizeOracleCompositionPolynomialRuntimeProved = false
leanPCCMinNormalizeOracleCompositionScope = "all-finite-direct-wire-implementations-under-explicit-proof-bearing-normalizer-and-oracle-stages-with-nonincreasing-semantic-normalization-lifted-strict-gains-exact-endpoint-transport-and-the-checked-well-founded-loop"
leanPCCMinRankOrderedOracleFormalized = true
leanPCCMinRankOrderedOracleAxiomAuditPassed = true
leanPCCMinRankOrderedOracleAuditedDeclarationCount = 15
leanPCCMinRankOrderedOracleEndpointProjectAssumptionFree = true
leanPCCMinRankOrderedOracleHasUnresolvedOutcome = false
leanPCCMinRankOrderedOracleCanonicalAllRanksFormalized = true
leanPCCMinRankOrderedOracleCompleteSilenceRequired = true
leanPCCMinRankOrderedOracleConstructsResolvers = false
leanPCCMinRankOrderedOracleConstructsSelectorRows = false
leanPCCMinRankOrderedOracleProvesZeroSlackClosure = false
leanPCCMinRankOrderedOraclePolynomialRuntimeProved = false
leanPCCMinRankOrderedOracleScope = "all-finite-direct-wire-implementations-under-explicit-proof-bearing-normalizer-hresolve-budgetresolve-arbitrary-finite-rank-selector-rows-typed-blocker-silence-and-zeroslack-closure-with-canonical-all-rank-scanning-and-the-checked-well-founded-loop"
leanPCCMinCheckedPacketRankedSelectorFormalized = true
leanPCCMinCheckedPacketRankedSelectorAxiomAuditPassed = true
leanPCCMinCheckedPacketRankedSelectorAuditedDeclarationCount = 15
leanPCCMinCheckedPacketRankedSelectorEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketRankedSelectorChecksEveryCanonicalHandle = true
leanPCCMinCheckedPacketRankedSelectorDerivesExactRankRows = true
leanPCCMinCheckedPacketRankedSelectorConstructsTerminalFamily = false
leanPCCMinCheckedPacketRankedSelectorConstructsResolvers = false
leanPCCMinCheckedPacketRankedSelectorProvesZeroSlackClosure = false
leanPCCMinCheckedPacketRankedSelectorPolynomialRuntimeProved = false
leanPCCMinCheckedPacketRankedSelectorScope = "all-finite-direct-wire-implementations-under-explicit-normalizer-hresolve-budgetresolve-supplied-grouped-packet-family-rank-map-data-only-claim-table-complete-checker-acceptance-and-zeroslack-silence-closure-with-canonical-exact-rank-row-derivation-and-the-checked-well-founded-loop"
leanPCCMinCheckedPacketHBZeroSlackBridgeFormalized = true
leanPCCMinCheckedPacketHBZeroSlackBridgeAxiomAuditPassed = true
leanPCCMinCheckedPacketHBZeroSlackBridgeAuditedDeclarationCount = 15
leanPCCMinCheckedPacketHBZeroSlackBridgeEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketHBZeroSlackBridgeChecksHBClosure = true
leanPCCMinCheckedPacketHBZeroSlackBridgeDerivesSelectorSilence = true
leanPCCMinCheckedPacketHBZeroSlackBridgeDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketHBZeroSlackBridgeConstructsPositiveSlackBridge = false
leanPCCMinCheckedPacketHBZeroSlackBridgeUnconditionalZeroSlack = false
leanPCCMinCheckedPacketHBZeroSlackBridgePolynomialRuntimeProved = false
leanPCCMinCheckedPacketHBZeroSlackBridgeScope = "all-finite-direct-wire-implementations-under-explicit-normalizer-hresolve-budgetresolve-supplied-grouped-packet-family-rank-map-data-only-claim-table-positive-slack-to-faithful-selector-bridge-and-checked-hb-no-outcome-closure-with-derived-selector-silence-conditional-zeroslack-and-the-checked-well-founded-loop"
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeFormalized = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeAuditedDeclarationCount = 12
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeDerivesGeneralBN6Packet = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeComputesSelectorFaithfulness = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeIndependentBindingRemoved = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeConstructsConstantActivation = false
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6HBZeroSlackBridgePolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6HBZeroSlackBridgeScope = "all-finite-direct-wire-implementations-under-explicit-normalizer-hresolve-budgetresolve-supplied-grouped-bn6-family-carrier-lower-bound-rank-map-route-clear-computed-payload-faithfulness-data-only-claim-table-positive-slack-to-constant-activation-bridge-and-checked-hb-no-outcome-closure-with-derived-conditional-zeroslack-and-the-checked-well-founded-loop"
leanPCCMinCheckedPacketBN6BCELActivationRouteFormalized = true
leanPCCMinCheckedPacketBN6BCELActivationRouteAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6BCELActivationRouteAuditedDeclarationCount = 15
leanPCCMinCheckedPacketBN6BCELActivationRouteEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6BCELActivationRouteTotalClassifier = true
leanPCCMinCheckedPacketBN6BCELActivationRouteDerivesConstantActivation = true
leanPCCMinCheckedPacketBN6BCELActivationRouteRetainsMismatchRoutes = true
leanPCCMinCheckedPacketBN6BCELActivationRouteDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6BCELActivationRouteUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6BCELActivationRoutePolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6BCELActivationRouteScope = "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-grouped-bn6-packet-family-with-total-carrier-cut-value-and-all-proper-cut-activation-classification-proof-bearing-mismatch-routes-derived-coherent-constant-activation-and-conditional-zeroslack"
leanPCCMinCheckedPacketBN6BCELDerivedFamilyFormalized = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyAuditedDeclarationCount = 14
leanPCCMinCheckedPacketBN6BCELDerivedFamilyEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyConstructsFamilyFromBCEL = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyDerivesCarrier = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyDerivesCutValue = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyEliminatesDuplicateMismatchRoutes = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyRetainsActivationMismatchRoute = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6BCELDerivedFamilyUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6BCELDerivedFamilyPolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6BCELDerivedFamilyScope = "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-grouped-cell-ledger-with-bcel-derived-family-carrier-cut-value-positivity-impossible-duplicate-data-routes-exact-proper-cut-activation-mismatch-or-conditional-zeroslack"
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingFormalized = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingAuditedDeclarationCount = 34
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingNormalizesSupportsInCarrier = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingConstructsSingletonConsumerSystems = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingCoalescesDuplicateFootprints = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingPreservesPayloadAtoms = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingDerivesCellsFromTerminalInput = false
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingPolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6BCELCanonicalGroupingScope = "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-raw-positive-support-payload-ledger-with-carrier-normalized-supports-canonical-singleton-consumer-systems-duplicate-footprint-coalescing-payload-preservation-and-exact-activation-mismatch-or-conditional-zeroslack"
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerFormalized = true
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerAuditedDeclarationCount = 9
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerRawMassConserved = true
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerUsesDirectRawCutLedger = true
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerDerivesCellsFromTerminalInput = false
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerDerivesConstantActivation = false
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerMismatchIsGain = false
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerPolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6BCELCanonicalCutLedgerScope = "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-raw-positive-cell-ledger-with-exact-canonical-grouped-to-raw-cut-mass-conservation-and-direct-raw-proper-cut-mismatch-or-conditional-zeroslack"
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisFormalized = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisAuditedDeclarationCount = 22
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisEquivalentToAllProperCuts = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisClassifierTotal = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisAvoidsProperCutPowerset = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisUsesDirectRawCutLedger = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisDerivesConstantActivation = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisDerivesCellsFromTerminalInput = false
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisRejectedRouteIsGain = false
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisPolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisScope = "arbitrary-finite-sparse-v53-shape-specific-constant-cut-basis-equivalent-to-all-proper-cuts-with-total-typed-classifier-and-direct-checked-bn6-bcel-hb-conditional-zeroslack-adapter-over-supplied-terminal-data"
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteFormalized = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteAxiomAuditPassed = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteAuditedDeclarationCount = 30
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteSingletonPairFamilyComplete = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteSingletonPairFamilyNodup = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteQuadraticListBound = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteEquivalentToAllProperCuts = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteClassifierTotal = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteReturnsExactRawMismatch = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteAvoidsProperCutPowerset = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteDerivesConditionalZeroSlack = true
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteDerivesCellsFromTerminalInput = false
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteMismatchIsGain = false
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteGlobalRankDecreaseProved = false
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteCompleteEncodedPolynomialRuntimeProved = false
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteUnconditionalZeroSlack = false
leanPCCMinCheckedPacketBN6BCELSparseActivationRouteScope = "arbitrary-finite-sparse-positive-v53-singleton-pair-proper-cut-equation-equivalent-to-all-proper-cuts-with-quadratic-list-bound-total-first-mismatch-classifier-and-direct-checked-raw-activation-mismatch-or-conditional-zeroslack-over-supplied-terminal-data"
leanResidualTerminalPkgCBN6PositiveCellizationFormalized = true
leanResidualTerminalPkgCBN6PositiveCellizationAxiomAuditPassed = true
leanResidualTerminalPkgCBN6PositiveCellizationAuditedDeclarationCount = 19
leanResidualTerminalPkgCBN6PositiveCellizationEndpointProjectAssumptionFree = true
leanResidualTerminalPkgCBN6PositiveCellizationSourceCellsArbitraryFinite = true
leanResidualTerminalPkgCBN6PositiveCellizationRawSupportsDerived = true
leanResidualTerminalPkgCBN6PositiveCellizationFootprintSizeDerivedFromActiveCut = true
leanResidualTerminalPkgCBN6PositiveCellizationPkgCCancellationProofBearing = true
leanResidualTerminalPkgCBN6PositiveCellizationActivationWeightConservedAllCuts = true
leanResidualTerminalPkgCBN6PositiveCellizationPayloadOrderPreserved = true
leanResidualTerminalPkgCBN6PositiveCellizationDerivesCellsFromTerminalInput = false
leanResidualTerminalPkgCBN6PositiveCellizationRestorerConstructedFromTerminalInput = false
leanResidualTerminalPkgCBN6PositiveCellizationCancellationIsGlobalGain = false
leanResidualTerminalPkgCBN6PositiveCellizationCompletePkgCBN6Integration = false
leanResidualTerminalPkgCBN6PositiveCellizationCompleteEncodedPolynomialRuntimeProved = false
leanResidualTerminalPkgCBN6PositiveCellizationUnconditionalZeroSlack = false
leanResidualTerminalPkgCBN6PositiveCellizationScope = "arbitrary-finite-supplied-active-v54-consumer-systems-over-one-carrier-classified-by-exact-pkgc-same-key-cancellation-or-derived-raw-bn6-positive-cells-with-payload-order-and-all-cut-activation-conservation-over-a-supplied-restorer"
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteFormalized = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteAxiomAuditPassed = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteAuditedDeclarationCount = 7
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteSourceCellsArbitraryFinite = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteRawCellsDerivedFromPkgCSource = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteActivationWeightConservedAllCuts = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRoutePkgCCancellationProofBearing = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteSparseCutLengthAtMostTwo = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteActivationMismatchReflectedToSourceLedger = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteConditionalZeroSlackOnly = true
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteDerivesSourcesFromTerminalInput = false
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteConstructsDownstreamTables = false
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteCancellationOrMismatchIsGlobalGain = false
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteCompletePkgCBN6Integration = false
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteCompleteEncodedPolynomialRuntimeProved = false
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteUnconditionalZeroSlack = false
leanPCCMinCheckedPacketPkgCBN6BCELSourceRouteScope = "arbitrary-finite-supplied-active-pkgc-source-ledger-over-the-exact-checked-bcel-nucleus-with-source-derived-raw-bn6-cells-exact-pkgc-cancellation-or-source-ledger-singleton-pair-activation-mismatch-and-conditional-zeroslack-under-supplied-checked-downstream-data"
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteFormalized = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteAxiomAuditPassed = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteAuditedDeclarationCount = 10
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteAmbientLedgerArbitraryFinite = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteAmbientOrderIndependent = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteMultiplicityPreserved = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteRemainderComputed = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteNoEmbeddingProofBearing = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteCandidateBN4KernelConstructed = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteResidualReductionExact = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteConditionalZeroSlackOnly = true
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteDerivesAmbientLedgerFromTerminalInput = false
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteDerivesSourcesFromTerminalInput = false
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteCancellationReductionIsGlobalGain = false
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteCompletePkgCBN6Integration = false
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteCompleteEncodedPolynomialRuntimeProved = false
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteUnconditionalZeroSlack = false
leanPCCMinCheckedPacketPkgCAmbientBN4ExtractionRouteScope = "arbitrary-finite-multiplicity-preserving-order-independent-extraction-of-generated-pkgc-cancellation-cells-from-a-supplied-candidate-bound-ambient-bn4-ledger-with-computed-remainder-exact-residual-reduction-or-proof-of-no-exact-embedding-composed-with-m202-conditional-zeroslack-and-source-activation-routing"
leanResidualTerminalPkgCRestorationCoverageAmbientRouteFormalized = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteAxiomAuditPassed = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteAuditedDeclarationCount = 17
leanResidualTerminalPkgCRestorationCoverageAmbientRouteEndpointProjectAssumptionFree = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteConsumerSystemArbitraryFinite = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteRestorationUniverseArbitraryFinite = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteAmbientLedgerArbitraryFinite = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteTypedRestorerRequired = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteHallDeficitProofBearing = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteCoverageCancellationConstructed = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteRemainderComputed = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteNoEmbeddingProofBearing = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteResidualReductionExact = true
leanResidualTerminalPkgCRestorationCoverageAmbientRouteMaterializesSemanticFullCandidates = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteDerivesRestorationUniverseFromTerminalInput = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteDerivesAmbientLedgerFromTerminalInput = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteHallRouteIsGlobalGain = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteCompletePkgCBN6Integration = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteCompleteEncodedPolynomialRuntimeProved = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteUnconditionalZeroSlack = false
leanResidualTerminalPkgCRestorationCoverageAmbientRouteScope = "arbitrary-finite-restoration-coordinate-coverage-classified-as-an-exact-q-restoration-hall-deficit-or-a-constructed-balanced-bn4-unit-cancellation-subledger-with-computed-arbitrary-order-ambient-remainder-exact-residual-reduction-or-proof-of-no-exact-embedding"
leanResidualTerminalPkgCRestorationCoverageBN6LedgerFormalized = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerAxiomAuditPassed = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerAuditedDeclarationCount = 11
leanResidualTerminalPkgCRestorationCoverageBN6LedgerEndpointProjectAssumptionFree = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerSourceLedgerArbitraryFinite = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerTypedRestorerRequired = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerAllSourceSingletonizationRequiredForCellization = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerFirstObstructionPreserved = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerBN6CellsConstructed = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerPayloadOrderPreserved = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerAllCutActivationConserved = true
leanResidualTerminalPkgCRestorationCoverageBN6LedgerDerivesRestorationUniverseFromTerminalInput = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerDerivesAmbientLedgerFromTerminalInput = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerHallRouteIsGlobalGain = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerComputedRemainderProvedEmpty = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerCompletePkgCBN6Integration = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerCompleteEncodedPolynomialRuntimeProved = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerUnconditionalZeroSlack = false
leanResidualTerminalPkgCRestorationCoverageBN6LedgerScope = "arbitrary-finite-supplied-active-pkgc-source-ledger-scanned-in-list-order-for-the-first-exact-restoration-hall-ambient-reduction-or-no-embedding-outcome-or-complete-derived-bn6-cellization-with-payload-order-and-all-cut-activation-conservation"
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteFormalized = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteAxiomAuditPassed = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteAuditedDeclarationCount = 4
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteSourceLedgerArbitraryFinite = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCandidateBoundAmbientLedgers = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteTypedRestorerRequired = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteRawBN6CellsDerived = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteFirstObstructionPreserved = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteConditionalZeroSlackOnly = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteActivationMismatchReflectedToSourceLedger = true
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteDerivesSourcesFromTerminalInput = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteConstructsDownstreamTables = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteHallRouteIsGlobalGain = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteComputedRemainderProvedEmpty = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCompletePkgCBN6Integration = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCompleteEncodedPolynomialRuntimeProved = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteUnconditionalZeroSlack = false
leanPCCMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteScope = "arbitrary-finite-candidate-bound-restoration-coverage-pkgc-source-ledger-with-first-exact-hall-ambient-reduction-or-no-embedding-outcome-or-derived-bn6-cellization-entering-the-checked-sparse-bcel-route-with-source-reflected-activation-mismatch-and-conditional-zeroslack"
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentFormalized = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentAxiomAuditPassed = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentAuditedDeclarationCount = 16
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentEndpointProjectAssumptionFree = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentArbitraryFinite = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentUnsignedChargeMassDerived = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentExactPermutationRequired = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentRemovedChargeStrictlyPositive = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentResidualLedgerPreserved = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentChargeSizeStrictlyDecreases = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentResidualRankChargeCoordinateDecreases = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentRankContextParametric = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentCallerSuppliedRankProofRequired = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentM206BranchesPreserved = true
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentHallRouteIsGlobalGain = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentAmbientMismatchIsGlobalRoute = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentActivationMismatchIsGlobalRoute = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentComputedRemainderProvedEmpty = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentCompleteGlobalRouteCoverage = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentCompletePkgCBN6Integration = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentCompleteEncodedPolynomialRuntimeProved = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentUnconditionalZeroSlack = false
leanPCCMinCheckedPacketPkgCRestorationCoverageChargeDescentScope = "arbitrary-finite-m206-restoration-coverage-ambient-embedding-with-mass-sensitive-unsigned-charge-decomposition-strict-remainder-charge-decrease-and-context-parametric-exact-terminal-residual-rank-charge-coordinate-descent-while-all-other-m206-outcomes-remain-explicit"
leanConcreteCookLevinBuilderFullScheduleCursorControllerFormalized = true
leanConcreteCookLevinBuilderFullScheduleCursorControllerAxiomAuditPassed = true
leanConcreteCookLevinBuilderFullScheduleCursorControllerAuditedDeclarationCount = 70
leanConcreteCookLevinBuilderFullScheduleCursorControllerExactRawTraceFormalized = true
leanConcreteCookLevinBuilderFullScheduleCursorControllerExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderFullScheduleCursorControllerFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderFullScheduleCursorControllerEmitsBodyTokens = false
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterAxiomAuditPassed = true
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterAuditedDeclarationCount = 51
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterLiteralRawMachineFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterExactRawTraceFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterDecodesPostHeaderCoordinate = false
leanConcreteCookLevinBuilderArbitrarySlotHeaderRouterEmitsBodyTokens = false
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderAxiomAuditPassed = true
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderAuditedDeclarationCount = 22
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderAllCoordinateSemanticDecoderFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderExactClauseWithinClauseReconstructionFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderDirectBodyTokenRouteFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderRawPostHeaderRemainderExtractionFormalized = true
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderRawDivisionFormalized = false
leanConcreteCookLevinBuilderArbitrarySlotPostHeaderDecoderRawBodyTokenEmissionFormalized = false
leanConcreteCookLevinBuilderPostHeaderRawDividerFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerAxiomAuditPassed = true
leanConcreteCookLevinBuilderPostHeaderRawDividerAuditedDeclarationCount = 57
leanConcreteCookLevinBuilderPostHeaderRawDividerLiteralRawMachineFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerExactRawTraceFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerCompiledRawSimulationFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerExactQuotientRemainderDecodeFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerExternalUnaryEncodedSizeQuadraticBoundFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerFailClosedBoundaryTimeoutFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawDividerRawBodyTokenEmissionFormalized = false
leanConcreteCookLevinBuilderPostHeaderRawLaunchFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawLaunchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPostHeaderRawLaunchAuditedDeclarationCount = 24
leanConcreteCookLevinBuilderPostHeaderRawLaunchExactHandoffFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawLaunchAllRoutesFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawLaunchSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawLaunchLiteralTapeBridgeFormalized = false
leanConcreteCookLevinBuilderPostHeaderRawLaunchRawBodyTokenEmissionFormalized = false
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeAxiomAuditPassed = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeAuditedDeclarationCount = 78
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeExactRouterTapeInputsFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeLiteralTapeBridgeFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeArbitraryWorkspacePreservedFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeShieldedDividerTraceFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeAllRoutesFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeCompiledSimulationFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderPostHeaderRawTapeBridgeRawBodyTokenEmissionFormalized = false
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierAxiomAuditPassed = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierAuditedDeclarationCount = 85
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierExactDividerTapeInputsFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierProblemClauseCountSidecarDerivedFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierArbitraryWorkspacePreservedFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierShieldedComparatorTraceFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierAllCoordinateBodyFinishAgreementFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierCompiledSimulationFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderPostDividerRawRouteClassifierRawBodyTokenEmissionFormalized = false
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchAuditedDeclarationCount = 30
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchCanonicalScheduleSelectionFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchPaddingBodyFinishTransitionFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchCanonicalSelectedTokenLaunchFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchCompiledSimulationFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchLiteralRawSelectionHandoffFormalized = false
leanConcreteCookLevinBuilderPostDividerSelectedTokenLaunchScheduleIterationFormalized = false
leanConcreteCookLevinBuilderCompleteScheduleIterationFormalized = true
leanConcreteCookLevinBuilderCompleteScheduleIterationAxiomAuditPassed = true
leanConcreteCookLevinBuilderCompleteScheduleIterationAuditedDeclarationCount = 12
leanConcreteCookLevinBuilderCompleteScheduleIterationAllCoordinatesFormalized = true
leanConcreteCookLevinBuilderCompleteScheduleIterationCompleteEncodedFormulaTokensFormalized = true
leanConcreteCookLevinBuilderCompleteScheduleIterationAggregateSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderCompleteScheduleIterationLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderCompleteScheduleIterationRawStageHandoffFormalized = false
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchAuditedDeclarationCount = 49
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchFiveRequestAlphabetFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchLiteralRequestTapeHandoffFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchCanonicalAllCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchExactCompiledTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchMalformedRequestTimeoutFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchOneStepShortTimeoutFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchRawCoordinateSelectorFormalized = false
leanConcreteCookLevinBuilderPhysicalOptionalTokenDispatchLiteralScheduleLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalDispatchScheduleFormalized = true
leanConcreteCookLevinBuilderPhysicalDispatchScheduleAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalDispatchScheduleAuditedDeclarationCount = 16
leanConcreteCookLevinBuilderPhysicalDispatchScheduleAllCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalDispatchScheduleCompleteEncodedFormulaTokensFormalized = true
leanConcreteCookLevinBuilderPhysicalDispatchScheduleExactPerCoordinateTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalDispatchScheduleAggregateSourceSizePolynomialBoundFormalized = true
leanConcreteCookLevinBuilderPhysicalDispatchScheduleRawCoordinateRequestDerived = false
leanConcreteCookLevinBuilderPhysicalDispatchScheduleLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalDispatchScheduleRawStageHandoffFormalized = false
leanConcreteCookLevinBuilderPhysicalFinishRequestFormalized = true
leanConcreteCookLevinBuilderPhysicalFinishRequestAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalFinishRequestAuditedDeclarationCount = 49
leanConcreteCookLevinBuilderPhysicalFinishRequestCanonicalFinishCoordinateDerived = true
leanConcreteCookLevinBuilderPhysicalFinishRequestProtectedBuilderSuffixFormalized = true
leanConcreteCookLevinBuilderPhysicalFinishRequestLiteralFinishRequestWritten = true
leanConcreteCookLevinBuilderPhysicalFinishRequestFixedComposedMachineRuleCount = 137
leanConcreteCookLevinBuilderPhysicalFinishRequestExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalFinishRequestCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalFinishRequestOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalFinishRequestExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalFinishRequestBodyOrPaddingRequestDerived = false
leanConcreteCookLevinBuilderPhysicalFinishRequestPrecedingClassifierSuffixHandoffFormalized = false
leanConcreteCookLevinBuilderPhysicalFinishRequestLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierPipelineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineAuditedDeclarationCount = 63
leanConcreteCookLevinBuilderPhysicalClassifierPipelineAllCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineFixedComposedMachineRuleCount = 711
leanConcreteCookLevinBuilderPhysicalClassifierPipelineExactStageHandoffsFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineRouteAgreementFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierPipelineBodyOrPaddingRequestDerived = false
leanConcreteCookLevinBuilderPhysicalClassifierPipelineLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestAuditedDeclarationCount = 36
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestFixedComposedMachineRuleCount = 721
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestFinishCoordinateDerived = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestClassifierVerdictSwapFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestExactRequestCellFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestWorkspacePreservationFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestBodyOrPaddingRequestDerived = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestDispatcherConnected = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishRequestLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationAuditedDeclarationCount = 57
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationFixedComposedMachineRuleCount = 740
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationFinishCoordinateDerived = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationClassifierPrefixDerived = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationClassifierPrefixBlankFreeFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationBlankSentinelFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationWorkspaceOrientationFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationMirroredDispatcherEntryFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationBodyOrPaddingRequestDerived = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationMirroredDispatcherExecuted = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishWorkspaceOrientationLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchAuditedDeclarationCount = 51
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchFixedMirroredDispatcherRuleCount = 64
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchFixedComposedMachineRuleCount = 813
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchGenericMachineReflectionFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchFullClassifierFinishMirroredDispatcherExecuted = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchCompleteCanonicalCNFOutputFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchBodyOrPaddingRequestDerived = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchAllClassifierRoutesConnected = false
leanConcreteCookLevinBuilderPhysicalClassifierFinishMirroredDispatchLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchAuditedDeclarationCount = 121
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchFixedRequestWriterRuleCount = 2
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchFixedOrientationRuleCount = 10
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchFixedMirroredDispatcherRuleCount = 64
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchFixedComposedMachineRuleCount = 814
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchFirstBodyIndexDerived = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchSeparatorRequestDerived = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchExactNextCanonicalPrefixFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchArbitraryBodyOrPaddingRequestDerived = false
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchAllClassifierRoutesConnected = false
leanConcreteCookLevinBuilderPhysicalClassifierFirstBodySeparatorMirroredDispatchLiteralRawLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchAuditedDeclarationCount = 82
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchFixedRequestRelayRuleCount = 14
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchFixedClassifierRelayMachineRuleCount = 734
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchFixedMirroredDispatcherRuleCount = 64
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchFixedComposedMachineRuleCount = 807
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchAllBodyCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchAllBodyAndPaddingRequestsStagedAndDispatched = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchCanonicalRequestStagedOnProtectedTape = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchRawRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchCombinedBodyFinishLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchExactNextCanonicalPrefixFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatchExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinAuditedDeclarationCount = 34
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinFixedRedirectRuleCount = 9
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinFixedComposedMachineRuleCount = 720
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinAllPostHeaderCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinArbitraryWorkspaceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinBodyZeroAdditionalStepsFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinFinishOneAdditionalStepFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinCommonContinuationStateFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinTapePreservingTerminalJoinFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinRawRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinRequestDispatchFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinRepeatedBuilderLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierTerminalJoinExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchAuditedDeclarationCount = 65
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchFixedRequestRelayRuleCount = 14
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchFixedClassifierRelayMachineRuleCount = 743
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchFixedMirroredDispatcherRuleCount = 64
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchFixedComposedMachineRuleCount = 816
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchAllPostHeaderCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchBodyAndFinishRoutesDispatched = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchCanonicalRequestStagedOnProtectedTape = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchRawRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchSuccessiveConfigurationsFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchRepeatedBuilderLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchExactNextCanonicalPrefixFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitAuditedDeclarationCount = 71
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitFixedSplitterRuleCount = 36
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitFixedComposedMachineRuleCount = 895
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitAllPostHeaderCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitCanonicalRequestStagedOnProtectedTape = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitPhysicalBodyRemainderSplitFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitFinishEndpointPreservedFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitClauseOccupancyFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitBodyRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitPaddingRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitSuccessiveConfigurationsFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitRepeatedBuilderLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitExternalInputSizePolynomialFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitAxiomAuditPassed = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitAuditedDeclarationCount = 91
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitFixedRouteRelayRuleCount = 20
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitFixedClassifierRelayMachineRuleCount = 749
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitFixedConditionalDispatcherRuleCount = 65
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitFixedComposedMachineRuleCount = 823
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitAllPostHeaderCoordinatesFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitCanonicalRequestStagedOnProtectedTape = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitPhysicalBodyFinishRouteDerived = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitBodyPendingMarkerFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitFinishRequestDerivedFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitBodyRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitPaddingRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitRawRequestSynthesisFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitSuccessiveConfigurationsFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitRepeatedBuilderLoopFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitExactNextCanonicalFinishPrefixFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitExactNextCanonicalBodyPrefixFormalized = false
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitExactWorkTraceFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitCompiledRawMachineFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitOneStepShortNonhaltingFormalized = true
leanConcreteCookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitExternalInputSizePolynomialFormalized = true
leanResidualTerminalRankWFFormalized = true
leanResidualTerminalRankWFAxiomAuditPassed = true
leanResidualTerminalRankWFScope = "fixed-ten-coordinate-natural-lexicographic-order-executable-comparison-accessibility-induction-and-kernel-well-foundedness"
leanResidualTerminalBN3RequestEnvelopeFormalized = true
leanResidualTerminalBN3RequestEnvelopeAxiomAuditPassed = true
leanResidualTerminalBN3RequestEnvelopeScope = "successful-computed-finite-bcel-anchor-nuclei-canonical-stable-request-identities-exact-singleton-minimal-consumers-duplicate-free-incidence-and-jointly-side-tight-full-or-quotient-basis-family"
leanResidualTerminalBN4ActivationCancellationFormalized = true
leanResidualTerminalBN4ActivationCancellationAxiomAuditPassed = true
leanResidualTerminalBN4ActivationCancellationScope = "successful-computed-finite-bn3-envelope-explicit-typed-cell-ledgers-activation-exact-complete-key-same-key-cancellation-and-exact-integer-mass-residuals"
leanResidualTerminalBN5FullShadowLocalizationFormalized = true
leanResidualTerminalBN5FullShadowLocalizationAxiomAuditPassed = true
leanResidualTerminalBN5FullShadowLocalizationScope = "all-finite-exact-coordinate-negative-unit-refinements-computed-cut-silence-complete-multiplicity-coverage-or-strict-hall-deficit-with-local-x1-nonsilence"
leanResidualTerminalPkgCSeparatingConsumersFormalized = true
leanResidualTerminalPkgCSeparatingConsumersAxiomAuditPassed = true
leanResidualTerminalPkgCSeparatingConsumersScope = "all-finite-explicit-minimal-consumer-antichains-pkgc-separating-consumer-first-pair-canonical-atoms-exact-coordinate-restoration-or-strict-hall-local-q"
leanResidualTerminalPkgCTypedRestorationFormalized = true
leanResidualTerminalPkgCTypedRestorationAxiomAuditPassed = true
leanResidualTerminalPkgCTypedRestorationScope = "all-finite-explicit-minimal-consumer-antichains-typed-full-restoration-candidates-coordinate-preserving-exact-multiplicity-coverage-no-hall-or-singletonized"
leanResidualTerminalPkgCSameKeyCancellationFormalized = true
leanResidualTerminalPkgCSameKeyCancellationAxiomAuditPassed = true
leanResidualTerminalPkgCSameKeyCancellationScope = "all-finite-explicit-minimal-consumer-antichains-typed-exact-coordinate-restoration-canonical-opposite-sign-bn4-ledger-every-key-balanced-empty-residual-or-singletonized-under-cancellation-silence"
leanResidualTerminalPkgCAmbientBN4LedgerFormalized = true
leanResidualTerminalPkgCAmbientBN4LedgerAxiomAuditPassed = true
leanResidualTerminalPkgCAmbientBN4LedgerScope = "all-finite-explicit-ambient-bn4-ledgers-exact-multiset-embedding-balanced-generated-subledger-removal-preserves-remainder-signed-mass-and-candidate-derived-canonical-atom-linkage"
leanResidualTerminalPkgCAmbientBN4ResidualReductionFormalized = true
leanResidualTerminalPkgCAmbientBN4ResidualReductionAxiomAuditPassed = true
leanResidualTerminalPkgCAmbientBN4ResidualReductionScope = "all-finite-explicit-ambient-bn4-ledgers-exact-balanced-subledger-removal-preserves-per-key-and-complete-canonical-executable-residual-ledgers-with-empty-remainder-corollary"
leanResidualTerminalConsumerAntichainNormalFormFormalized = true
leanResidualTerminalConsumerAntichainNormalFormAxiomAuditPassed = true
leanResidualTerminalConsumerAntichainNormalFormScope = "all-finite-minimal-consumer-antichains-monotone-empty-false-nonzero-iff-disjoint-and-pkgc-singletonized-exact-v54-consumer-antichain-cut-indicator"
leanResidualTerminalConstantCutHypergraphRigidityFormalized = true
leanResidualTerminalConstantCutHypergraphRigidityAxiomAuditPassed = true
leanResidualTerminalConstantCutHypergraphRigidityScope = "all-finite-nonnegative-weighted-hypergraphs-constant-cut-hypergraph-rigidity-v53-q2-q3-q4-classification"
leanResidualTerminalBN6HypergraphPacketFormalized = true
leanResidualTerminalBN6HypergraphPacketAxiomAuditPassed = true
leanResidualTerminalBN6HypergraphPacketScope = "all-finite-explicit-grouped-v54-activation-to-v53-grouped-hypergraph-packet-bn6-pair-mixed-triple-fullspan-with-payload-witnesses"
leanResidualTerminalPacketSelectorSeedsFormalized = true
leanResidualTerminalPacketSelectorSeedsAxiomAuditPassed = true
leanResidualTerminalPacketSelectorSeedsScope = "all-finite-explicit-bn6-packet-conclusions-payload-backed-pair-balanced-triple-or-fullspan-selector-seed-input-extraction"
leanResidualTerminalPacketSelectorUniverseFormalized = true
leanResidualTerminalPacketSelectorUniverseAxiomAuditPassed = true
leanResidualTerminalPacketSelectorUniverseScope = "all-finite-explicit-bn6-grouped-families-exact-grouped-footprint-payload-selector-universe-membership"
leanResidualTerminalPacketDescentNoLowerBindingFormalized = true
leanResidualTerminalPacketDescentNoLowerBindingAxiomAuditPassed = true
leanResidualTerminalPacketDescentNoLowerBindingScope = "all-arbitrary-finite-canonical-packet-handles-exhaustive-local-descent-no-lower-row-rejected-under-checked-positive-packet-semantic-HN-budget-HB-selector-silence-and-HB-closure"
leanResidualTerminalPacketNoLowerLedgerFormalized = true
leanResidualTerminalPacketNoLowerLedgerAxiomAuditPassed = true
leanResidualTerminalPacketNoLowerLedgerScope = "all-arbitrary-finite-five-row-Packet-no-lower-ledger-positive-Packet-exclusion-under-computed-semantic-HN-budget-HB-selector-silence-and-HB-closure"
leanResidualTerminalHResolveCoverageLedgerFormalized = true
leanResidualTerminalHResolveCoverageLedgerAxiomAuditPassed = true
leanResidualTerminalHResolveCoverageLedgerScope = "all-arbitrary-finite-supplied-HResolve-candidates-unique-route-ledger-and-NoHereditary-sidecar-excludes-exact-and-gain-under-decidable-supplied-predicates"
leanResidualTerminalHResolveSupportResolverFormalized = true
leanResidualTerminalHResolveSupportResolverAxiomAuditPassed = true
leanResidualTerminalHResolveSupportResolverScope = "all-finite-direct-wire-candidates-terminal-derived-duplicate-free-support-universe-computed-exact-or-gain-with-semantic-minimum-or-strict-equivalent-gain-evidence"
leanResidualTerminalBudgetEnvelopeResolverFormalized = true
leanResidualTerminalBudgetEnvelopeResolverAxiomAuditPassed = true
leanResidualTerminalBudgetEnvelopeResolverScope = "all-finite-direct-wire-candidates-terminal-derived-computed-budget-envelope-exact-gain-or-NoBudget-over-canonical-support-universe"
leanResidualTerminalBudgetNoLowerLedgerFormalized = true
leanResidualTerminalBudgetNoLowerLedgerAxiomAuditPassed = true
leanResidualTerminalBudgetNoLowerLedgerScope = "all-finite-direct-wire-candidates-terminal-derived-budget-feasible-gain-exclusion-over-complete-canonical-support-ledger"
leanResidualTerminalPacketBudgetNoLowerCompositionFormalized = true
leanResidualTerminalPacketBudgetNoLowerCompositionAxiomAuditPassed = true
leanResidualTerminalPacketBudgetNoLowerCompositionScope = "all-finite-direct-wire-candidates-same-candidate-terminal-budget-and-Packet-two-branch-no-lower-gain-and-positive-Packet-exclusion"
leanResidualTerminalHResolveHDisjointFamilyFormalized = true
leanResidualTerminalHResolveHDisjointFamilyAxiomAuditPassed = true
leanResidualTerminalHResolveHDisjointFamilyScope = "all-arbitrary-finite-supplied-eight-domain-hereditary-footprints-deterministic-maximal-H-disjoint-family-with-exact-selected-blocker-routes"
leanResidualTerminalHNBWLCertifiedPathMinimumFormalized = true
leanResidualTerminalHNBWLCertifiedPathMinimumAxiomAuditPassed = true
leanResidualTerminalHNBWLCertifiedPathMinimumScope = "all-nonempty-finite-supplied-four-coordinate-certified-path-families-exact-lexicographic-minimum-with-explicit-governed-family-completeness"
leanResidualTerminalHResolveCertifiedPathFamilyFormalized = true
leanResidualTerminalHResolveCertifiedPathFamilyAxiomAuditPassed = true
leanResidualTerminalHResolveCertifiedPathFamilyScope = "all-duplicate-free-finite-supplied-proof-bearing-hereditary-candidates-maximal-H-disjoint-family-with-exact-certified-path-minima-and-selected-blocker-routes"
leanResidualTerminalHResolveZeroSlackSidecarFormalized = true
leanResidualTerminalHResolveZeroSlackSidecarAxiomAuditPassed = true
leanResidualTerminalHResolveZeroSlackSidecarScope = "all-arbitrary-finite-proof-bearing-HResolve-NoHereditary-sidecars-with-checked-coverage-and-semantic-exact-gain-bindings"
leanResidualTerminalBudgetZeroSlackSidecarFormalized = true
leanResidualTerminalBudgetZeroSlackSidecarAxiomAuditPassed = true
leanResidualTerminalBudgetZeroSlackSidecarScope = "all-finite-direct-wire-candidates-proof-bearing-Budget-NoBudget-sidecars-with-checked-terminal-envelope-exclusion-and-semantic-exact-gain-bindings"
leanResidualTerminalSelectorHBZeroSlackSidecarFormalized = true
leanResidualTerminalSelectorHBZeroSlackSidecarAxiomAuditPassed = true
leanResidualTerminalSelectorHBZeroSlackSidecarScope = "all-arbitrary-finite-proof-bearing-selector-silence-and-HB-closure-sidecars-with-checked-typed-bottom-rows-all-node-inactivity-and-well-founded-dependencies"
leanResidualTerminalPacketBudgetNoLowerZeroSlackSidecarFormalized = true
leanResidualTerminalPacketBudgetNoLowerZeroSlackSidecarAxiomAuditPassed = true
leanResidualTerminalPacketBudgetNoLowerZeroSlackSidecarScope = "all-arbitrary-finite-proof-bearing-same-candidate-Packet-budget-two-branch-no-lower-sidecars-with-semantic-minimum-and-gain-and-positive-Packet-exclusion"
leanResidualTerminalBCELPacketNoLowerZeroSlackSidecarFormalized = true
leanResidualTerminalBCELPacketNoLowerZeroSlackSidecarAxiomAuditPassed = true
leanResidualTerminalBCELPacketNoLowerZeroSlackSidecarScope = "all-arbitrary-finite-proof-bearing-BCEL-constant-activation-to-positive-Packet-contradiction-against-the-same-checked-no-lower-family"
leanResidualTerminalZeroSlackPacketSelectorHBCoherenceFormalized = true
leanResidualTerminalZeroSlackPacketSelectorHBCoherenceAxiomAuditPassed = true
leanResidualTerminalZeroSlackPacketSelectorHBCoherenceScope = "all-arbitrary-finite-proof-bearing-same-family-Selector-HB-Packet-and-BCEL-ZeroSlack-coherence-derived-from-one-accepted-Packet-budget-certificate"
leanSaturatePositiveFormalized = false
leanBCELReadyFormalized = false
leanResidualTerminalProjectionSquareFormalized = true
leanResidualTerminalProjectionPhysicalInvariantFormalized = true
leanResidualTerminalProjectionProfileExactFormalized = true
leanResidualTerminalProjectionMeetJoinCommuteFormalized = true
leanResidualTerminalProjectionPushoutCommuteFormalized = true
leanResidualTerminalProjectionSquareAxiomAuditPassed = true
leanResidualTerminalProjectionSquareScope = "all-finite-direct-wire-candidates-explicit-terminal-dependency-systems-computed-saturated-support-squares-and-forgetful-terminal-projections"
leanResidualTerminalSideTightMinimumArithmeticFormalized = true
leanResidualTerminalSideTightSignedSlackIdentityFormalized = true
leanResidualTerminalSideTightFailClosedGateFormalized = true
leanResidualTerminalSideTightCanonicalFullBasisFormalized = true
leanResidualTerminalSideTightCanonicalQuotientBasisFormalized = true
leanResidualTerminalSideTightMinimumAxiomAuditPassed = true
leanResidualTerminalSideTightMinimumScope = "all-finite-terminal-projection-four-corner-families-and-independently-attained-full-and-quotient-minimum-bases"
leanResidualTerminalFourCornerCarrierTransportFormalized = true
leanResidualTerminalFourCornerCarrierExactEndpointsFormalized = true
leanResidualTerminalFourCornerCarrierInjectiveCoordinatesFormalized = true
leanResidualTerminalFourCornerCarrierProfileTransportFormalized = true
leanResidualTerminalFourCornerCarrierFailClosedPhysicalTransportFormalized = true
leanResidualTerminalFourCornerCarrierAxiomAuditPassed = true
leanResidualTerminalFourCornerCarrierScope = "all-finite-computed-saturated-terminal-support-squares-and-canonical-physical-profile-transport-coordinates"
leanResidualTerminalFourCornerOptimaCarrierCompatibleFormalized = true
leanResidualTerminalFourCornerOptimaFaithfulAmbientizationFormalized = true
leanResidualTerminalFourCornerOptimaReferenceMinimumPreservedFormalized = true
leanResidualTerminalFourCornerOptimaLocalizedMinimaFormalized = true
leanResidualTerminalFourCornerOptimaSharedObserverProjectionFormalized = true
leanResidualTerminalFourCornerOptimaAxiomAuditPassed = true
leanResidualTerminalFourCornerOptimaCarrierScope = "all-finite-computed-saturated-terminal-support-squares-one-reversible-ambient-carrier-and-shared-observer-projection"
leanResidualTerminalFourCornerOptimumCoherenceClassifierFormalized = true
leanResidualTerminalFourCornerOptimumFirstFailureFormalized = true
leanResidualTerminalFourCornerOptimumRetainedSemanticsFormalized = true
leanResidualTerminalFourCornerOptimumProfileTransportFormalized = true
leanResidualTerminalFourCornerOptimumModeFirewallFormalized = true
leanResidualTerminalFourCornerOptimumSideTightTupleFactsFormalized = true
leanResidualTerminalFourCornerOptimumCoherenceAxiomAuditPassed = true
leanResidualTerminalFourCornerOptimumCoherenceScope = "all-finite-computed-terminal-support-squares-observers-projections-and-full-or-quotient-modes-coherent-tuple-or-deterministic-first-failure"
leanResidualTerminalFourCornerOptimumLocalRouteClassifierFormalized = true
leanResidualTerminalFourCornerOptimumRouteSoundnessFormalized = true
leanResidualTerminalFourCornerOptimumRouteSilenceFormalized = true
leanResidualTerminalFourCornerOptimumSideTightCompletionUnderRouteSilenceFormalized = true
leanResidualTerminalFourCornerOptimumExactCompletionValuesFormalized = true
leanResidualTerminalFourCornerOptimumPromotionFirewallRetained = true
leanResidualTerminalFourCornerSideTightCompletionAxiomAuditPassed = true
leanResidualTerminalFourCornerSideTightCompletionScope = "all-finite-computed-terminal-support-squares-observers-and-full-or-quotient-modes-side-tight-coherent-completion-under-exact-local-route-silence"
leanResidualTerminalFourCornerArbitraryFamilyCoherenceFormalized = true
leanResidualTerminalFourCornerExactMinimumFamilyEnumerated = true
leanResidualTerminalFourCornerTightBasisFamilyComplete = true
leanResidualTerminalFourCornerSignedTightBasisMaximumFormalized = true
leanResidualTerminalFourCornerTightBasisMaximumEqualsDeltaFormalized = true
leanResidualTerminalFourCornerTightBasisMaximumAxiomAuditPassed = true
leanResidualTerminalFourCornerTightBasisMaximumScope = "all-finite-computed-terminal-support-squares-observers-and-full-or-quotient-modes-complete-tight-basis-family-and-signed-maximum-under-exact-local-route-silence"
leanResidualTerminalCoherentFourCornerBasisFormalized = true
leanResidualTerminalCoherentFourCornerBasisScope = "conditional-on-exact-mode-appropriate-local-route-silence-not-universal-bn2-square-legitimacy"
leanPCCMinPolynomialRuntimeFormalized = false
leanConcreteCNFSATInPFormalized = false
concretePublicationGate.passed = false
leanWireZeroUnaryClosureFormalized = true
leanWireZeroUnaryClosureAxiomAuditPassed = true
leanWireZeroUnaryClosureAuditedDeclarationCount = 27
leanWireZeroUnaryClosureWholeSelectionTheorem = "PNP.DirectWire.WireZeroUnaryClosure.whole_selected"
leanWireZeroUnaryClosureWholeExteriorTheorem = "PNP.DirectWire.WireZeroUnaryClosure.whole_exterior"
leanWireZeroUnaryClosureWholeGateCountTheorem = "PNP.DirectWire.WireZeroUnaryClosure.whole_gateCount"
leanWireZeroUnaryClosureWholeNotProperTheorem = "PNP.DirectWire.WireZeroUnaryClosure.whole_not_proper"
leanWireZeroUnaryClosureZeroExteriorSelectionTheorem = "PNP.DirectWire.WireZeroUnaryClosure.all_gates_of_zero_exterior"
leanWireZeroUnaryClosureWholeGainCheckedTheorem = "PNP.DirectWire.WireZeroUnaryClosure.WholeGain.checked"
leanWireZeroUnaryClosureWholeRecognitionTheorem = "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_isSome_iff"
leanWireZeroUnaryClosureWholeCompletenessTheorem = "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_complete"
leanWireZeroUnaryClosureGainFullFieldTheorem = "PNP.DirectWire.WireZeroUnaryClosure.Gain.full_field"
leanWireZeroUnaryClosureGainBranchBoundaryTheorem = "PNP.DirectWire.WireZeroUnaryClosure.Gain.branch_boundary"
leanWireZeroUnaryClosureGainExactAccountingTheorem = "PNP.DirectWire.WireZeroUnaryClosure.Gain.exact_accounting"
leanWireZeroUnaryClosureCombinedRecognitionTheorem = "PNP.DirectWire.WireZeroUnaryClosure.nextGain_isSome_iff"
leanWireZeroUnaryClosureCombinedNoResultTheorem = "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_iff"
leanWireZeroUnaryClosureCombinedCompletenessTheorem = "PNP.DirectWire.WireZeroUnaryClosure.nextGain_complete"
leanWireZeroUnaryClosureCombinedNoGainExclusionTheorem = "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_excludes"
leanWireZeroUnaryClosureNormalizationAccountingTheorem = "PNP.DirectWire.WireZeroUnaryClosure.normalization_accounting"
leanWireZeroUnaryClosureNormalizationIterationBoundTheorem = "PNP.DirectWire.WireZeroUnaryClosure.normalization_iterations"
leanWireZeroUnaryClosureTraceCheckedTheorem = "PNP.DirectWire.WireZeroUnaryClosure.Trace.checked"
leanWireZeroUnaryClosureTraceSearchCallBoundTheorem = "PNP.DirectWire.WireZeroUnaryClosure.Trace.searchCalls_le"
leanWireZeroUnaryClosureClosureCheckedTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_checked"
leanWireZeroUnaryClosureStoppedClosureTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_of_stopped"
leanWireZeroUnaryClosureClosureIdempotenceTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_idempotent"
leanWireZeroUnaryClosureScopedTerminalNoGainTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_no_smaller_zeroUnary"
leanWireZeroUnaryClosureReferenceMinimumInvarianceTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_referenceMinimum"
leanWireZeroUnaryClosureResidualSlackAccountingTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_residualSlack"
leanWireZeroUnaryClosureResidualSlackIterationBoundTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_gainIterations_le_residualSlack"
leanWireZeroUnaryClosureResidualSlackSearchCallBoundTheorem = "PNP.DirectWire.WireZeroUnaryClosure.run_searchCalls_le_residualSlack"
leanWireZeroUnaryClosureWholeSpanBranchDerived = true
leanWireZeroUnaryClosureProperAndWholeZeroUnaryCompletenessProved = true
leanWireZeroUnaryClosureActualGainRestartClosureProved = true
leanWireZeroUnaryClosureFullComputationalFieldPreservationProved = true
leanWireZeroUnaryClosureCommonPhysicalAndScopedQuiescenceProved = true
leanWireZeroUnaryClosureExactGateAndResidualSlackAccountingProved = true
leanWireZeroUnaryClosureIdempotenceProved = true
leanWireZeroUnaryClosureCallerSuppliedFamilyRequired = false
leanWireZeroUnaryClosureReferenceMinimumUsedInExecution = false
leanWireZeroUnaryClosureAllBoundaryWidthsCovered = false
leanWireZeroUnaryClosureNoResultProvesGlobalMinimality = false
leanWireZeroUnaryClosureArbitraryObligationDAGsCovered = false
leanWireZeroUnaryClosureFullManuscriptCarrierProved = false
leanWireZeroUnaryClosureCompleteObligationCalculusProved = false
leanWireZeroUnaryClosureCompletePackageEProved = false
leanWireZeroUnaryClosurePolynomialRuntimeProved = false
leanWireZeroUnaryClosureScope = "all-finite-computational-wire-derived-proper-and-whole-zero-or-one-actual-boundary-search-full-field-gain-normalization-restart-closure-common-scoped-quiescence-idempotence-exact-gate-and-residual-slack-accounting-no-global-minimum-or-total-encoded-polynomial-runtime"
leanSourceBoundedPhysicalBoundaryFormalized = true
leanSourceBoundedPhysicalBoundaryAxiomAuditPassed = true
leanSourceBoundedPhysicalBoundaryAuditedDeclarationCount = 23
leanSourceBoundedPhysicalBoundaryUniqueMembershipTheorem = "PNP.DirectWire.SourceListOrder.mem_unique"
leanSourceBoundedPhysicalBoundaryUniqueNoDuplicatesTheorem = "PNP.DirectWire.SourceListOrder.unique_nodup"
leanSourceBoundedPhysicalBoundaryUniqueLengthBoundTheorem = "PNP.DirectWire.SourceListOrder.unique_length_le"
leanSourceBoundedPhysicalBoundaryCanonicalMembershipTheorem = "PNP.DirectWire.SourceListOrder.mem_canonical"
leanSourceBoundedPhysicalBoundaryCanonicalNoDuplicatesTheorem = "PNP.DirectWire.SourceListOrder.canonical_nodup"
leanSourceBoundedPhysicalBoundaryCanonicalLengthBoundTheorem = "PNP.DirectWire.SourceListOrder.canonical_length_le"
leanSourceBoundedPhysicalBoundaryCanonicalOrderTheorem = "PNP.DirectWire.SourceListOrder.canonical_ordered"
leanSourceBoundedPhysicalBoundaryOrderedReferenceUniquenessTheorem = "PNP.DirectWire.SourceListOrder.ordered_eq_of_mem"
leanSourceBoundedPhysicalBoundaryCanonicalReferenceTheorem = "PNP.DirectWire.SourceListOrder.canonical_eq_reference"
leanSourceBoundedPhysicalBoundaryCoordinateInjectivityTheorem = "PNP.DirectWire.TerminalSupportWire.orderCode_injective"
leanSourceBoundedPhysicalBoundaryAmbientReferenceOrderTheorem = "PNP.DirectWire.allTerminalSupportWires_strictOrder"
leanSourceBoundedPhysicalBoundarySourceOccurrenceMembershipTheorem = "PNP.DirectWire.Source.mem_terminalWireOccurrences_iff"
leanSourceBoundedPhysicalBoundarySourceOccurrenceBoundTheorem = "PNP.DirectWire.Source.terminalWireOccurrences_length"
leanSourceBoundedPhysicalBoundaryProgramOccurrenceBoundTheorem = "PNP.DirectWire.terminalSourceWireOccurrences_length"
leanSourceBoundedPhysicalBoundaryCrossingSourceCompletenessTheorem = "PNP.DirectWire.terminalBoundaryWire_mem_sourceOccurrences"
leanSourceBoundedPhysicalBoundarySourceDrivenReferenceTheorem = "PNP.DirectWire.terminalBoundaryPortsSourceDriven_eq_reference"
leanSourceBoundedPhysicalBoundarySourceDrivenLengthBoundTheorem = "PNP.DirectWire.terminalBoundaryPortsSourceDriven_length"
leanSourceBoundedPhysicalBoundarySourceDrivenNoDuplicatesTheorem = "PNP.DirectWire.terminalBoundaryPortsSourceDriven_nodup"
leanSourceBoundedPhysicalBoundarySourceDrivenOrderTheorem = "PNP.DirectWire.terminalBoundaryPortsSourceDriven_ordered"
leanSourceBoundedPhysicalBoundaryActiveReferenceTheorem = "PNP.DirectWire.terminalBoundaryPorts_reference"
leanSourceBoundedPhysicalBoundaryActiveLengthBoundTheorem = "PNP.DirectWire.terminalBoundaryPorts_length"
leanSourceBoundedPhysicalBoundaryActiveNoDuplicatesTheorem = "PNP.DirectWire.terminalBoundaryPorts_nodup"
leanSourceBoundedPhysicalBoundaryActiveOrderTheorem = "PNP.DirectWire.terminalBoundaryPorts_ordered"
leanSourceBoundedPhysicalBoundaryActualGateSourceOccurrencesDerived = true
leanSourceBoundedPhysicalBoundaryExactOrderedReferenceEqualityProved = true
leanSourceBoundedPhysicalBoundaryOccurrenceAndBoundaryLengthBoundsProved = true
leanSourceBoundedPhysicalBoundaryDuplicateFreeCanonicalOrderProved = true
leanSourceBoundedPhysicalBoundaryActiveExtractorUsesSourceOccurrences = true
leanSourceBoundedPhysicalBoundaryExistingPhysicalInterfacesPreserved = true
leanSourceBoundedPhysicalBoundaryUnusedInputEnumerationRequired = false
leanSourceBoundedPhysicalBoundaryCallerSuppliedBoundaryRequired = false
leanSourceBoundedPhysicalBoundaryCallerSuppliedCompletenessRequired = false
leanSourceBoundedPhysicalBoundaryRuntimeExecutionIsProofAuthority = false
leanSourceBoundedPhysicalBoundaryFullManuscriptCarrierProved = false
leanSourceBoundedPhysicalBoundaryCompleteObligationCalculusProved = false
leanSourceBoundedPhysicalBoundaryCompletePackageEProved = false
leanSourceBoundedPhysicalBoundaryGlobalMinimalityProved = false
leanSourceBoundedPhysicalBoundaryPolynomialRuntimeProved = false
leanSourceBoundedPhysicalBoundaryScope = "all-finite-program-dimensions-actual-gate-source-derived-physical-crossings-exact-ordered-ambient-reference-equality-duplicate-free-canonical-order-twice-gate-count-occurrence-and-boundary-bounds-active-extraction-no-unused-input-scan-or-total-encoded-polynomial-runtime"
leanContextAwareSquareTransportFormalized = true
leanContextAwareSquareTransportAxiomAuditPassed = true
leanContextAwareSquareTransportAuditedDeclarationCount = 14
leanContextAwareSquareTransportSelectedGateSemanticsTheorem = "PNP.DirectWire.terminalOpenGateEvaluation_pullback"
leanContextAwareSquareTransportRetainedInterfaceSemanticsTheorem = "PNP.DirectWire.terminalOpenSupportSemantics_pullback"
leanContextAwareSquareTransportIdentityTheorem = "PNP.DirectWire.terminalBoundaryPullback_identity"
leanContextAwareSquareTransportCompositionTheorem = "PNP.DirectWire.terminalBoundaryPullback_compose"
leanContextAwareSquareTransportSquareLegGateInclusionTheorem = "PNP.DirectWire.TerminalOptimumLegTransport.selectedGateTransport"
leanContextAwareSquareTransportLeftPathTheorem = "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_left"
leanContextAwareSquareTransportRightPathTheorem = "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_right"
leanContextAwareSquareTransportSquarePathEqualityTheorem = "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_square"
leanContextAwareSquareTransportExtractedRetainedSemanticsTheorem = "PNP.DirectWire.TerminalOptimumLegTransport.extracted_retained_semantics"
leanContextAwareSquareTransportRealizationRetainedSemanticsTheorem = "PNP.DirectWire.TerminalOptimumLegTransport.realization_retained_semantics"
leanContextAwareSquareTransportFullFamilyRetainedSemanticsTheorem = "PNP.DirectWire.TerminalFourCornerOptimumFamily.full_retained_semantics"
leanContextAwareSquareTransportQuotientFamilyRetainedSemanticsTheorem = "PNP.DirectWire.TerminalFourCornerOptimumFamily.quotient_retained_semantics"
leanContextAwareSquareTransportCanonicalFullRetainedSemanticsTheorem = "PNP.DirectWire.TerminalFourCornerCarrier.canonicalFull_retained_semantics"
leanContextAwareSquareTransportCanonicalQuotientRetainedSemanticsTheorem = "PNP.DirectWire.TerminalFourCornerCarrier.canonicalQuotient_retained_semantics"
leanContextAwareSquareTransportComputedBoundaryPullbackDerived = true
leanContextAwareSquareTransportArbitraryOpenValuationsCovered = true
leanContextAwareSquareTransportInternalizedWireValuesComputed = true
leanContextAwareSquareTransportSelectedGateAndInterfaceSemanticsProved = true
leanContextAwareSquareTransportIdentityAndCompositionProved = true
leanContextAwareSquareTransportSquareLegMapsDerived = true
leanContextAwareSquareTransportTwoPathValuationEqualityProved = true
leanContextAwareSquareTransportRetainedRealizerOutputsProved = true
leanContextAwareSquareTransportCanonicalFullAndQuotientComparisonProved = true
leanContextAwareSquareTransportExistingAmbientClassifierPreserved = true
leanContextAwareSquareTransportCallerSuppliedTransportRequired = false
leanContextAwareSquareTransportCallerSuppliedCorrectnessRequired = false
leanContextAwareSquareTransportWholeCircuitValuationsOnly = false
leanContextAwareSquareTransportArbitraryObserverEqualityProved = false
leanContextAwareSquareTransportPhysicalMinimumGluingProved = false
leanContextAwareSquareTransportChargeAndObligationOwnershipProved = false
leanContextAwareSquareTransportFullManuscriptCarrierProved = false
leanContextAwareSquareTransportCompleteObligationCalculusProved = false
leanContextAwareSquareTransportCompletePackageEProved = false
leanContextAwareSquareTransportGlobalRouteCoverageProved = false
leanContextAwareSquareTransportUnconditionalZeroSlackProved = false
leanContextAwareSquareTransportExactGeneralPCCMinProved = false
leanContextAwareSquareTransportPolynomialRuntimeProved = false
leanContextAwareSquareTransportRuntimeExecutionIsProofAuthority = false
leanContextAwareSquareTransportScope = "arbitrary-finite-nested-supports-all-open-boundary-valuations-computed-internalized-wire-substitution-selected-gate-and-interface-preservation-identity-composition-four-corner-path-equality-retained-full-and-quotient-realizer-outputs-no-arbitrary-observer-equality-or-charge-gluing-or-global-runtime"
leanWireCausalExpansionFormalized = true
leanWireCausalExpansionAxiomAuditPassed = true
leanWireCausalExpansionAuditedDeclarationCount = 29
leanWireCausalExpansionRankDecreaseTheorem = "PNP.DirectWire.WireCausalExpansion.graph_rank_decreases"
leanWireCausalExpansionGraphWellFoundedTheorem = "PNP.DirectWire.WireCausalExpansion.graph_wellFounded"
leanWireCausalExpansionCompileSuccessTheorem = "PNP.DirectWire.WireCausalExpansion.compile_success"
leanWireCausalExpansionCompiledResultTheorem = "PNP.DirectWire.WireCausalExpansion.compiled_spec"
leanWireCausalExpansionPhysicalGateCountTheorem = "PNP.DirectWire.WireCausalExpansion.expanded_gateCount"
leanWireCausalExpansionAllOpenMaskedOutputTheorem = "PNP.DirectWire.WireCausalExpansion.masked_replacement_output"
leanWireCausalExpansionReplacementSourceValueTheorem = "PNP.DirectWire.WireCausalExpansion.replacementSource_eval"
leanWireCausalExpansionOriginalSourceValueTheorem = "PNP.DirectWire.WireCausalExpansion.originalSource_eval"
leanWireCausalExpansionGraphSolutionTheorem = "PNP.DirectWire.WireCausalExpansion.values_solution"
leanWireCausalExpansionOrderedOutputSemanticsTheorem = "PNP.DirectWire.WireCausalExpansion.expanded_semantics"
leanWireCausalExpansionPaidSavingIffTheorem = "PNP.DirectWire.WireCausalExpansion.expanded_smaller_iff"
leanWireCausalExpansionSingleInterfaceSavingTheorem = "PNP.DirectWire.WireCausalExpansion.single_interface_smaller"
leanWireCausalExpansionInterfaceNoDuplicatesTheorem = "PNP.DirectWire.WireCausalExpansion.interface_nodup"
leanWireCausalExpansionPhysicalProducerIdentityTheorem = "PNP.DirectWire.WireCausalExpansion.interface_owner_injective"
leanWireCausalExpansionExteriorOwnershipTheorem = "PNP.DirectWire.WireCausalExpansion.exteriorPosition_injective"
leanWireCausalExpansionCopyOwnershipTheorem = "PNP.DirectWire.WireCausalExpansion.copyPosition_injective"
leanWireCausalExpansionDisjointOwnershipTheorem = "PNP.DirectWire.WireCausalExpansion.exteriorPosition_ne_copyPosition"
leanWireCausalExpansionRawOwnershipCoverageTheorem = "PNP.DirectWire.WireCausalExpansion.raw_node_ownership"
leanWireCausalExpansionEmittedOwnershipCoverageTheorem = "PNP.DirectWire.WireCausalExpansion.expanded_gate_ownership"
leanWireCausalExpansionActualOutputSourceTheorem = "PNP.DirectWire.WireCausalExpansion.expanded_source"
leanWireCausalExpansionLiteralOutputSharingTheorem = "PNP.DirectWire.WireCausalExpansion.expanded_source_equal"
leanWireCausalExpansionCarrierOutputTheorem = "PNP.DirectWire.WireCausalExpansion.expandedCarrier_output"
leanWireCausalExpansionCarrierFieldTheorem = "PNP.DirectWire.WireCausalExpansion.expandedCarrier_field"
leanWireCausalExpansionCarrierPhysicalGateCountTheorem = "PNP.DirectWire.WireCausalExpansion.expandedCarrier_gateCount"
leanWireCausalExpansionCarrierPaidSavingIffTheorem = "PNP.DirectWire.WireCausalExpansion.expandedCarrier_smaller_iff"
leanWireCausalExpansionProperAndPaidSavingTheorem = "PNP.DirectWire.WireCausalExpansion.expandedCarrier_proper_and_smaller"
leanWireCausalExpansionLiteralFieldSharingTheorem = "PNP.DirectWire.WireCausalExpansion.expandedCarrier_source_equal"
leanWireCausalExpansionR5CoordinateTheorem = "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_coordinate"
leanWireCausalExpansionR5OriginalFullSourceTheorem = "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_fullWitness"
leanWireCausalExpansionArbitrarySupportAndBoundaryWidthsCovered = true
leanWireCausalExpansionSourceDerivedRankProved = true
leanWireCausalExpansionUnconditionalCompilationProved = true
leanWireCausalExpansionCompleteOpenMaskSemanticsProved = true
leanWireCausalExpansionEveryOrderedOutputPreservedUnderFullAgreement = true
leanWireCausalExpansionEveryComputationalFieldPreservedUnderFullAgreement = true
leanWireCausalExpansionUniquePhysicalCopyOwnershipProved = true
leanWireCausalExpansionEveryEmittedGateOwned = true
leanWireCausalExpansionLiteralRepeatedSourceSharingProved = true
leanWireCausalExpansionOriginalR5CoordinateAndFullValueTransportProved = true
leanWireCausalExpansionExactExteriorPlusCopiesGateCountProved = true
leanWireCausalExpansionPaidSavingIffProved = true
leanWireCausalExpansionPropernessSeparate = true
leanWireCausalExpansionExistingLiteralCompilerPreserved = true
leanWireCausalExpansionCallerSuppliedRankRequired = false
leanWireCausalExpansionCallerSuppliedCompilerSuccessRequired = false
leanWireCausalExpansionCallerSuppliedFinalSemanticsRequired = false
leanWireCausalExpansionSemanticsWithoutLocalAgreementProved = false
leanWireCausalExpansionWholeCircuitValuationsOnly = false
leanWireCausalExpansionQuotientOnlyFieldAgreementSufficient = false
leanWireCausalExpansionUnpaidLocalSavingTransportProved = false
leanWireCausalExpansionMatchedKappaPullExpandProved = false
leanWireCausalExpansionArbitraryObserverEqualityProved = false
leanWireCausalExpansionFullManuscriptCarrierProved = false
leanWireCausalExpansionCompleteObligationCalculusProved = false
leanWireCausalExpansionCompletePackageEProved = false
leanWireCausalExpansionGlobalRouteCoverageProved = false
leanWireCausalExpansionUnconditionalSaturatePositiveProved = false
leanWireCausalExpansionUnconditionalBCELReadyProved = false
leanWireCausalExpansionUnconditionalZeroSlackProved = false
leanWireCausalExpansionExactGeneralPCCMinProved = false
leanWireCausalExpansionPolynomialRuntimeProved = false
leanWireCausalExpansionRuntimeExecutionIsProofAuthority = false
leanWireCausalExpansionScope = "arbitrary-finite-computational-supports-and-boundary-widths-source-derived-rank-total-causal-physical-expansion-all-open-mask-semantics-under-full-local-agreement-all-outputs-and-full-fields-exact-exterior-plus-producer-copies-unique-complete-ownership-literal-sharing-original-R5-source-transport-paid-saving-iff-no-matched-kappa-global-route-or-polynomial-runtime"
leanWireObligationHistoryFormalized = true
leanWireObligationHistoryAxiomAuditPassed = true
leanWireObligationHistoryAuditedDeclarationCount = 46
leanWireObligationHistoryDependencySchedulerSuccessIffTheorem = "PNP.DependencyScheduler.compile_success_iff"
leanWireObligationHistoryDependencySchedulerFailureIffTheorem = "PNP.DependencyScheduler.compile_failure_iff"
leanWireObligationHistoryRawOrderSuccessIffTheorem = "PNP.DirectWire.WireObligationHistory.orderEvents_success_iff"
leanWireObligationHistoryRawOrderFailureIffTheorem = "PNP.DirectWire.WireObligationHistory.orderEvents_failure_iff"
leanWireObligationHistoryCreationSourceSnapshotTheorem = "PNP.DirectWire.WireObligationHistory.State.create_source_snapshot"
leanWireObligationHistoryActualRestorationChargeTheorem = "PNP.DirectWire.WireObligationHistory.State.restore_gate_charge"
leanWireObligationHistoryNormalizationBalanceTheorem = "PNP.DirectWire.WireObligationHistory.State.normalize_gate_balance"
leanWireObligationHistoryMatchedDischargeBindingTheorem = "PNP.DirectWire.WireObligationHistory.Transition.dischargeRecord_binding"
leanWireObligationHistoryCreationLifecycleTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle"
leanWireObligationHistoryDependencyOrderTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before"
leanWireObligationHistoryExactlyOnceCountTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_count"
leanWireObligationHistoryUniqueEventIdentitiesTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_identities_nodup"
leanWireObligationHistoryFullFieldTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field"
leanWireObligationHistoryOrdinaryOutputTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output"
leanWireObligationHistoryPhysicalGateBalanceTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance"
leanWireObligationHistoryArbitraryFiniteEventGraphsCovered = true
leanWireObligationHistoryDuplicateAndMissingReferencesRejected = true
leanWireObligationHistoryIntrinsicCreationDependenciesComputed = true
leanWireObligationHistoryCyclicGraphsRejected = true
leanWireObligationHistoryActualEvolvingCarrierExecuted = true
leanWireObligationHistorySourceBoundCreationAndDischargeRecords = true
leanWireObligationHistoryCreationClosesStrictlyLater = true
leanWireObligationHistoryPhysicalNormalizationPreservesOpenSnapshots = true
leanWireObligationHistoryFullReadsRequireClosedField = true
leanWireObligationHistoryFinalOpenObligationsRejected = true
leanWireObligationHistoryComputedSourceIdentityR6 = true
leanWireObligationHistoryActualCapturedMaterializerR8 = true
leanWireObligationHistoryCompleteAppendedMaterializersCharged = true
leanWireObligationHistoryNoFreeCrossSnapshotSharing = true
leanWireObligationHistoryAllValuationFullOutputAndFieldPreservation = true
leanWireObligationHistoryCallerSuppliedOrderRequired = false
leanWireObligationHistoryCallerSuppliedRankRequired = false
leanWireObligationHistoryCallerSuppliedStateRequired = false
leanWireObligationHistoryCallerSuppliedFullWitnessRequired = false
leanWireObligationHistoryCallerSuppliedChargesRequired = false
leanWireObligationHistoryAcyclicityImpliesValidLifecycle = false
leanWireObligationHistoryConfluenceOfUnderspecifiedEventGraphsProved = false
leanWireObligationHistoryQuotientAgreementClosesObligation = false
leanWireObligationHistoryR5ProjectionRemovesPhysicalGates = false
leanWireObligationHistoryFullR7SemanticsProved = false
leanWireObligationHistoryAllManuscriptRewriteFamiliesProved = false
leanWireObligationHistoryAllManuscriptNormalizationFamiliesProved = false
leanWireObligationHistoryArbitraryObserverOrProfileTransportProved = false
leanWireObligationHistoryMatchedKappaPullExpandProved = false
leanWireObligationHistoryFullManuscriptCarrierProved = false
leanWireObligationHistoryCompletePackageEProved = false
leanWireObligationHistoryGlobalRouteCoverageProved = false
leanWireObligationHistoryUnconditionalSaturatePositiveProved = false
leanWireObligationHistoryUnconditionalBCELReadyProved = false
leanWireObligationHistoryUnconditionalZeroSlackProved = false
leanWireObligationHistoryExactGeneralPCCMinProved = false
leanWireObligationHistoryPolynomialRuntimeProved = false
leanWireObligationHistoryRuntimeExecutionIsProofAuthority = false
leanWireObligationHistoryScope = "arbitrary-finite-raw-event-graphs-computed-order-actual-evolving-carriers-source-bound-R5-R6-R8-full-read-records-strictly-later-matched-discharge-all-full-outputs-and-fields-exact-charged-materializer-and-normalization-gate-balance-no-complete-package-E-global-route-or-polynomial-runtime"
leanWireHistoryArbitrarySupportFormalized = true
leanWireHistoryArbitrarySupportAxiomAuditPassed = true
leanWireHistoryArbitrarySupportAuditedDeclarationCount = 24
leanWireHistoryArbitrarySupportExtractionCausalLevelsTheorem = "PNP.DirectWire.extractTerminalSupport_causal_levels"
leanWireHistoryArbitrarySupportExtractionCausalIndexTheorem = "PNP.DirectWire.extractTerminalSupport_causal_index"
leanWireHistoryArbitrarySupportPhysicalNormalizationCausalBoundTheorem = "PNP.DirectWire.CausalBound.physical_normalization_output_bound"
leanWireHistoryArbitrarySupportCapturedRestorationCausalBoundTheorem = "PNP.DirectWire.WireObligationRestoration.join_causalBounds"
leanWireHistoryArbitrarySupportClosedHistoryCausalInvariantTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant"
leanWireHistoryArbitrarySupportClosedHistoryFieldCausalBoundTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound"
leanWireHistoryArbitrarySupportLiteralGraphRankDecreaseTheorem = "PNP.DirectWire.ArbitrarySupportSplice.graph_causal_rank_decreases"
leanWireHistoryArbitrarySupportLiteralGraphWellFoundedTheorem = "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_causalInterfaceBound"
leanWireHistoryArbitrarySupportClosedHistoryEquivalentTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_equivalent"
leanWireHistoryArbitrarySupportDerivedInterfaceBoundTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_causalInterfaceBound"
leanWireHistoryArbitrarySupportClosedHistoryCompilationTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles"
leanWireHistoryArbitrarySupportOrderedOutputSemanticsTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics"
leanWireHistoryArbitrarySupportCompletePhysicalAccountingTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting"
leanWireHistoryArbitrarySupportStrictGainTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain"
leanWireHistoryArbitrarySupportRawConstructorCompleteTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete"
leanWireHistoryArbitrarySupportRawConstructorSoundTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound"
leanWireHistoryArbitrarySupportNoAdditionalRejectionTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff"
leanWireHistoryArbitrarySupportArbitraryFiniteCandidateSupportAndEventDimensionsCovered = true
leanWireHistoryArbitrarySupportZeroDuplicateOrdinaryOutputsInExtractedCarrier = true
leanWireHistoryArbitrarySupportCurrentAndPendingSnapshotCausalBoundsDerived = true
leanWireHistoryArbitrarySupportActualPhysicalNormalizerAndCapturedMaterializerUsed = true
leanWireHistoryArbitrarySupportSourceIdentityCancellationPreserved = true
leanWireHistoryArbitrarySupportLiteralOneCopySpliceAfterEveryAcceptedClosedHistory = true
leanWireHistoryArbitrarySupportEveryOrderedOriginalOutputPreserved = true
leanWireHistoryArbitrarySupportCompleteMaterializerChargesIncluded = true
leanWireHistoryArbitrarySupportStrictGainRequiresRemovalsExceedCharges = true
leanWireHistoryArbitrarySupportSpliceStageAddsNoRejection = true
leanWireHistoryArbitrarySupportCallerSuppliedReplacementRequired = false
leanWireHistoryArbitrarySupportCallerSuppliedRankOrOrderRequired = false
leanWireHistoryArbitrarySupportCallerSuppliedSemanticCertificateRequired = false
leanWireHistoryArbitrarySupportBooleanEquivalenceAloneEnsuresAcyclicity = false
leanWireHistoryArbitrarySupportSupportRecordsAndRawEventsDerivedFromEveryInput = false
leanWireHistoryArbitrarySupportFullR7SemanticsProved = false
leanWireHistoryArbitrarySupportAllManuscriptRewriteAndNormalizationFamiliesProved = false
leanWireHistoryArbitrarySupportArbitraryObserverOrFullProfileTransportProved = false
leanWireHistoryArbitrarySupportMatchedKappaPullExpandProved = false
leanWireHistoryArbitrarySupportFullManuscriptCarrierProved = false
leanWireHistoryArbitrarySupportCompletePackageEProved = false
leanWireHistoryArbitrarySupportTerminalFamiliesDerived = false
leanWireHistoryArbitrarySupportGloballySuccessfulRewriteStrategyDerived = false
leanWireHistoryArbitrarySupportGlobalRouteCoverageProved = false
leanWireHistoryArbitrarySupportUnconditionalSaturatePositiveProved = false
leanWireHistoryArbitrarySupportUnconditionalBCELReadyProved = false
leanWireHistoryArbitrarySupportUnconditionalZeroSlackProved = false
leanWireHistoryArbitrarySupportExactGeneralPCCMinProved = false
leanWireHistoryArbitrarySupportPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanWireHistoryArbitrarySupportRuntimeExecutionIsProofAuthority = false
leanWireHistoryArbitrarySupportScope = "arbitrary-finite-source-extraction-closed-R5-R6-R8-history-derived-current-and-snapshot-causality-literal-one-copy-splice-all-ordered-outputs-complete-removal-charge-equation-no-additional-rejection-no-derived-terminal-family-global-route-or-polynomial-runtime"
leanComputedR7HistoryFormalized = true
leanComputedR7HistoryAxiomAuditPassed = true
leanComputedR7HistoryAuditedDeclarationCount = 41
leanComputedR7HistoryActualCompilerDependencyBoundTheorem = "PNP.DirectWire.RawNandCausalBound.compile_bounds"
leanComputedR7HistoryWholeCarrierDependencyBoundTheorem = "PNP.DirectWire.WireUnaryCausalBound.expanded_causalBounds"
leanComputedR7HistoryRawRecordRoundTripTheorem = "PNP.DirectWire.WireObligationHistory.decodeRecord_encode"
leanComputedR7HistoryRawRecordSourceTheorem = "PNP.DirectWire.WireObligationHistory.decodeRecord_source"
leanComputedR7HistoryRawListRoundTripTheorem = "PNP.DirectWire.WireObligationHistory.decodeRecords_encode"
leanComputedR7HistoryRawListSourceTheorem = "PNP.DirectWire.WireObligationHistory.decodeRecords_source"
leanComputedR7HistoryRecognitionIffTheorem = "PNP.DirectWire.WireObligationHistory.computeR7_isSome_iff"
leanComputedR7HistoryCapturedFullValueTheorem = "PNP.DirectWire.WireObligationHistory.State.restoreR7_full_value"
leanComputedR7HistoryActualMaterializerChargeTheorem = "PNP.DirectWire.WireObligationHistory.State.restoreR7_gate_charge"
leanComputedR7HistoryOtherPendingSnapshotsTheorem = "PNP.DirectWire.WireObligationHistory.State.restoreR7_other_pending"
leanComputedR7HistoryTransitionCausalInvariantTheorem = "PNP.DirectWire.WireObligationHistory.State.restoreR7_causalInvariant"
leanComputedR7HistorySourceCreationLifecycleTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle"
leanComputedR7HistoryClosedHistoryCompilationTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles"
leanComputedR7HistoryCompletePhysicalAccountingTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting"
leanComputedR7HistoryNoAdditionalRejectionTheorem = "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff"
leanComputedR7HistoryArbitraryFiniteCarrierSupportAndEventDimensionsCovered = true
leanComputedR7HistoryWholeListCoordinatesPreserved = true
leanComputedR7HistoryExactZeroUnaryRecognitionDerived = true
leanComputedR7HistoryCapturedCreationIdentityRequired = true
leanComputedR7HistoryActualComputedReplacementAndMaterializerUsed = true
leanComputedR7HistoryCurrentAndPendingSnapshotCausalBoundsDerived = true
leanComputedR7HistoryCompleteMaterializerChargesIncluded = true
leanComputedR7HistoryLiteralOneCopySpliceAddsNoRejection = true
leanComputedR7HistoryCallerSuppliedReplacementRequired = false
leanComputedR7HistoryCallerSuppliedTruthTableRequired = false
leanComputedR7HistoryCallerSuppliedRankOrOrderRequired = false
leanComputedR7HistoryCallerSuppliedSemanticCertificateRequired = false
leanComputedR7HistoryBooleanEquivalenceAloneBoundsDependencies = false
leanComputedR7HistorySupportRecordsAndRawEventsDerivedFromEveryInput = false
leanComputedR7HistoryFullManuscriptR7SemanticsProved = false
leanComputedR7HistoryAllManuscriptRewriteAndNormalizationFamiliesProved = false
leanComputedR7HistoryArbitraryObserverOrFullProfileTransportProved = false
leanComputedR7HistoryCompletePackageEProved = false
leanComputedR7HistoryTerminalFamiliesDerived = false
leanComputedR7HistoryGloballySuccessfulRewriteStrategyDerived = false
leanComputedR7HistoryGlobalRouteCoverageProved = false
leanComputedR7HistoryUnconditionalSaturatePositiveProved = false
leanComputedR7HistoryUnconditionalBCELReadyProved = false
leanComputedR7HistoryUnconditionalZeroSlackProved = false
leanComputedR7HistoryExactGeneralPCCMinProved = false
leanComputedR7HistoryPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanComputedR7HistoryRuntimeExecutionIsProofAuthority = false
leanComputedR7HistoryScope = "arbitrary-finite-computational-carriers-raw-record-lists-exact-zero-unary-recognition-source-derived-R7-captured-creation-full-discharge-actual-materializer-charges-derived-causality-closed-R5-R6-R7-R8-histories-literal-one-copy-splice-no-new-rejection-no-derived-global-strategy-or-complete-manuscript-calculus-or-polynomial-runtime"
leanSourceDerivedHistoryOwnershipFormalized = true
leanSourceDerivedHistoryOwnershipAxiomAuditPassed = true
leanSourceDerivedHistoryOwnershipAuditedDeclarationCount = 78
leanSourceDerivedHistoryOwnershipTerminalExtractionPhysicalOriginTheorem = "PNP.DirectWire.terminalExtractionOrigin_gateIndex"
leanSourceDerivedHistoryOwnershipNormalizationPhysicalPartitionTheorem = "PNP.DirectWire.PhysicalGateProvenance.normalized_partition"
leanSourceDerivedHistoryOwnershipClosedHistoryPhysicalOwnershipTheorem = "PNP.DirectWire.WireObligationHistory.ClosedHistory.physical_ownership"
leanSourceDerivedHistoryOwnershipCompilerPhysicalOriginInverseTheorem = "PNP.DirectWire.CompiledRawNandGraph.position_physicalOrigin"
leanSourceDerivedHistoryOwnershipCompilerPhysicalOriginPermutationTheorem = "PNP.DirectWire.CompiledRawNandGraph.physicalOrigins_perm"
leanSourceDerivedHistoryOwnershipAmbientOriginalCoordinatePartitionTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.original_coordinate_partition"
leanSourceDerivedHistoryOwnershipAmbientPhysicalOwnershipTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.physical_ownership"
leanSourceDerivedHistoryOwnershipSourceOnlyConstructorProjectionTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.compileOwned_result"
leanSourceDerivedHistoryOwnershipSourceOnlyConstructorSemanticsTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.semantics"
leanSourceDerivedHistoryOwnershipDerivedEventRequestsDisjointTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventRequests_disjoint"
leanSourceDerivedHistoryOwnershipActualRawEventOwnershipTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_some_iff"
leanSourceDerivedHistoryOwnershipFixedRemainderTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_none_iff"
leanSourceDerivedHistoryOwnershipHistoricalChargeCompletenessTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.charged_origin"
leanSourceDerivedHistoryOwnershipSurvivingAllocationCompletenessTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.live_allocated_event"
leanSourceDerivedHistoryOwnershipSupportRestrictionTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.support_restrict"
leanSourceDerivedHistoryOwnershipActualExtractedGateCountTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_gateCount"
leanSourceDerivedHistoryOwnershipActualChargeIdentityTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_chargeIdentity"
leanSourceDerivedHistoryOwnershipWholeChargeTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_wholeCharge"
leanSourceDerivedHistoryOwnershipIndependentOpenSemanticsTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_semantics"
leanSourceDerivedHistoryOwnershipInducedBoundaryTheorem = "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_induced"
leanSourceDerivedHistoryOwnershipArbitraryFiniteCarrierSupportAndEventDimensionsCovered = true
leanSourceDerivedHistoryOwnershipLiteralNormalizerRetainedOriginsDerived = true
leanSourceDerivedHistoryOwnershipRemovedOriginsAreExactComplement = true
leanSourceDerivedHistoryOwnershipExecutingEventAndLocalGateAllocationLabelsDerived = true
leanSourceDerivedHistoryOwnershipHistoricalChargesSurviveLaterRemoval = true
leanSourceDerivedHistoryOwnershipActualTopologicalCompilerPositionsUsed = true
leanSourceDerivedHistoryOwnershipExteriorPhysicalGatesRetainedExactlyOnce = true
leanSourceDerivedHistoryOwnershipDerivedEventRequestsDisjoint = true
leanSourceDerivedHistoryOwnershipSupportRestrictionPreservesOwners = true
leanSourceDerivedHistoryOwnershipExistingConstructorAcceptanceAndResultPreserved = true
leanSourceDerivedHistoryOwnershipCallerSuppliedOwnerFamilyRequired = false
leanSourceDerivedHistoryOwnershipCallerSuppliedProvenanceOrPartitionRequired = false
leanSourceDerivedHistoryOwnershipCallerSuppliedChargeOrTopologicalOrderRequired = false
leanSourceDerivedHistoryOwnershipCallerSuppliedSuccessfulSpliceCertificateRequired = false
leanSourceDerivedHistoryOwnershipArbitraryCountPreservingPermutationIsProvenance = false
leanSourceDerivedHistoryOwnershipHistoricalChargesEqualSurvivingOwnedSize = false
leanSourceDerivedHistoryOwnershipSupportRecordsAndRawEventsDerivedFromEveryInput = false
leanSourceDerivedHistoryOwnershipCompleteManuscriptCarrierAndRewriteCalculusProved = false
leanSourceDerivedHistoryOwnershipArbitraryObserverOrFullProfileTransportProved = false
leanSourceDerivedHistoryOwnershipMatchedKappaArbitrarySupportPullExpandProved = false
leanSourceDerivedHistoryOwnershipCompletePackageEProved = false
leanSourceDerivedHistoryOwnershipTerminalFamiliesDerived = false
leanSourceDerivedHistoryOwnershipGloballySuccessfulRewriteStrategyDerived = false
leanSourceDerivedHistoryOwnershipGlobalRouteCoverageProved = false
leanSourceDerivedHistoryOwnershipUnconditionalSaturatePositiveProved = false
leanSourceDerivedHistoryOwnershipUnconditionalBCELReadyProved = false
leanSourceDerivedHistoryOwnershipUnconditionalZeroSlackProved = false
leanSourceDerivedHistoryOwnershipExactGeneralPCCMinProved = false
leanSourceDerivedHistoryOwnershipPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanSourceDerivedHistoryOwnershipRuntimeExecutionIsProofAuthority = false
leanSourceDerivedHistoryOwnershipScope = "arbitrary-finite-computational-histories-source-derived-literal-normalization-origins-executing-event-local-allocation-labels-live-removed-charged-nodup-partition-actual-topological-splice-positions-one-copy-exterior-disjoint-derived-requests-support-stable-extracted-charges-no-supplied-owner-or-partition-no-global-strategy-or-complete-manuscript-calculus-or-polynomial-runtime"
leanDescendantHistoryOwnershipFormalized = true
leanDescendantHistoryOwnershipAxiomAuditPassed = true
leanDescendantHistoryOwnershipAuditedDeclarationCount = 84
leanDescendantHistoryOwnershipRawRecordRoundTripTheorem = "PNP.DirectWire.WireDescendantHistory.decodeRecords_encode"
leanDescendantHistoryOwnershipRawRecordSourceTheorem = "PNP.DirectWire.WireDescendantHistory.decodeRecords_source"
leanDescendantHistoryOwnershipRawEventRoundTripTheorem = "PNP.DirectWire.WireDescendantHistory.decodeEvents_encode"
leanDescendantHistoryOwnershipRawEventSourceTheorem = "PNP.DirectWire.WireDescendantHistory.decodeEvents_source"
leanDescendantHistoryOwnershipActualStageResultTheorem = "PNP.DirectWire.WireDescendantHistory.StageCompilation.existing_result"
leanDescendantHistoryOwnershipLiteralPhysicalPositionTheorem = "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_physicalOrigin_position"
leanDescendantHistoryOwnershipOriginalCoordinateLiftTheorem = "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_original"
leanDescendantHistoryOwnershipAllocatedCoordinateLiftTheorem = "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_allocated"
leanDescendantHistoryOwnershipPhysicalOwnershipTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.physical_ownership"
leanDescendantHistoryOwnershipPhysicalOriginInjectiveTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_origin_injective"
leanDescendantHistoryOwnershipCompleteProgramSemanticsTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.semantics"
leanDescendantHistoryOwnershipActualExecutionSizeBalanceTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.gate_balance"
leanDescendantHistoryOwnershipHistoricalChargePersistenceTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charge_survives"
leanDescendantHistoryOwnershipInvalidLaterStagePropagationTheorem = "PNP.DirectWire.WireDescendantHistory.compile_tail_none"
leanDescendantHistoryOwnershipRawEventKeyDistinctnessTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.inputEventKeys_nodup"
leanDescendantHistoryOwnershipHistoricalChargeRawEventTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_charged_origin"
leanDescendantHistoryOwnershipSurvivingAllocationRawEventTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_live_allocated_event"
leanDescendantHistoryOwnershipDerivedEventRequestsDisjointTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventRequests_disjoint"
leanDescendantHistoryOwnershipActualRawEventOwnershipTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_some_iff"
leanDescendantHistoryOwnershipFixedOriginalRemainderTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_none_iff"
leanDescendantHistoryOwnershipSupportRestrictionTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.support_restrict"
leanDescendantHistoryOwnershipExtractedGateCountTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_gateCount"
leanDescendantHistoryOwnershipExtractedChargeIdentityTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_chargeIdentity"
leanDescendantHistoryOwnershipWholeSurvivingChargeTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_wholeCharge"
leanDescendantHistoryOwnershipOpenPieceSemanticsTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_semantics"
leanDescendantHistoryOwnershipInducedPieceBoundaryTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_induced"
leanDescendantHistoryOwnershipFinalNetGainTheorem = "PNP.DirectWire.WireDescendantHistory.GainResult.strictGain"
leanDescendantHistoryOwnershipFinalResidualDescentTheorem = "PNP.DirectWire.WireDescendantHistory.GainResult.strictResidualDescent"
leanDescendantHistoryOwnershipFinalGainAcceptanceIffTheorem = "PNP.DirectWire.WireDescendantHistory.compileGain_exists_iff"
leanDescendantHistoryOwnershipArbitraryFiniteDimensionsAndStageListsCovered = true
leanDescendantHistoryOwnershipCurrentDescendantCoordinatesDecodedFromRawInput = true
leanDescendantHistoryOwnershipActualLiteralCompilerPositionsCompose = true
leanDescendantHistoryOwnershipStageEventAndLocalAllocationIdentitiesDerived = true
leanDescendantHistoryOwnershipHistoricalChargesSurviveLaterRemoval = true
leanDescendantHistoryOwnershipActualExecutionTotalsMatchPersistentLedger = true
leanDescendantHistoryOwnershipLiveRemovedPartitionHasNoDuplicateIdentities = true
leanDescendantHistoryOwnershipReusedLocalEventNumbersRemainStageDistinct = true
leanDescendantHistoryOwnershipAllAllocationsTraceToActualInputEvents = true
leanDescendantHistoryOwnershipDerivedEventRequestsDisjoint = true
leanDescendantHistoryOwnershipSupportRestrictionPreservesOwners = true
leanDescendantHistoryOwnershipMalformedLaterStageRejectsCompleteProgram = true
leanDescendantHistoryOwnershipFinalNetGainAllowsIntermediateExpansion = true
leanDescendantHistoryOwnershipExistingClosedLocalHistoryLanguagePreserved = true
leanDescendantHistoryOwnershipCallerSuppliedIntermediateImplementationsRequired = false
leanDescendantHistoryOwnershipCallerSuppliedOwnerFamilyRequired = false
leanDescendantHistoryOwnershipCallerSuppliedProvenanceOrPartitionRequired = false
leanDescendantHistoryOwnershipCallerSuppliedChargeOrRankRequired = false
leanDescendantHistoryOwnershipCallerSuppliedSuccessfulHistoryCertificateRequired = false
leanDescendantHistoryOwnershipSemanticOracleUsedByFinalGainAdapter = false
leanDescendantHistoryOwnershipHistoricalChargesEqualSurvivingOwnedSize = false
leanDescendantHistoryOwnershipEachIntermediateStageMustStrictlyDecrease = false
leanDescendantHistoryOwnershipAcceptedPrefixReturnedAfterLaterRejection = false
leanDescendantHistoryOwnershipRawStagesDerivedFromEveryInput = false
leanDescendantHistoryOwnershipOpenObligationsTransportedAcrossSupports = false
leanDescendantHistoryOwnershipCompleteManuscriptCarrierAndRewriteCalculusProved = false
leanDescendantHistoryOwnershipMatchedKappaArbitrarySupportPullExpandProved = false
leanDescendantHistoryOwnershipProperSupportVerifyDWProved = false
leanDescendantHistoryOwnershipCompleteChargeSoundnessProved = false
leanDescendantHistoryOwnershipCompletePackageEProved = false
leanDescendantHistoryOwnershipTerminalFamiliesDerived = false
leanDescendantHistoryOwnershipGloballySuccessfulRewriteStrategyDerived = false
leanDescendantHistoryOwnershipGlobalRouteCoverageProved = false
leanDescendantHistoryOwnershipUnconditionalSaturatePositiveProved = false
leanDescendantHistoryOwnershipUnconditionalBCELReadyProved = false
leanDescendantHistoryOwnershipUnconditionalZeroSlackProved = false
leanDescendantHistoryOwnershipExactGeneralPCCMinProved = false
leanDescendantHistoryOwnershipPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanDescendantHistoryOwnershipRuntimeExecutionIsProofAuthority = false
leanDescendantHistoryOwnershipScope = "arbitrary-finite-raw-stage-sequences-actual-descendant-decoding-persistent-stage-event-local-physical-origins-exact-live-removed-historical-charge-partition-derived-input-event-owners-support-stable-extracted-charges-final-net-gain-with-intermediate-expansion-no-supplied-intermediates-or-owners-or-oracles-no-open-obligation-transport-or-global-strategy-or-polynomial-runtime"
leanProperDescendantCertificatesFormalized = true
leanProperDescendantCertificatesAxiomAuditPassed = true
leanProperDescendantCertificatesAuditedDeclarationCount = 33
leanProperDescendantCertificatesArbitraryLabelCausalBoundTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.output_dependency_bound"
leanProperDescendantCertificatesDerivedOuterCompilationTheorem = "PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_compiles"
leanProperDescendantCertificatesCompleteOuterCompilationTheorem = "PNP.DirectWire.WireDescendantProperSupport.compile_complete"
leanProperDescendantCertificatesProperSupportIffTheorem = "PNP.DirectWire.WireDescendantProperSupport.proper_iff_exterior_positive"
leanProperDescendantCertificatesAmbientHistoricalAccountingTheorem = "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.charge_accounting"
leanProperDescendantCertificatesCompleteAcceptanceIffTheorem = "PNP.DirectWire.WireDescendantCertificate.verify_exists_iff"
leanProperDescendantCertificatesSourceRoundTripTheorem = "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.records_source"
leanProperDescendantCertificatesOrdinaryOutputPreservationTheorem = "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.output"
leanProperDescendantCertificatesLiteralFieldPreservationTheorem = "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.field"
leanProperDescendantCertificatesStrictGainTheorem = "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictGain"
leanProperDescendantCertificatesStrictResidualDescentTheorem = "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictResidualDescent"
leanProperDescendantCertificatesFailedCompleteProgramRejectionTheorem = "PNP.DirectWire.WireDescendantCertificate.verify_run_none"
leanProperDescendantCertificatesWholeSupportRejectionTheorem = "PNP.DirectWire.WireDescendantCertificate.verify_not_proper"
leanProperDescendantCertificatesNondecreaseRejectionTheorem = "PNP.DirectWire.WireDescendantCertificate.verify_no_gain"
leanProperDescendantCertificatesArbitraryFiniteDimensionsAndProgramsCovered = true
leanProperDescendantCertificatesRawSourceOnlyCertificate = true
leanProperDescendantCertificatesCompleteProgramRequired = true
leanProperDescendantCertificatesOuterAcyclicityDerivedFromExecution = true
leanProperDescendantCertificatesProperPhysicalSupportRequired = true
leanProperDescendantCertificatesStrictFinalLocalSavingRequired = true
leanProperDescendantCertificatesAllOrdinaryOutputsAndLiteralFieldsPreserved = true
leanProperDescendantCertificatesExteriorOccursExactlyOnce = true
leanProperDescendantCertificatesActualHistoricalChargeRemovalBalancePreserved = true
leanProperDescendantCertificatesIntermediateExpansionAllowed = true
leanProperDescendantCertificatesCallerSuppliedCorrectnessOrIntermediateCircuitRequired = false
leanProperDescendantCertificatesCallerSuppliedOrderOrSuccessfulSpliceRequired = false
leanProperDescendantCertificatesCallerSuppliedCostsOrOwnersRequired = false
leanProperDescendantCertificatesAcceptedPrefixReturnedAfterLaterRejection = false
leanProperDescendantCertificatesRejectedCertificateProvesLocalMinimality = false
leanProperDescendantCertificatesAcceptedCertificateForEveryNonminimalInputProved = false
leanProperDescendantCertificatesGloballySuccessfulStrategyDerived = false
leanProperDescendantCertificatesFullManuscriptVerifyDWProved = false
leanProperDescendantCertificatesFullManuscriptProfilesAndRuleFamiliesProved = false
leanProperDescendantCertificatesOpenObligationsTransportedAcrossSupports = false
leanProperDescendantCertificatesCompleteChargeSoundnessProved = false
leanProperDescendantCertificatesCompletePackageEProved = false
leanProperDescendantCertificatesTerminalFamiliesDerived = false
leanProperDescendantCertificatesGlobalRouteCoverageProved = false
leanProperDescendantCertificatesUnconditionalSaturatePositiveProved = false
leanProperDescendantCertificatesUnconditionalBCELReadyProved = false
leanProperDescendantCertificatesUnconditionalZeroSlackProved = false
leanProperDescendantCertificatesExactGeneralPCCMinProved = false
leanProperDescendantCertificatesPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanProperDescendantCertificatesRuntimeExecutionIsProofAuthority = false
leanProperDescendantCertificatesScope = "arbitrary-finite-computational-wire-carriers-source-only-raw-records-and-complete-descendant-programs-derived-causal-literal-splice-proper-support-strict-final-saving-all-output-and-field-preservation-exact-historical-costs-intermediate-expansion-no-global-certificate-discovery-or-full-manuscript-profiles-or-polynomial-runtime"
leanOpenObligationProgramsFormalized = true
leanOpenObligationProgramsAxiomAuditPassed = true
leanOpenObligationProgramsAuditedDeclarationCount = 144
leanOpenObligationProgramsPendingSnapshotPreservationTheorem = "PNP.DirectWire.WireOpenSupportSplice.transfer_pending"
leanOpenObligationProgramsCompleteDependencyOrderTheorem = "PNP.DirectWire.WireOpenProgram.orderEvents_success_iff"
leanOpenObligationProgramsCompleteExecutionAcceptanceTheorem = "PNP.DirectWire.WireOpenProgram.compile_exists_iff"
leanOpenObligationProgramsFinalClosureTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.closed"
leanOpenObligationProgramsCreationLifecycleTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle"
leanOpenObligationProgramsFullFieldRestorationTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field"
leanOpenObligationProgramsCompleteOuterCompilationTheorem = "PNP.DirectWire.WireOpenProperSupport.compile_complete"
leanOpenObligationProgramsActualCompilerOwnershipTheorem = "PNP.DirectWire.WireOpenProperSupport.ownership_compiled_position"
leanOpenObligationProgramsCompleteAcceptanceIffTheorem = "PNP.DirectWire.WireOpenCertificate.verify_exists_iff"
leanOpenObligationProgramsSourceRoundTripTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source"
leanOpenObligationProgramsOrdinaryOutputPreservationTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output"
leanOpenObligationProgramsLiteralFieldPreservationTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field"
leanOpenObligationProgramsHistoricalAccountingTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting"
leanOpenObligationProgramsPhysicalOwnershipTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership"
leanOpenObligationProgramsStrictGainTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain"
leanOpenObligationProgramsStrictResidualDescentTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent"
leanOpenObligationProgramsFailedCompleteProgramRejectionTheorem = "PNP.DirectWire.WireOpenCertificate.verify_program_none"
leanOpenObligationProgramsWholeSupportRejectionTheorem = "PNP.DirectWire.WireOpenCertificate.verify_not_proper"
leanOpenObligationProgramsNondecreaseRejectionTheorem = "PNP.DirectWire.WireOpenCertificate.verify_no_gain"
leanOpenObligationProgramsArbitraryFiniteDimensionsAndProgramsCovered = true
leanOpenObligationProgramsRawSourceOnlyCertificate = true
leanOpenObligationProgramsInitialStateInternallyDerived = true
leanOpenObligationProgramsCompleteRawMixedProgramRequired = true
leanOpenObligationProgramsComputedDependencyOrderRequired = true
leanOpenObligationProgramsIntrinsicCreationReferencesRequired = true
leanOpenObligationProgramsSamePendingSnapshotsPreserved = true
leanOpenObligationProgramsOpenObligationsTransportedAcrossSupports = true
leanOpenObligationProgramsFullModeR6R7R8DischargeRequired = true
leanOpenObligationProgramsFinalAmbientLedgerClosureRequired = true
leanOpenObligationProgramsOuterAcyclicityDerivedFromExecution = true
leanOpenObligationProgramsProperPhysicalSupportRequired = true
leanOpenObligationProgramsStrictFinalLocalSavingRequired = true
leanOpenObligationProgramsAllOrdinaryOutputsAndLiteralFieldsPreserved = true
leanOpenObligationProgramsExteriorOccursExactlyOnce = true
leanOpenObligationProgramsActualHistoricalChargeRemovalBalancePreserved = true
leanOpenObligationProgramsPhysicalOwnershipComputed = true
leanOpenObligationProgramsActualCompilerPositionMapsUsed = true
leanOpenObligationProgramsComputedOuterPositionNamespaces = true
leanOpenObligationProgramsLaterRemovedAllocationChargesRetained = true
leanOpenObligationProgramsIntermediateExpansionAllowed = true
leanOpenObligationProgramsInnerClosedHistoryLanguagePreserved = true
leanOpenObligationProgramsCallerSuppliedCorrectnessOrIntermediateCircuitRequired = false
leanOpenObligationProgramsCallerSuppliedInitialStateOrSnapshotRequired = false
leanOpenObligationProgramsCallerSuppliedOrderOrSuccessfulSpliceRequired = false
leanOpenObligationProgramsCallerSuppliedCostsOrOwnersRequired = false
leanOpenObligationProgramsAcceptedPrefixReturnedAfterLaterRejection = false
leanOpenObligationProgramsRejectedCertificateProvesLocalMinimality = false
leanOpenObligationProgramsAcceptedCertificateForEveryNonminimalInputProved = false
leanOpenObligationProgramsGloballySuccessfulStrategyDerived = false
leanOpenObligationProgramsFullManuscriptVerifyDWProved = false
leanOpenObligationProgramsFullManuscriptProfilesAndRuleFamiliesProved = false
leanOpenObligationProgramsCompleteChargeSoundnessProved = false
leanOpenObligationProgramsCompletePackageEProved = false
leanOpenObligationProgramsTerminalFamiliesDerived = false
leanOpenObligationProgramsGlobalRouteCoverageProved = false
leanOpenObligationProgramsUnconditionalSaturatePositiveProved = false
leanOpenObligationProgramsUnconditionalBCELReadyProved = false
leanOpenObligationProgramsUnconditionalZeroSlackProved = false
leanOpenObligationProgramsExactGeneralPCCMinProved = false
leanOpenObligationProgramsPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanOpenObligationProgramsRuntimeExecutionIsProofAuthority = false
leanOpenObligationProgramsScope = "arbitrary-finite-source-only-complete-mixed-programs-computed-order-open-snapshot-transport-full-mode-discharge-final-closure-derived-proper-literal-splice-strict-saving-all-observations-actual-physical-ownership-and-historical-costs-no-global-discovery-or-full-manuscript-profiles-or-polynomial-runtime"
leanStructuralReindexingFormalized = true
leanStructuralReindexingAxiomAuditPassed = true
leanStructuralReindexingAuditedDeclarationCount = 108
leanStructuralReindexingActualCompilerSourceFidelityTheorem = "PNP.DirectWire.RawNandWireStructure.compile_sources"
leanStructuralReindexingRawSwapDecodeTheorem = "PNP.DirectWire.StructuralReindexing.GateRenaming.decode_isSome"
leanStructuralReindexingDerivedCompilationTheorem = "PNP.DirectWire.StructuralReindexing.compiled_accepted"
leanStructuralReindexingLiteralSourceTheorem = "PNP.DirectWire.StructuralReindexing.result_sources"
leanStructuralReindexingLiteralOutputTheorem = "PNP.DirectWire.StructuralReindexing.result_output_source"
leanStructuralReindexingArbitraryRecordRoundTripTheorem = "PNP.DirectWire.StructuralReindexing.forward_backward_records"
leanStructuralReindexingBoundaryCorrespondenceTheorem = "PNP.DirectWire.StructuralReindexing.descendant_boundary"
leanStructuralReindexingInterfaceCorrespondenceTheorem = "PNP.DirectWire.StructuralReindexing.descendant_interface"
leanStructuralReindexingIndependentOpenSemanticsTheorem = "PNP.DirectWire.StructuralReindexing.open_support_pullback"
leanStructuralReindexingReplacementCompatibilityTheorem = "PNP.DirectWire.StructuralReindexing.pullReplacement_compatible"
leanStructuralReindexingMatchedSurchargeTheorem = "PNP.DirectWire.StructuralReindexing.matched_surcharge"
leanStructuralReindexingExactSignedSavingTheorem = "PNP.DirectWire.StructuralReindexing.replacement_saving_preserved"
leanStructuralReindexingRawDependencyCorrespondenceTheorem = "PNP.DirectWire.StructuralReindexing.splice_dependencies"
leanStructuralReindexingAcyclicityEquivalenceTheorem = "PNP.DirectWire.StructuralReindexing.splice_wellFounded_iff"
leanStructuralReindexingCompilationEquivalenceTheorem = "PNP.DirectWire.StructuralReindexing.splice_compile_success_iff"
leanStructuralReindexingRejectionEquivalenceTheorem = "PNP.DirectWire.StructuralReindexing.splice_compile_failure_iff"
leanStructuralReindexingActualPhysicalPositionTheorem = "PNP.DirectWire.StructuralReindexing.splice_physical_position"
leanStructuralReindexingCompiledLiteralSourcesTheorem = "PNP.DirectWire.StructuralReindexing.splice_compiled_sources"
leanStructuralReindexingCompiledLiteralOutputTheorem = "PNP.DirectWire.StructuralReindexing.splice_compiled_output_source"
leanStructuralReindexingComputedPredecessorAcceptanceTheorem = "PNP.DirectWire.StructuralReindexing.pullCompiledSplice_accepted"
leanStructuralReindexingCompleteReplacementTransportTheorem = "PNP.DirectWire.StructuralReindexing.literal_replacement_transport"
leanStructuralReindexingArbitraryFiniteDimensionsAndDescendantRecordsCovered = true
leanStructuralReindexingCompleteCheckedRawSwapSequenceRequired = true
leanStructuralReindexingActualCompilerPlacementAndInverseUsed = true
leanStructuralReindexingCanonicalPortAndOwnershipBijectionsDerived = true
leanStructuralReindexingAllIndependentBoundaryValuationsCovered = true
leanStructuralReindexingLiteralInputAndOutputReplacementRewiring = true
leanStructuralReindexingBothMatchedSignedSurchargesZero = true
leanStructuralReindexingExactLocalAndWholeSignedSavingPreserved = true
leanStructuralReindexingBothDependencyAndRejectionDirectionsProved = true
leanStructuralReindexingAcceptedDescendantSpliceRequiredForCompiledPullback = true
leanStructuralReindexingOpenReplacementCompatibilityRequiredForSemantics = true
leanStructuralReindexingCallerSuppliedPredecessorCompilerOrOrderRequired = false
leanStructuralReindexingCallerSuppliedTransportMapsRequired = false
leanStructuralReindexingCallerSuppliedSourceFidelityRequired = false
leanStructuralReindexingPaddingUsed = false
leanStructuralReindexingAllCompatibleSplicesAcyclicProved = false
leanStructuralReindexingArbitraryPermutationEncodingComplete = false
leanStructuralReindexingFullManuscriptProfileSemanticsProved = false
leanStructuralReindexingAllNormalizationAndMaterializerRulesProved = false
leanStructuralReindexingFullManuscriptVerifyDWProved = false
leanStructuralReindexingCompleteChargeSoundnessAndPackageEProved = false
leanStructuralReindexingGlobalCertificateDiscoveryProved = false
leanStructuralReindexingTerminalFamiliesDerived = false
leanStructuralReindexingGlobalRouteCoverageProved = false
leanStructuralReindexingUnconditionalSaturatePositiveProved = false
leanStructuralReindexingUnconditionalBCELReadyProved = false
leanStructuralReindexingUnconditionalZeroSlackProved = false
leanStructuralReindexingExactGeneralPCCMinProved = false
leanStructuralReindexingPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanStructuralReindexingRuntimeExecutionIsProofAuthority = false
leanStructuralReindexingScope = "arbitrary-finite-checked-raw-swaps-and-descendant-records-derived-canonical-port-and-ownership-bijections-independent-open-semantics-literal-replacement-rewiring-zero-matched-surcharge-exact-signed-saving-bidirectional-raw-dependency-and-acceptance-actual-compiled-physical-transport-no-full-profiles-or-materializers-or-global-or-polynomial-claim"
leanStructuralProgramsFormalized = true
leanStructuralProgramsAxiomAuditPassed = true
leanStructuralProgramsAuditedDeclarationCount = 63
leanStructuralProgramsGateCausalLabelTheorem = "PNP.DirectWire.StructuralReindexing.result_gate_level"
leanStructuralProgramsLiteralFieldSourceTheorem = "PNP.DirectWire.WireCarrier.reindex_field_source"
leanStructuralProgramsPendingSnapshotTheorem = "PNP.DirectWire.WireObligationHistory.State.reindex_pending"
leanStructuralProgramsRawCurrentCarrierDecodeTheorem = "PNP.DirectWire.WireStructuralState.execute_isSome"
leanStructuralProgramsRawRejectionTheorem = "PNP.DirectWire.WireStructuralState.execute_failure_iff"
leanStructuralProgramsLocalPhysicalOwnershipTheorem = "PNP.DirectWire.WireStructuralState.Receipt.physical_ownership"
leanStructuralProgramsHistoricalOriginTheorem = "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_origin"
leanStructuralProgramsHistoricalChargesTheorem = "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged"
leanStructuralProgramsHistoricalRemovalsTheorem = "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed"
leanStructuralProgramsCompleteProgramLifecycleTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle"
leanStructuralProgramsCompleteProgramCausalInvariantTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant"
leanStructuralProgramsCompleteProgramPhysicalOwnershipTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership"
leanStructuralProgramsCompleteCertificateSoundnessTheorem = "PNP.DirectWire.WireOpenCertificate.verify_sound"
leanStructuralProgramsStrictResidualDescentTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent"
leanStructuralProgramsCheckedRawStructuralActionsDerived = true
leanStructuralProgramsCurrentCarrierBoundsUsed = true
leanStructuralProgramsCompleteRawSwapSequenceRequired = true
leanStructuralProgramsExactPendingSnapshotsPreserved = true
leanStructuralProgramsLiteralFieldSourcesPreserved = true
leanStructuralProgramsWholeOutputAndFieldSemanticsPreserved = true
leanStructuralProgramsAllInputCausalLabelsPreserved = true
leanStructuralProgramsStructuralAllocationsAndRemovalsZero = true
leanStructuralProgramsPreviousGlobalOwnersPreserved = true
leanStructuralProgramsCompleteChargeAndRemovalHistoryPreserved = true
leanStructuralProgramsCompleteAcceptedProgramRequired = true
leanStructuralProgramsClosedFinalLedgerRequired = true
leanStructuralProgramsProperSupportRequired = true
leanStructuralProgramsStrictSignedSavingRequired = true
leanStructuralProgramsCallerSuppliedOrderingOrMapsRequired = false
leanStructuralProgramsCallerSuppliedCausalOrOwnershipWitnessRequired = false
leanStructuralProgramsReorderingAloneEarnsStrictSaving = false
leanStructuralProgramsAcceptsSuccessfulPrefixAfterFailedTail = false
leanStructuralProgramsFullManuscriptProfileSemanticsProved = false
leanStructuralProgramsAllNormalizationAndMaterializerRulesProved = false
leanStructuralProgramsFullManuscriptVerifyDWProved = false
leanStructuralProgramsCompleteChargeSoundnessAndPackageEProved = false
leanStructuralProgramsGlobalCertificateDiscoveryProved = false
leanStructuralProgramsTerminalFamiliesDerived = false
leanStructuralProgramsGlobalRouteCoverageProved = false
leanStructuralProgramsUnconditionalSaturatePositiveProved = false
leanStructuralProgramsUnconditionalBCELReadyProved = false
leanStructuralProgramsUnconditionalZeroSlackProved = false
leanStructuralProgramsExactGeneralPCCMinProved = false
leanStructuralProgramsPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanStructuralProgramsRuntimeExecutionIsProofAuthority = false
leanStructuralProgramsScope = "arbitrary-finite-source-only-complete-programs-computed-current-carrier-raw-structural-actions-literal-field-wires-exact-causal-labels-pending-snapshots-zero-local-cost-prior-global-owners-and-history-closed-ledger-proper-support-strict-saving-no-global-discovery-or-full-manuscript-or-polynomial-claim"
leanComputationalRecodingFormalized = true
leanComputationalRecodingAxiomAuditPassed = true
leanComputationalRecodingAuditedDeclarationCount = 88
leanComputationalRecodingStructuralExactEncodingTheorem = "PNP.DirectWire.StructuralReindexing.GateRenaming.decode_encode"
leanComputationalRecodingStructuralEncodingLengthTheorem = "PNP.DirectWire.StructuralReindexing.GateRenaming.encode_length_le"
leanComputationalRecodingLiteralInverseCheckTheorem = "PNP.DirectWire.WireCarrierRecoding.check_iff"
leanComputationalRecodingLiteralGateBalanceTheorem = "PNP.DirectWire.WireCarrierRecoding.result_gate_balance"
leanComputationalRecodingCausalGuardTheorem = "PNP.DirectWire.WireCarrier.dependencyGuard_iff"
leanComputationalRecodingPendingSnapshotTheorem = "PNP.DirectWire.WireObligationHistory.State.recode_pending"
leanComputationalRecodingLocalPhysicalOwnershipTheorem = "PNP.DirectWire.WireRecodingState.Receipt.physical_ownership"
leanComputationalRecodingRawDecodeRoundTripTheorem = "PNP.DirectWire.WireRecodingInput.decode_encode"
leanComputationalRecodingRawAcceptanceTheorem = "PNP.DirectWire.WireRecodingInput.execute_success_iff"
leanComputationalRecodingCompleteProgramGateBalanceTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.gate_balance"
leanComputationalRecodingCompleteProgramLifecycleTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle"
leanComputationalRecodingCompleteProgramPhysicalOwnershipTheorem = "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership"
leanComputationalRecodingCompleteCertificateSoundnessTheorem = "PNP.DirectWire.WireOpenCertificate.verify_sound"
leanComputationalRecodingStrictResidualDescentTheorem = "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent"
leanComputationalRecodingExistingRawCodecReused = true
leanComputationalRecodingBothDimensionsChecked = true
leanComputationalRecodingCompleteLiteralRecodersRequired = true
leanComputationalRecodingBothFullInverseEquationsChecked = true
leanComputationalRecodingAllInputCausalLabelsChecked = true
leanComputationalRecodingOrdinaryOutputsAndHiddenFieldsCovered = true
leanComputationalRecodingExactPendingSnapshotsPreserved = true
leanComputationalRecodingLiteralEncoderDecoderGatesCharged = true
leanComputationalRecodingActualNormalizerDeletionMapsUsed = true
leanComputationalRecodingDerivedEncoderDecoderAllocationPhases = true
leanComputationalRecodingHistoricalChargesAndOwnersPreserved = true
leanComputationalRecodingCompleteAcceptedProgramRequired = true
leanComputationalRecodingClosedFinalLedgerRequired = true
leanComputationalRecodingProperSupportRequired = true
leanComputationalRecodingStrictSignedSavingRequired = true
leanComputationalRecodingCallerSuppliedCorrectnessOrderCausalOrOwnerWitnessRequired = false
leanComputationalRecodingRecodingDischargesOpenObligations = false
leanComputationalRecodingSemanticReversibilityImpliesPhysicalCancellation = false
leanComputationalRecodingSemanticReversibilityAloneEarnsSaving = false
leanComputationalRecodingInverseCheckEnumeratesAllFieldValuations = true
leanComputationalRecodingFullManuscriptProfileSemanticsProved = false
leanComputationalRecodingAllRecodingAndNormalizationRulesProved = false
leanComputationalRecodingFullManuscriptVerifyDWProved = false
leanComputationalRecodingCompleteChargeSoundnessAndPackageEProved = false
leanComputationalRecodingGlobalCertificateDiscoveryProved = false
leanComputationalRecodingTerminalFamiliesDerived = false
leanComputationalRecodingGlobalRouteCoverageProved = false
leanComputationalRecodingUnconditionalSaturatePositiveProved = false
leanComputationalRecodingUnconditionalBCELReadyProved = false
leanComputationalRecodingUnconditionalZeroSlackProved = false
leanComputationalRecodingExactGeneralPCCMinProved = false
leanComputationalRecodingPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanComputationalRecodingRuntimeExecutionIsProofAuthority = false
leanComputationalRecodingScope = "arbitrary-finite-source-only-complete-programs-existing-raw-codec-both-literal-recoders-exact-inverse-and-syntactic-causal-checks-pending-snapshots-actual-allocations-deletions-and-global-ownership-closed-ledger-proper-support-strict-saving-no-global-discovery-full-manuscript-or-polynomial-claim"
leanSourceDerivedZeroCostExposureFormalized = true
leanSourceDerivedZeroCostExposureAxiomAuditPassed = true
leanSourceDerivedZeroCostExposureAuditedDeclarationCount = 22
leanSourceDerivedZeroCostExposureMinimumTheorem = "PNP.DirectWire.ZeroCostExposure.referenceMinimum_extend"
leanSourceDerivedZeroCostExposureSlackTheorem = "PNP.DirectWire.ZeroCostExposure.residualSlack_extend"
leanSourceDerivedZeroCostExposureRecognitionTheorem = "PNP.DirectWire.ZeroCostExposure.recognize_success_iff"
leanSourceDerivedZeroCostExposureGateRefusalTheorem = "PNP.DirectWire.ZeroCostExposure.recognize_gate_none_iff"
leanSourceDerivedZeroCostExposureTupleAcceptanceTheorem = "PNP.DirectWire.ZeroCostExposure.compileLayout_available_iff"
leanSourceDerivedZeroCostExposureCarrierMinimumTheorem = "PNP.DirectWire.WireCarrier.exposed_referenceMinimum_of_checkLayout"
leanSourceDerivedZeroCostExposureCarrierSlackTheorem = "PNP.DirectWire.WireCarrier.exposed_residualSlack_of_checkLayout"
leanSourceDerivedZeroCostExposureCarrierPreservationTheorem = "PNP.DirectWire.WireCarrier.checked_exposure_preserves_problem"
leanSourceDerivedZeroCostExposureArbitraryFiniteDimensionsCovered = true
leanSourceDerivedZeroCostExposureLiteralInputConstantAndOldOutputAliasesCovered = true
leanSourceDerivedZeroCostExposureBothRealizationTransfersProved = true
leanSourceDerivedZeroCostExposureActualSourceRecognitionComputed = true
leanSourceDerivedZeroCostExposureEveryRequestedFieldChecked = true
leanSourceDerivedZeroCostExposureActualCarrierMinimumAndSlackPreserved = true
leanSourceDerivedZeroCostExposureCallerSuppliedObserverMinimumOrCorrectnessRequired = false
leanSourceDerivedZeroCostExposureConstructorOrRecognizerEnumeratesSemanticMinima = false
leanSourceDerivedZeroCostExposureAllSemanticallyFreeExposuresRecognized = false
leanSourceDerivedZeroCostExposureRefusalImpliesPackageERoute = false
leanSourceDerivedZeroCostExposureNoPhysicalGateIncreaseAloneImpliesZeroCost = false
leanSourceDerivedZeroCostExposureUniquePhysicalChargeAloneForcesMinimumIncrease = false
leanSourceDerivedZeroCostExposureArbitraryPositiveCostTransparencyProved = false
leanSourceDerivedZeroCostExposureFullManuscriptProfileSemanticsProved = false
leanSourceDerivedZeroCostExposureTerminalFamiliesDerived = false
leanSourceDerivedZeroCostExposureGlobalRouteCoverageProved = false
leanSourceDerivedZeroCostExposureUnconditionalSaturatePositiveProved = false
leanSourceDerivedZeroCostExposureUnconditionalBCELReadyProved = false
leanSourceDerivedZeroCostExposureUnconditionalZeroSlackProved = false
leanSourceDerivedZeroCostExposureExactGeneralPCCMinProved = false
leanSourceDerivedZeroCostExposurePolynomialRuntimeOutputAndCertificateBoundsProved = false
leanSourceDerivedZeroCostExposureScope = "arbitrary-finite-literal-input-constant-old-output-alias-extension-projection-exact-minimum-slack-source-derived-tuple-recognition-actual-carrier-no-semantic-completeness-positive-cost-global-route-or-polynomial-claim"
leanWireProfileExposureFormalized = true
leanWireProfileExposureAxiomAuditPassed = true
leanWireProfileExposureAuditedDeclarationCount = 35
leanWireProfileExposureFullComparisonTheorem = "PNP.DirectWire.WireProfile.full_iff"
leanWireProfileExposureQuotientComparisonTheorem = "PNP.DirectWire.WireProfile.quotient_iff"
leanWireProfileExposureFullLiftTheorem = "PNP.DirectWire.WireProfile.full_lift_iff"
leanWireProfileExposureAttainedQuotientWitnessTheorem = "PNP.DirectWire.WireProfile.quotientWitness_matches"
leanWireProfileExposureExposureBalanceTheorem = "PNP.DirectWire.WireProfile.exposure_states_balance"
leanWireProfileExposureExactTransferTheorem = "PNP.DirectWire.WireProfile.exposure_moves_exact_slack_to_defect"
leanWireProfileExposureNonLiftabilityTheorem = "PNP.DirectWire.WireProfile.exposure_loss_has_unliftable_quotient_witness"
leanWireProfileExposureOrdinarySlackTheorem = "PNP.DirectWire.WireProfile.source_slack_balance"
leanWireProfileExposureNormalizationTheorem = "PNP.DirectWire.WireProfile.normalize_fullEquivalent"
leanWireProfileExposureCheckedSpliceTheorem = "PNP.DirectWire.WireProfile.splice_fullEquivalent"
leanWireProfileExposureArbitraryFiniteDimensionsCovered = true
leanWireProfileExposureOrdinaryOutputsPreservedInBothModes = true
leanWireProfileExposureActualWireValuesAtAllValuations = true
leanWireProfileExposureMinimaAndAttainedWitnessesDerived = true
leanWireProfileExposureExposureTransfersSlackToDefect = true
leanWireProfileExposureCallerSuppliedObserverOrMinimumRequired = false
leanWireProfileExposureQuotientWitnessAloneIsFullReplacement = false
leanWireProfileExposureAllGateFieldsAreCanonicalTerminalFamily = false
leanWireProfileExposureCompleteManuscriptProfileGrammarProved = false
leanWireProfileExposureForcedCostTransparencyProved = false
leanWireProfileExposureCompletePackageEOrGlobalRoutesProved = false
leanWireProfileExposureTerminalFamiliesDerived = false
leanWireProfileExposureUnconditionalSaturatePositiveProved = false
leanWireProfileExposureUnconditionalBCELReadyProved = false
leanWireProfileExposureUnconditionalZeroSlackProved = false
leanWireProfileExposureExactPolynomialPCCMinProved = false
leanWireProfileExposurePolynomialRuntimeOutputAndCertificateBoundsProved = false
leanWireProfileExposureReferenceMinimizationIsExhaustive = true
leanWireProfileExposureScope = "arbitrary-finite-actual-wire-profile-values-all-input-valuations-mandatory-ordinary-outputs-full-quotient-lift-attained-minima-exact-exposure-slack-defect-transfer-checked-normalization-splice-no-full-manuscript-global-route-or-polynomial-claim"
leanWireProfileRestorationFormalized = true
leanWireProfileRestorationAxiomAuditPassed = true
leanWireProfileRestorationAuditedDeclarationCount = 19
leanWireProfileRestorationQuotientAgreementTheorem = "PNP.DirectWire.WireProfileRestoration.quotientAgreement_iff"
leanWireProfileRestorationFullRestorationTheorem = "PNP.DirectWire.WireProfileRestoration.paidWitness_fullEquivalent"
leanWireProfileRestorationChargeBoundTheorem = "PNP.DirectWire.WireProfileRestoration.projectionDefect_le_charge"
leanWireProfileRestorationPaidOverheadTheorem = "PNP.DirectWire.WireProfileRestoration.paidWitness_exact_overhead"
leanWireProfileRestorationReclaimedBoundTheorem = "PNP.DirectWire.WireProfileRestoration.reclaimed_le_overhead"
leanWireProfileRestorationNormalizedOverheadTheorem = "PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_overhead"
leanWireProfileRestorationStrictGainTheorem = "PNP.DirectWire.WireProfileRestoration.normalizedWitness_smaller_iff"
leanWireProfileRestorationCheckedGainTheorem = "PNP.DirectWire.WireProfileRestoration.CheckedGain.checked"
leanWireProfileRestorationUnaryMinimumTheorem = "PNP.DirectWire.WireProfileRestoration.unary_fullMinimum"
leanWireProfileRestorationUnaryGainTheorem = "PNP.DirectWire.WireProfileRestoration.unary_smaller_iff_fullSlack_positive"
leanWireProfileRestorationArbitraryFiniteDimensionsCovered = true
leanWireProfileRestorationOrdinaryOutputsAndActualFieldsPreserved = true
leanWireProfileRestorationExistingSharedMaterializerReused = true
leanWireProfileRestorationActualPhysicalChargeAndSavingsComputed = true
leanWireProfileRestorationExactRemainingOverheadDerived = true
leanWireProfileRestorationStrictOriginalSizeComparisonChecked = true
leanWireProfileRestorationExistingUnaryMinimumCompatibilityProved = true
leanWireProfileRestorationUnaryCompatibilityHasArbitraryOutputAndFieldWidths = true
leanWireProfileRestorationPositiveSlackRefusalAndUnaryRecoveryKernelChecked = true
leanWireProfileRestorationCallerSuppliedWitnessMinimumOrCorrectnessRequired = false
leanWireProfileRestorationChargeEqualsProjectionDefectProved = false
leanWireProfileRestorationNormalizerIsSemanticallyComplete = false
leanWireProfileRestorationNoGainImpliesZeroSlack = false
leanWireProfileRestorationUnaryCompletenessExtendedToArbitraryInputs = false
leanWireProfileRestorationCompleteManuscriptProfileGrammarProved = false
leanWireProfileRestorationTerminalFamiliesDerived = false
leanWireProfileRestorationCompletePackageEOrGlobalRoutesProved = false
leanWireProfileRestorationUnconditionalSaturatePositiveProved = false
leanWireProfileRestorationUnconditionalBCELReadyProved = false
leanWireProfileRestorationUnconditionalZeroSlackProved = false
leanWireProfileRestorationExactPolynomialPCCMinProved = false
leanWireProfileRestorationPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanWireProfileRestorationReferenceMinimizationIsExhaustive = true
leanWireProfileRestorationRuntimeExecutionIsProofAuthority = false
leanWireProfileRestorationScope = "arbitrary-finite-actual-wire-full-restoration-shared-materializer-charge-defect-upper-bound-paid-and-normalized-exact-overhead-checked-strict-gain-existing-one-input-minimum-compatibility-no-general-completeness-or-polynomial-claim"
leanComputedWireProfileFormalized = true
leanComputedWireProfileAxiomAuditPassed = true
leanComputedWireProfileAuditedDeclarationCount = 72
leanComputedWireProfileUniformSourceTheorem = "PNP.DirectWire.WireProfileAvailability.sourceMatches_iff"
leanComputedWireProfileFullMinimumBridgeTheorem = "PNP.DirectWire.WireProfileAvailability.full_minimum"
leanComputedWireProfileQuotientMinimumBridgeTheorem = "PNP.DirectWire.WireProfileAvailability.quotient_minimum"
leanComputedWireProfileAmbientCoherenceTheorem = "PNP.DirectWire.WireProfileAmbient.model_observe_coherent"
leanComputedWireProfileDerivedFieldSupportTheorem = "PNP.DirectWire.WireProfileFieldClosed.available"
leanComputedWireProfileSemanticRetractionTheorem = "PNP.DirectWire.SemanticGateRetraction.semantics"
leanComputedWireProfileIndependentFieldLowerBoundTheorem = "PNP.DirectWire.FreshNandCost.gateCount_lower_bound"
leanComputedWireProfileIndependentFieldMinimumTheorem = "PNP.DirectWire.FreshNandCost.referenceMinimum_extend"
leanComputedWireProfileCoupledFullMinimumTheorem = "PNP.DirectWire.ComputedWireProfileCost.full_minimum"
leanComputedWireProfileCoupledQuotientMinimumTheorem = "PNP.DirectWire.ComputedWireProfileCost.quotient_minimum"
leanComputedWireProfileCoupledMinimumGapTheorem = "PNP.DirectWire.ComputedWireProfileCost.minimum_gap"
leanComputedWireProfileArbitraryFiniteDimensionsCovered = true
leanComputedWireProfileOneSourceUniformAcrossAllValuationsRequired = true
leanComputedWireProfileModelAndFieldPreservingSupportComputed = true
leanComputedWireProfileObserverPaddingAndRewordingCoherenceProved = true
leanComputedWireProfileExactCostForArbitraryIndependentFreshFieldWidthsProved = true
leanComputedWireProfileCallerSuppliedModelMinimumSupportOrCorrectnessRequired = false
leanComputedWireProfileSemanticRetractionHasExplicitUniformConstantHypothesis = true
leanComputedWireProfileRetractionHypothesisDischargedForIndependentFieldFamily = true
leanComputedWireProfileExtractedSupportIsProperSmallerOrOptimalProved = false
leanComputedWireProfileArbitraryManuscriptFieldAdditivityProved = false
leanComputedWireProfileSharedMaterializerChargeEqualsProjectionDefectProved = false
leanComputedWireProfileCompleteManuscriptProfileGrammarProved = false
leanComputedWireProfileTerminalFamiliesDerived = false
leanComputedWireProfileCompletePackageEOrGlobalRoutesProved = false
leanComputedWireProfileUnconditionalSaturatePositiveProved = false
leanComputedWireProfileUnconditionalBCELReadyProved = false
leanComputedWireProfileUnconditionalZeroSlackProved = false
leanComputedWireProfileExactPolynomialPCCMinProved = false
leanComputedWireProfilePolynomialRuntimeOutputAndCertificateBoundsProved = false
leanComputedWireProfileAvailabilityAndReferenceMinimizationAreExhaustive = true
leanComputedWireProfileRuntimeExecutionIsProofAuthority = false
leanComputedWireProfileScope = "arbitrary-finite-computed-uniform-wire-availability-ambient-observer-coherence-source-derived-field-preserving-support-exact-independent-fresh-nand-cost-and-terminal-model-coupling-no-arbitrary-field-additivity-global-route-or-polynomial-claim"
leanClosedSupportProfileFormalized = true
leanClosedSupportProfileAxiomAuditPassed = true
leanClosedSupportProfileAuditedDeclarationCount = 24
leanClosedSupportProfileRetainedSourceTheorem = "PNP.DirectWire.ClosedSupportObservation.available_iff_retained_source"
leanClosedSupportProfileComputedTableTheorem = "PNP.DirectWire.ClosedSupportObservation.available_eq_tableAvailable"
leanClosedSupportProfileSeedUnionTheorem = "PNP.DirectWire.ClosedSupportUnion.available_append"
leanClosedSupportProfileFiniteFamilyTheorem = "PNP.DirectWire.ClosedSupportUnion.available_flatten"
leanClosedSupportProfileRequestedFieldsTheorem = "PNP.DirectWire.ClosedSupportProfile.projected_fieldValue"
leanClosedSupportProfileActualCornerTheorem = "PNP.DirectWire.ClosedSupportSquare.corner_fieldValue"
leanClosedSupportProfileCornerAgreementTheorem = "PNP.DirectWire.ClosedSupportSquare.corners_fieldValue_equal"
leanClosedSupportProfileArbitraryFiniteDimensionsCovered = true
leanClosedSupportProfileComputedSupportAndMatchingTable = true
leanClosedSupportProfileUniformFieldValuesAtActualCornersProved = true
leanClosedSupportProfileCallerSuppliedClosureOrCorrectnessRequired = false
leanClosedSupportProfileOrdinaryOutputEquivalenceProved = false
leanClosedSupportProfileCompleteManuscriptProjectionSquareProved = false
leanClosedSupportProfileProperPositiveSupportProved = false
leanClosedSupportProfileDuplicateIsNormalizedTerminalCounterexample = false
leanClosedSupportProfileCompletePackageEOrGlobalRoutesProved = false
leanClosedSupportProfileUnconditionalSaturatePositiveProved = false
leanClosedSupportProfileUnconditionalBCELReadyProved = false
leanClosedSupportProfileUnconditionalZeroSlackProved = false
leanClosedSupportProfileExactPolynomialPCCMinProved = false
leanClosedSupportProfilePolynomialRuntimeOutputAndCertificateBoundsProved = false
leanClosedSupportProfileSourceMatchingAndInfluenceAreExhaustive = true
leanClosedSupportProfileRuntimeExecutionIsProofAuthority = false
leanClosedSupportProfileScope = "arbitrary-finite-computed-closed-support-observations-source-alternatives-union-and-profile-seeded-actual-square-corner-compatibility-no-ordinary-output-proper-positive-full-profile-or-polynomial-claim"
leanClosedSupportFullGainFormalized = true
leanClosedSupportFullGainAxiomAuditPassed = true
leanClosedSupportFullGainAuditedDeclarationCount = 27
leanClosedSupportFullGainPrimaryInputSpecializationTheorem = "PNP.DirectWire.ClosedSupportFullGain.prefixSource_value"
leanClosedSupportFullGainRetainedFieldTheorem = "PNP.DirectWire.ClosedSupportFullGain.prefixField_value"
leanClosedSupportFullGainWholeCarrierTheorem = "PNP.DirectWire.ClosedSupportFullGain.result_fullEquivalent"
leanClosedSupportFullGainExactGateBalanceTheorem = "PNP.DirectWire.ClosedSupportFullGain.result_exact_accounting"
leanClosedSupportFullGainWholeFullSlackBalanceTheorem = "PNP.DirectWire.ClosedSupportFullGain.result_fullSlack_balance"
leanClosedSupportFullGainLocalSlackBoundTheorem = "PNP.DirectWire.ClosedSupportFullGain.localFullSlack_le_global"
leanClosedSupportFullGainCheckedRouteTheorem = "PNP.DirectWire.ClosedSupportFullGain.improvement?_sound"
leanClosedSupportFullGainStrictGainTheorem = "PNP.DirectWire.ClosedSupportFullGain.improvement?_strictGain"
leanClosedSupportFullGainArbitraryFiniteDimensionsCovered = true
leanClosedSupportFullGainComputedClosedSupportAndFullMinimum = true
leanClosedSupportFullGainComplementAndReconnectionDerived = true
leanClosedSupportFullGainUniformOutputsAndComputationalFieldsPreserved = true
leanClosedSupportFullGainCallerSuppliedObserverReplacementOrCorrectnessRequired = false
leanClosedSupportFullGainLocalFullSlackExactlyRetiredFromWhole = true
leanClosedSupportFullGainProperPositiveSupportDiscoveryProved = false
leanClosedSupportFullGainWholeSpanIsProperLocalVerifyDW = false
leanClosedSupportFullGainCompleteManuscriptProfileGrammarProved = false
leanClosedSupportFullGainGlobalRouteCoverageProved = false
leanClosedSupportFullGainUnconditionalSaturatePositiveProved = false
leanClosedSupportFullGainUnconditionalBCELReadyProved = false
leanClosedSupportFullGainUnconditionalZeroSlackProved = false
leanClosedSupportFullGainExactPolynomialPCCMinProved = false
leanClosedSupportFullGainPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanClosedSupportFullGainReferenceMinimumMatchingAndInfluenceAreExhaustive = true
leanClosedSupportFullGainRuntimeExecutionIsProofAuthority = false
leanClosedSupportFullGainScope = "arbitrary-finite-computed-closed-support-full-minimum-derived-physical-complement-uniform-whole-output-and-computational-field-equivalence-exact-gate-and-full-slack-balance-checked-strict-descent-no-proper-positive-discovery-complete-profile-global-route-or-polynomial-claim"
leanClosedWholeMinimumFormalized = true
leanClosedWholeMinimumAxiomAuditPassed = true
leanClosedWholeMinimumAuditedDeclarationCount = 22
leanClosedWholeMinimumDerivedWholeSeedTheorem = "PNP.DirectWire.ClosedWholeMinimum.support_gateCount"
leanClosedWholeMinimumExactOrdinaryInterfaceTheorem = "PNP.DirectWire.ClosedWholeMinimum.interface_iff_output"
leanClosedWholeMinimumComputedFieldAvailabilityTheorem = "PNP.DirectWire.ClosedWholeMinimum.available_all"
leanClosedWholeMinimumSizePreservingComparisonTheorem = "PNP.DirectWire.ClosedWholeMinimum.forward_gateCount"
leanClosedWholeMinimumExactMinimumTheorem = "PNP.DirectWire.ClosedWholeMinimum.full_minimum"
leanClosedWholeMinimumAttainedMinimumTheorem = "PNP.DirectWire.ClosedWholeMinimum.result_optimal"
leanClosedWholeMinimumExactFullSlackTheorem = "PNP.DirectWire.ClosedWholeMinimum.fullSlack_eq"
leanClosedWholeMinimumPostReferenceSlackTheorem = "PNP.DirectWire.ClosedWholeMinimum.result_zero_fullSlack"
leanClosedWholeMinimumCheckedNoImprovementTheorem = "PNP.DirectWire.ClosedWholeMinimum.improvement_none_iff"
leanClosedWholeMinimumArbitraryFiniteDimensionsCovered = true
leanClosedWholeMinimumSeedInterfaceAndObserverDerived = true
leanClosedWholeMinimumIndependentFullReferenceMinimaEqual = true
leanClosedWholeMinimumComputedResultAttainsFullReferenceMinimum = true
leanClosedWholeMinimumCallerSuppliedEqualityMinimumOrCorrectnessRequired = false
leanClosedWholeMinimumWholeSpanIsProperLocalVerifyDW = false
leanClosedWholeMinimumProperPositiveSupportDiscoveryProved = false
leanClosedWholeMinimumCompleteManuscriptProfileGrammarProved = false
leanClosedWholeMinimumGlobalRouteCoverageProved = false
leanClosedWholeMinimumUnconditionalSaturatePositiveProved = false
leanClosedWholeMinimumUnconditionalBCELReadyProved = false
leanClosedWholeMinimumUnconditionalZeroSlackProved = false
leanClosedWholeMinimumExactPolynomialPCCMinProved = false
leanClosedWholeMinimumPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanClosedWholeMinimumReferenceSearchRemainsExhaustive = true
leanClosedWholeMinimumRuntimeExecutionIsProofAuthority = false
leanClosedWholeMinimumScope = "arbitrary-finite-derived-whole-gate-seed-computed-ordinary-interface-full-field-availability-size-preserving-two-way-reference-minimum-equality-attained-whole-full-minimum-no-proper-local-manuscript-zeroslack-global-route-or-polynomial-claim"
leanClosedSupportNestedGainFormalized = true
leanClosedSupportNestedGainAxiomAuditPassed = true
leanClosedSupportNestedGainAuditedDeclarationCount = 36
leanClosedSupportNestedGainPhysicalDifferenceTheorem = "PNP.DirectWire.ClosedSupportNestedGain.support_count_decomposition"
leanClosedSupportNestedGainExactOrdinaryInterfaceTheorem = "PNP.DirectWire.ClosedSupportNestedGain.outputSource_value"
leanClosedSupportNestedGainExactFieldObservationTheorem = "PNP.DirectWire.ClosedSupportNestedGain.extended_available"
leanClosedSupportNestedGainFullMinimumCostBoundTheorem = "PNP.DirectWire.ClosedSupportNestedGain.full_minimum_cost_balance"
leanClosedSupportNestedGainQuotientMinimumCostBoundTheorem = "PNP.DirectWire.ClosedSupportNestedGain.quotient_minimum_cost_balance"
leanClosedSupportNestedGainFullSlackMonotonicityTheorem = "PNP.DirectWire.ClosedSupportNestedGain.full_slack_le"
leanClosedSupportNestedGainQuotientSlackMonotonicityTheorem = "PNP.DirectWire.ClosedSupportNestedGain.quotient_slack_le"
leanClosedSupportNestedGainPhysicalInclusionPositivityTheorem = "PNP.DirectWire.ClosedSupportNestedGain.positive_mono"
leanClosedSupportNestedGainRawSeedInclusionTheorem = "PNP.DirectWire.ClosedSupportNestedGain.included_of_seed_subset"
leanClosedSupportNestedGainRawSeedPositivityTheorem = "PNP.DirectWire.ClosedSupportNestedGain.seed_positive"
leanClosedSupportNestedGainArbitraryFiniteDimensionsCovered = true
leanClosedSupportNestedGainSupportsDifferenceAndBindingsDerived = true
leanClosedSupportNestedGainAmbientInputsRetained = true
leanClosedSupportNestedGainExactFalseAndTrueFieldObservationsPreserved = true
leanClosedSupportNestedGainFullAndQuotientComparisonsDerived = true
leanClosedSupportNestedGainCallerSuppliedCostOrFieldEqualityRequired = false
leanClosedSupportNestedGainInitialRawWitnessPositivityPreservationProved = false
leanClosedSupportNestedGainProperPositiveSupportDiscoveryProved = false
leanClosedSupportNestedGainCompleteManuscriptProfileGrammarProved = false
leanClosedSupportNestedGainGlobalRouteCoverageProved = false
leanClosedSupportNestedGainUnconditionalSaturatePositiveProved = false
leanClosedSupportNestedGainUnconditionalBCELReadyProved = false
leanClosedSupportNestedGainUnconditionalZeroSlackProved = false
leanClosedSupportNestedGainExactPolynomialPCCMinProved = false
leanClosedSupportNestedGainPolynomialRuntimeOutputAndCertificateBoundsProved = false
leanClosedSupportNestedGainReferenceSearchRemainsExhaustive = true
leanClosedSupportNestedGainRuntimeExecutionIsProofAuthority = false
leanClosedSupportNestedGainScope = "arbitrary-finite-computed-completed-nested-support-derived-physical-difference-common-ambient-exact-ordinary-and-field-comparisons-full-and-quotient-cost-bounds-slack-and-combined-positivity-transport-no-initial-completion-manuscript-global-route-or-polynomial-claim"
leanClosedSupportNestedGainEveryIntermediateEventTransparencyProved = false
leanClosedSupportNestedGainProjectionDefectAloneMonotonicityProved = false

Static fail-closed boundary: missing, malformed, stale, or digest-mismatched data never enables theorem publication.

Compiled inventory SHA-256: 8cffec40ac5786f31bb8538967e79529423316f217bfee319e8423b81cf91bc3. This identifies the exact inventory bytes, not theorem correctness.

Compiled environment

Exact inventory counts

The current release manifest pins the inventory coordinate, digest and source identity. These identify the exact published artefact, not theorem correctness.

52,539 public declarations; 28,788 theorem-kind declarations; 11,841 assumption-free theorem-kind declarations; 21,622 private compiler auxiliaries excluded; 643 modules; 0 project axioms.

The inventory is emitted from Lean environment constants and axiom collection. It is not inferred from source text, JSON claims, checker acceptance, or report prose.

Show all 258 formal milestone records

Inventory-derived publication map

256 scoped milestones earned; 2 global milestones unearned

Formal artefact coverage is 256 of 258 scoped milestone rows. The static rows below are conservative fallback copy. When validation succeeds, JavaScript replaces them from the exact status payload.

Wire-backed computational profiles and exposure balance

For arbitrary finite input, ordinary-output and computational-field widths, full comparison preserves the ordinary Boolean outputs and every actual wire-backed field at every input valuation. Quotient comparison masks only selected profile constraints and still preserves every ordinary output. Exact characterization, full-lift, attained-witness and universal lower-bound theorems establish quotient minimum <= full minimum <= physical gate count. Full slack plus projection defect equals physical size minus quotient minimum. Exposure masks that both retain a fixed comparison mask preserve that quotient minimum and the combined measure; nested masks transfer exactly the lost full slack into projection defect. Loss of positive full slack to zero yields an attained quotient witness with a strict deficit that cannot be used as a full witness. Forgetting all profile constraints recovers the ordinary semantic minimum. The actual all-gate source tuple, checked normalization and checked splicing connect this model to computational wire carriers without a supplied observer, semantic minimum or correctness certificate for the comparison model.

This is a proposed reconstruction of computational profile comparison, not the complete manuscript ten-role grammar or a derived governed terminal family. Ordinary outgoing Boolean interface wires cannot be forgotten. The all-gate field tuple is source-derived but is not asserted to be a canonical terminal profile. Conservation of full slack plus projection defect proves neither forced-cost transparency nor a Package E route, positive-slack activation, global rank decrease or route coverage. A quotient witness cannot be used as a full replacement without restoring every omitted field. Checked splicing still requires an equivalent open replacement and successful compilation; global discovery is not proved. Reference minima and attained witnesses use exhaustive finite minimization, not a polynomial algorithm. Unconditional SaturatePositive, BCELReady and ZeroSlack, exact polynomial PCCMin, encoded-input runtime, output and certificate bounds, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global proof gate closes, and P = NP is not proved.

Reviewed theorem interfaces (35)

PNP.DirectWire.WireProfile.mask_implementation
PNP.DirectWire.WireProfile.mask_fieldValue
PNP.DirectWire.WireProfile.full_iff
PNP.DirectWire.WireProfile.quotient_iff
PNP.DirectWire.WireProfile.full_to_quotient
PNP.DirectWire.WireProfile.full_lift_iff
PNP.DirectWire.WireProfile.fullWitness_gateCount
PNP.DirectWire.WireProfile.fullWitness_matches
PNP.DirectWire.WireProfile.fullMinimum_le_physical
PNP.DirectWire.WireProfile.quotientMinimum_le_full
PNP.DirectWire.WireProfile.quotientWitness_gateCount
PNP.DirectWire.WireProfile.quotientWitness_matches
PNP.DirectWire.WireProfile.quotient_candidate_lower_bound
PNP.DirectWire.WireProfile.full_candidate_lower_bound
PNP.DirectWire.WireProfile.fullSlack_add_projectionDefect
PNP.DirectWire.WireProfile.exposure_balance
PNP.DirectWire.WireProfile.exposure_preserves_positive_alternative
PNP.DirectWire.WireProfile.quotient_minimum_cannot_lift_of_positive_defect
PNP.DirectWire.WireProfile.exposure_loss_has_unliftable_quotient_witness
PNP.DirectWire.WireProfile.allGateFields_value
PNP.DirectWire.WireProfile.allGateFields_positive_alternative
PNP.DirectWire.WireProfile.quotientMinimum_forget_all
PNP.DirectWire.WireProfile.source_slack_balance
PNP.DirectWire.WireProfile.source_positive_alternative
PNP.DirectWire.WireProfile.mask_absorb_equivalent
PNP.DirectWire.WireProfile.quotientMinimum_mask_active
PNP.DirectWire.WireProfile.fullMinimum_mask_mono
PNP.DirectWire.WireProfile.exposure_states_balance
PNP.DirectWire.WireProfile.exposure_moves_exact_slack_to_defect
PNP.DirectWire.WireProfile.normalize_fullEquivalent
PNP.DirectWire.WireProfile.fullMinimum_normalize
PNP.DirectWire.WireProfile.quotientMinimum_normalize
PNP.DirectWire.WireProfile.splice_fullEquivalent
PNP.DirectWire.WireProfile.fullMinimum_splice
PNP.DirectWire.WireProfile.quotientMinimum_splice

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-274: formal artefact coverage becomes 250 of 252; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-derived zero-cost alias exposure

For arbitrary finite input, ordinary-output and extra-field widths, a literal output extension adds only input, constant or existing-output aliases and a literal projection recovers the original outputs without allocating gates. Both constructions transfer arbitrary equivalent realizations, proving exact equality of the semantic reference minimum and residual slack. A source-derived recognizer scans the actual output wires; a gate field is accepted exactly when an ordinary output names that same wire. The tuple compiler derives every alias and accepts exactly when all requested fields have such literal references. The actual WireCarrier exposure therefore preserves physical gate count, semantic minimum and slack whenever this executable source check accepts. Constructors and recognition do not enumerate truth tables or minimum implementations and do not receive an observer, semantic minimum, route or correctness certificate from the caller.

This covers the literal input/constant/old-output alias class, not every semantically free exposure or arbitrary hidden internal wire. Refusal proves neither semantic impossibility nor a Package E gain or route. Adding no physical gates need not preserve the semantic minimum, and unique physical ownership or an extra recorded charge does not force an equal minimum increase. The concrete counterexamples are regression and obstruction evidence, not new global progress. The existing fresh-independent-input materializer theorem is reused, not re-awarded. Full manuscript profiles, positive-cost transparency for arbitrary materializers, terminal-family derivation, global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and complete encoded-input polynomial runtime, output and certificate bounds remain open. No fixed weighted checkpoint or global proof gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (22)

PNP.DirectWire.ZeroCostExposure.Reference.toSource_eval
PNP.DirectWire.ZeroCostExposure.extend_gateCount
PNP.DirectWire.ZeroCostExposure.project_gateCount
PNP.DirectWire.ZeroCostExposure.extend_original
PNP.DirectWire.ZeroCostExposure.extend_field
PNP.DirectWire.ZeroCostExposure.project_semantics
PNP.DirectWire.ZeroCostExposure.extend_equivalent
PNP.DirectWire.ZeroCostExposure.project_equivalent
PNP.DirectWire.ZeroCostExposure.project_extend_equivalent
PNP.DirectWire.ZeroCostExposure.referenceMinimum_extend
PNP.DirectWire.ZeroCostExposure.residualSlack_extend
PNP.DirectWire.ZeroCostExposure.compileLayout_success_iff
PNP.DirectWire.ZeroCostExposure.compileLayout_sound
PNP.DirectWire.ZeroCostExposure.recognize_success_iff
PNP.DirectWire.ZeroCostExposure.recognize_isSome_iff
PNP.DirectWire.ZeroCostExposure.recognize_none_iff
PNP.DirectWire.ZeroCostExposure.recognize_gate_none_iff
PNP.DirectWire.ZeroCostExposure.checkLayout_iff
PNP.DirectWire.ZeroCostExposure.compileLayout_available_iff
PNP.DirectWire.WireCarrier.exposed_referenceMinimum_of_checkLayout
PNP.DirectWire.WireCarrier.exposed_residualSlack_of_checkLayout
PNP.DirectWire.WireCarrier.checked_exposure_preserves_problem

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-18-273: formal artefact coverage becomes 249 of 251; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Structural reordering in complete source-only replacement programs

For arbitrary finite computational wire carriers, raw swap sequences, dependency graphs and complete offered replacement programs, computed structural actions preserve the literal exposed field sources, ordered output values and exact syntactic causal labels. The raw decoder validates the entire sequence against the current carrier, not the initial gate count. The exact pending snapshot function, charge count and removal count are preserved. Local physical ownership comes from the actual backward gate bijection, and the complete program lifts it through the prior ledger without resetting earlier allocations or removals. Structural actions interleave with primitive obligations and descendant-support programs while preserving full output and field semantics, creation-to-discharge bindings, unique event identities, causal invariants and physical ownership. The existing proper-support certificate verifier over this expanded action language still requires a complete accepted program, a closed final ledger and actual strict signed saving. Invalid later operations reject the whole program rather than returning a successful prefix; reordering alone earns no strict saving. Callers supply raw data, not correctness, transport, order, causality or ownership witnesses.

This is integration of checked offered programs, not a successful certificate-discovery strategy for every input. Finite executions are regression evidence, not theorem authority. The computational carrier does not establish full manuscript profile semantics or all R1-R9 and N1-N10 rules. Full manuscript VerifyDW, ChargeSoundness and Package E, global certificate discovery, terminal-family derivation and global route coverage remain open. There is no encoded-input polynomial runtime, output-size or certificate-size theorem for the complete construction. Unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global gate closes, and P = NP is not proved.

Reviewed theorem interfaces (63)

PNP.DirectWire.StructuralReindexing.result_gate_level
PNP.DirectWire.StructuralReindexing.result_source_level
PNP.DirectWire.StructuralReindexing.result_output_level
PNP.DirectWire.WireCarrier.reindex_exposed
PNP.DirectWire.WireCarrier.reindex_gateCount
PNP.DirectWire.WireCarrier.reindex_backward_forward
PNP.DirectWire.WireCarrier.reindex_forward_backward
PNP.DirectWire.WireCarrier.reindex_output
PNP.DirectWire.WireCarrier.reindex_field
PNP.DirectWire.WireCarrier.reindex_field_source
PNP.DirectWire.WireCarrier.reindex_exposed_level
PNP.DirectWire.WireCarrier.reindex_output_level
PNP.DirectWire.WireCarrier.reindex_field_level
PNP.DirectWire.WireCarrier.reindex_causalBounds
PNP.DirectWire.WireObligationHistory.State.reindex_pending
PNP.DirectWire.WireObligationHistory.State.reindex_charged
PNP.DirectWire.WireObligationHistory.State.reindex_removed
PNP.DirectWire.WireObligationHistory.State.reindex_gateCount
PNP.DirectWire.WireObligationHistory.State.reindex_causalInvariant
PNP.DirectWire.WireStructuralState.execute_isSome
PNP.DirectWire.WireStructuralState.execute_failure_iff
PNP.DirectWire.WireStructuralState.Receipt.ownership_origin
PNP.DirectWire.WireStructuralState.Receipt.ownership_origin_forward
PNP.DirectWire.WireStructuralState.Receipt.ownership_origin_injective
PNP.DirectWire.WireStructuralState.Receipt.ownership_live_members
PNP.DirectWire.WireStructuralState.Receipt.ownership_not_allocated
PNP.DirectWire.WireStructuralState.Receipt.ownership_charged
PNP.DirectWire.WireStructuralState.Receipt.ownership_removed
PNP.DirectWire.WireStructuralState.Receipt.ownership_wellFormed
PNP.DirectWire.WireStructuralState.Receipt.physical_ownership
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_origin
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed
PNP.DirectWire.WireOpenProgram.orderEvents_success_iff
PNP.DirectWire.WireOpenProgram.orderEvents_failure_iff
PNP.DirectWire.WireOpenProgram.execute_failed_tail
PNP.DirectWire.WireOpenProgram.CompiledProgram.full_output
PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field
PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle
PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_count
PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_identities_nodup
PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant
PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_origin_injective
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_charge_origin
PNP.DirectWire.WireOpenProgram.compile_exists_iff
PNP.DirectWire.WireOpenProgram.compile_none_iff
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.proper_support
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle
PNP.DirectWire.WireOpenCertificate.verify_exists_iff
PNP.DirectWire.WireOpenCertificate.verify_sound
PNP.DirectWire.WireOpenCertificate.verify_decode_none
PNP.DirectWire.WireOpenCertificate.verify_program_none
PNP.DirectWire.WireOpenCertificate.verify_not_proper
PNP.DirectWire.WireOpenCertificate.verify_no_gain

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-271: formal artefact coverage becomes 247 of 249; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computational recoding in complete source-only replacement programs

For arbitrary finite computational wire carriers, literal NAND encoder and decoder circuits, dependency graphs and complete offered replacement programs, raw recoding actions reuse the existing circuit format and validate both dimensions and every gate and output reference. A complete finite check derives both inverse equations. An independent exact syntactic dependency guard covers all ordinary outputs and hidden fields for every natural-valued input labelling. Actual encoder and decoder gates are appended, normalized and charged; actual compiler maps determine deletions and disjoint allocation identities. Recoding retains the entire pending snapshot function and cannot create or discharge an obligation. Complete-program execution lifts those physical identities through prior history, preserves full semantics, costs, causal invariants and creation-to-discharge bindings, and rejects an invalid later action rather than accepting a prefix. The proper-support certificate verifier still requires complete execution, a closed final ledger and strict actual saving. The existing structural decoder also has a constructive exact encoding of every finite gate bijection with at most one swap per gate. Callers supply raw data, not correctness, causal, ordering, ownership or cost authority.

This checks offered computational programs, not a successful certificate-discovery strategy for every input. The inverse checker enumerates all field valuations; finite termination and a bounded structural swap list do not establish uniformly polynomial encoded runtime or certificate size. Semantic reversibility does not imply physical cancellation or strict saving. Full manuscript profiles, all R1-R9 and N1-N10 rules, full VerifyDW, ChargeSoundness and Package E remain open. Terminal-family derivation, global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global proof gate closes, and P = NP is not proved.

Reviewed theorem interfaces (88)

PNP.DirectWire.StructuralReindexing.GateRenaming.decode_encode
PNP.DirectWire.StructuralReindexing.GateRenaming.encode_length_le
PNP.DirectWire.StructuralReindexing.GateRenaming.validCode_encode
PNP.DirectWire.WireCarrierRecoding.roundTripCheck_iff
PNP.DirectWire.WireCarrierRecoding.check_iff
PNP.DirectWire.WireCarrierRecoding.compile_success_iff
PNP.DirectWire.WireCarrierRecoding.appendMap_gateCount
PNP.DirectWire.WireCarrierRecoding.appendMap_output
PNP.DirectWire.WireCarrierRecoding.appendMap_field
PNP.DirectWire.WireCarrierRecoding.encoded_output
PNP.DirectWire.WireCarrierRecoding.encoded_field
PNP.DirectWire.WireCarrierRecoding.result_output
PNP.DirectWire.WireCarrierRecoding.result_field
PNP.DirectWire.WireCarrierRecoding.result_gate_balance
PNP.DirectWire.CausalBound.levels_bounded_iff
PNP.DirectWire.CausalBound.source_bounded_iff
PNP.DirectWire.CausalBound.sourceDependencyGuard_iff
PNP.DirectWire.CausalBound.candidateDependencyGuard_iff
PNP.DirectWire.WireCarrier.dependencyGuard_iff
PNP.DirectWire.WireObligationHistory.State.recode_pending
PNP.DirectWire.WireObligationHistory.State.recode_charged
PNP.DirectWire.WireObligationHistory.State.recode_removed
PNP.DirectWire.WireObligationHistory.State.recode_causalInvariant
PNP.DirectWire.WireRecodingState.execute_success_iff
PNP.DirectWire.WireRecodingState.execute_failure_iff
PNP.DirectWire.WireRecodingState.Receipt.pending
PNP.DirectWire.WireRecodingState.Receipt.causalInvariant
PNP.DirectWire.WireRecodingState.Receipt.gate_balance
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.encoder_positions
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.encoded_origin
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.decoder_positions
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.ledger_origin
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.ledger_charged
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.ledger_removed_length
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.ledger_partition
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.allocation_phases_nodup
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.physical_ownership
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.labelled_live
PNP.DirectWire.WireCarrierRecoding.PhysicalAccounting.labelled_physical_ownership
PNP.DirectWire.WireRecodingState.Receipt.physical_ownership
PNP.DirectWire.WireRecodingInput.decode_encode
PNP.DirectWire.WireRecodingInput.decode_elaboration_none
PNP.DirectWire.WireRecodingInput.decode_success_iff
PNP.DirectWire.WireRecodingInput.execute_success_iff
PNP.DirectWire.WireRecodingInput.execute_encoder_none
PNP.DirectWire.WireRecodingInput.execute_decoder_none
PNP.DirectWire.WireRecodingInput.Receipt.pending
PNP.DirectWire.WireRecodingInput.Receipt.charged_eq
PNP.DirectWire.WireRecodingInput.Receipt.removed_eq
PNP.DirectWire.WireRecodingInput.Receipt.causalInvariant
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_origin
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed
PNP.DirectWire.WireOpenProgram.orderEvents_success_iff
PNP.DirectWire.WireOpenProgram.orderEvents_failure_iff
PNP.DirectWire.WireOpenProgram.execute_failed_tail
PNP.DirectWire.WireOpenProgram.CompiledProgram.full_output
PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field
PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle
PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_count
PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_identities_nodup
PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant
PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_origin_injective
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_charge_origin
PNP.DirectWire.WireOpenProgram.compile_exists_iff
PNP.DirectWire.WireOpenProgram.compile_none_iff
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.proper_support
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle
PNP.DirectWire.WireOpenCertificate.verify_exists_iff
PNP.DirectWire.WireOpenCertificate.verify_sound
PNP.DirectWire.WireOpenCertificate.verify_decode_none
PNP.DirectWire.WireOpenCertificate.verify_program_none
PNP.DirectWire.WireOpenCertificate.verify_not_proper
PNP.DirectWire.WireOpenCertificate.verify_no_gain
PNP.DirectWire.WireOpenProgram.Transition.charged_eq
PNP.DirectWire.WireOpenProgram.Transition.removed_eq
PNP.DirectWire.WireOpenProgram.Transition.causalInvariant
PNP.DirectWire.WireOpenProgram.Transition.local_physical_ownership
PNP.DirectWire.WireOpenProgram.CompiledProgram.gate_balance

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-18-272: formal artefact coverage becomes 248 of 250; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Structural reordering and arbitrary-support replacement transport

For arbitrary finite computational wire candidates and checked finite raw index-swap sequences, structural reindexing constructs the raw graph and its successful compilation from the original circuit. Actual compiler placement and inverse placement determine literal gate-source pairs and ordered output references. For every descendant primitive-record list, including empty, full and duplicate-bearing lists, the construction derives the predecessor records and canonical boundary, interface, selected-gate and exterior bijections. Open support functions agree for every independent boundary valuation. A replacement is pulled back by literal input and output rewiring without padding; support and replacement counts agree, both matched signed surcharges are zero, and exact signed saving and strict gain are preserved. Complete raw splices have corresponding source pairs, outputs and dependency edges, with equivalent acyclicity and compiler success or rejection in both directions. Actual compiled-position maps preserve exterior and replacement ownership and literal sources. An actually accepted compatible descendant splice computes an accepted predecessor splice preserving whole-circuit semantics and exact local and whole signed savings. No predecessor compilation, order, transport map or source-fidelity witness is supplied.

This closes the computational structural-reordering component of arbitrary-support replacement transport, not full manuscript profile semantics: transported profile labels are not a proof of profile semantics. It does not establish completeness of the raw-swap encoding for every abstract permutation, all R1-R9 or N1-N10 rules, or the remaining normalization and materializer transport. Open replacement compatibility is required for semantic preservation, and actual descendant compiler acceptance is required for compiled pullback; a compatible arbitrary replacement need not be acyclic. Full manuscript VerifyDW, ChargeSoundness and Package E, global certificate discovery, terminal-family derivation and global route coverage remain open. There is no encoded-input polynomial runtime, output-size or certificate-size theorem for the complete construction. Unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin, deterministic CNFSAT in P and the eligible root remain open. Finite execution fixtures are regression evidence, not theorem authority. No fixed weighted checkpoint or global gate closes, and P = NP is not proved.

Reviewed theorem interfaces (108)

PNP.DirectWire.RawNandWireStructure.initial_faithful
PNP.DirectWire.RawNandWireStructure.apply_faithful
PNP.DirectWire.RawNandWireStructure.run_faithful
PNP.DirectWire.RawNandWireStructure.finish_sources
PNP.DirectWire.RawNandWireStructure.compile_sources
PNP.DirectWire.RawNandWireStructure.physicalOrigin_sources
PNP.DirectWire.StructuralReindexing.GateRenaming.forward_injective
PNP.DirectWire.StructuralReindexing.GateRenaming.backward_injective
PNP.DirectWire.StructuralReindexing.GateRenaming.decode_isSome
PNP.DirectWire.StructuralReindexing.sourceMap_compose
PNP.DirectWire.StructuralReindexing.sourceMap_eq_gate_iff
PNP.DirectWire.StructuralReindexing.sourceMap_eval
PNP.DirectWire.StructuralReindexing.graph_edge_ordered
PNP.DirectWire.StructuralReindexing.graph_wellFounded
PNP.DirectWire.StructuralReindexing.compile_isSome
PNP.DirectWire.StructuralReindexing.compiled_accepted
PNP.DirectWire.StructuralReindexing.backward_forward
PNP.DirectWire.StructuralReindexing.forward_backward
PNP.DirectWire.StructuralReindexing.forwardGate_injective
PNP.DirectWire.StructuralReindexing.backwardGate_injective
PNP.DirectWire.StructuralReindexing.translated_source
PNP.DirectWire.StructuralReindexing.result_sources
PNP.DirectWire.StructuralReindexing.result_output_source
PNP.DirectWire.StructuralReindexing.result_gateCount
PNP.DirectWire.StructuralReindexing.graph_solution
PNP.DirectWire.StructuralReindexing.result_semantics
PNP.DirectWire.StructuralReindexing.attempt_isSome
PNP.DirectWire.StructuralReindexing.attempt_semantics
PNP.DirectWire.StructuralReindexing.attempt_gateCount
PNP.DirectWire.StructuralReindexing.backward_forward_wire
PNP.DirectWire.StructuralReindexing.forward_backward_wire
PNP.DirectWire.StructuralReindexing.backward_forward_record
PNP.DirectWire.StructuralReindexing.forward_backward_record
PNP.DirectWire.StructuralReindexing.forwardRecord_injective
PNP.DirectWire.StructuralReindexing.backward_forward_records
PNP.DirectWire.StructuralReindexing.forward_backward_records
PNP.DirectWire.StructuralReindexing.forwardRecord_mem
PNP.DirectWire.StructuralReindexing.selected_forward
PNP.DirectWire.StructuralReindexing.external_forward
PNP.DirectWire.StructuralReindexing.backward_forward_source
PNP.DirectWire.StructuralReindexing.sourceMap_forward_injective
PNP.DirectWire.StructuralReindexing.source_wire_map
PNP.DirectWire.StructuralReindexing.source_wire_iff
PNP.DirectWire.StructuralReindexing.uses_forward
PNP.DirectWire.StructuralReindexing.boundary_forward
PNP.DirectWire.StructuralReindexing.externalConsumer_forward
PNP.DirectWire.StructuralReindexing.globalOutput_forward
PNP.DirectWire.StructuralReindexing.interface_forward
PNP.DirectWire.StructuralReindexing.boundary_ports_forward
PNP.DirectWire.StructuralReindexing.interface_ports_forward
PNP.DirectWire.StructuralReindexing.descendant_boundary
PNP.DirectWire.StructuralReindexing.descendant_interface
PNP.DirectWire.StructuralReindexing.selected_backward
PNP.DirectWire.StructuralReindexing.pull_push_boundary_valuation
PNP.DirectWire.StructuralReindexing.push_pull_boundary_valuation
PNP.DirectWire.StructuralReindexing.selected_gate_count
PNP.DirectWire.StructuralReindexing.exterior_gate_count
PNP.DirectWire.StructuralReindexing.external_wire_value_preserved
PNP.DirectWire.StructuralReindexing.open_gate_preserved
PNP.DirectWire.StructuralReindexing.open_support_preserved
PNP.DirectWire.StructuralReindexing.open_support_pullback
PNP.DirectWire.StructuralReindexing.extracted_support_preserved
PNP.DirectWire.StructuralReindexing.renameInputs_gateSources
PNP.DirectWire.StructuralReindexing.pullReplacement_program
PNP.DirectWire.StructuralReindexing.pullReplacement_gate_sources
PNP.DirectWire.StructuralReindexing.pullReplacement_output_source
PNP.DirectWire.StructuralReindexing.pullReplacement_gate_count
PNP.DirectWire.StructuralReindexing.pullReplacement_semantics
PNP.DirectWire.StructuralReindexing.pullReplacement_compatible
PNP.DirectWire.StructuralReindexing.support_gate_count
PNP.DirectWire.StructuralReindexing.support_surcharge_zero
PNP.DirectWire.StructuralReindexing.replacement_surcharge_zero
PNP.DirectWire.StructuralReindexing.matched_surcharge
PNP.DirectWire.StructuralReindexing.replacement_saving_preserved
PNP.DirectWire.StructuralReindexing.strict_gain_pullback
PNP.DirectWire.StructuralReindexing.spliceForward_exterior
PNP.DirectWire.StructuralReindexing.spliceForward_replacement
PNP.DirectWire.StructuralReindexing.spliceBackward_exterior
PNP.DirectWire.StructuralReindexing.spliceBackward_replacement
PNP.DirectWire.StructuralReindexing.splice_backward_forward
PNP.DirectWire.StructuralReindexing.splice_forward_backward
PNP.DirectWire.StructuralReindexing.splice_boundarySource_forward
PNP.DirectWire.StructuralReindexing.splice_replacementSource_forward
PNP.DirectWire.StructuralReindexing.splice_sources
PNP.DirectWire.StructuralReindexing.splice_output_source
PNP.DirectWire.StructuralReindexing.splice_dependencies
PNP.DirectWire.StructuralReindexing.splice_wellFounded_iff
PNP.DirectWire.StructuralReindexing.splice_compile_success_iff
PNP.DirectWire.StructuralReindexing.splice_compile_failure_iff
PNP.DirectWire.StructuralReindexing.splice_physical_backward_forward
PNP.DirectWire.StructuralReindexing.splice_physical_forward_backward
PNP.DirectWire.StructuralReindexing.splice_physical_position
PNP.DirectWire.StructuralReindexing.splice_physical_exterior
PNP.DirectWire.StructuralReindexing.splice_physical_replacement
PNP.DirectWire.StructuralReindexing.splice_compiled_sources
PNP.DirectWire.StructuralReindexing.splice_compiled_output_source
PNP.DirectWire.StructuralReindexing.splice_compiled_gate_count
PNP.DirectWire.StructuralReindexing.splice_compiled_semantics
PNP.DirectWire.StructuralReindexing.pull_splice_isSome
PNP.DirectWire.StructuralReindexing.pullCompiledSplice_accepted
PNP.DirectWire.StructuralReindexing.literal_replacement_transport
PNP.DirectWire.terminalOpenGateEvaluation_sourceEquation
PNP.DirectWire.terminalOpenWireValue_boundary_get
PNP.DirectWire.terminalOpenWireValue_external_absent
PNP.DirectWire.ArbitrarySupportSplice.boundarySource_input
PNP.DirectWire.ArbitrarySupportSplice.boundarySource_gate
PNP.DirectWire.ArbitrarySupportSplice.originalSource_exterior
PNP.DirectWire.ArbitrarySupportSplice.originalSource_interface

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-270: formal artefact coverage becomes 246 of 248; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Open obligations across complete descendant-support programs

For arbitrary finite computational wire carriers, raw outer support records and raw mixed programs, source-only verification computes the complete dependency order, including intrinsic creation references, and executes every primitive or actual descendant-support splice from its internally constructed initial state. The same pending creations and captured full-value snapshots persist across intervening support changes until genuine full-mode R6, R7 or R8 discharge; final ambient closure is required. Execution-derived causal bounds construct the literal outer splice. Acceptance is exactly complete decoding and finally closed execution on a proper physical support with strict final saving. The result preserves all ordinary outputs and literal fields, includes the exterior once, and reconstructs unique original/allocation ownership through the actual compiler positions. Computed outer-position namespaces distinguish nested event identities; historical charges and removals survive later allocation deletion. Temporary expansion is allowed; malformed, cyclic, missing or duplicate references, unfinished ledgers, failed tails, whole supports and final nondecrease reject. No intermediate carrier, schedule, snapshot, correctness, cost, owner, rank or splice witness is supplied.

This verifies offered arbitrary finite mixed programs in the computational wire-carrier language; inner descendant histories retain their existing closed-history boundary. It does not find an accepted certificate for every nonminimal input, establish local minimality after rejection, or construct a globally successful strategy. Full manuscript profiles and all R1-R9 and N1-N10 rule families, matched-kappa arbitrary-support Pull/Expand, full manuscript VerifyDW, ChargeSoundness and Package E, and terminal-family derivation remain open. There is no bound on temporary growth or encoded-input polynomial runtime, output size or certificate size. Global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin, deterministic CNFSAT in P and the eligible root remain open. Finite runtime fixtures are regression evidence, not theorem authority. No fixed weighted checkpoint or global gate closes, and P = NP is not proved.

Reviewed theorem interfaces (144)

PNP.DirectWire.WireOpenSupportSplice.transfer_pending
PNP.DirectWire.WireOpenSupportSplice.transfer_keep
PNP.DirectWire.WireOpenSupportSplice.transfer_snapshot
PNP.DirectWire.WireOpenSupportSplice.transfer_charge
PNP.DirectWire.WireOpenSupportSplice.transfer_removal
PNP.DirectWire.WireOpenSupportSplice.transfer_output
PNP.DirectWire.WireOpenSupportSplice.transfer_available
PNP.DirectWire.WireOpenSupportSplice.transfer_balance
PNP.DirectWire.WireOpenSupportSplice.replacement_dependency_bound
PNP.DirectWire.WireOpenSupportSplice.result_exposed_dependency_bound
PNP.DirectWire.WireOpenSupportSplice.result_causal_bounds
PNP.DirectWire.WireOpenSupportSplice.transfer_causal_invariant
PNP.DirectWire.WireOpenSupportSplice.Receipt.pending
PNP.DirectWire.WireOpenSupportSplice.Receipt.records_source
PNP.DirectWire.WireOpenSupportSplice.execute_of_compiled
PNP.DirectWire.WireOpenSupportSplice.execute_exists_iff
PNP.DirectWire.WireOpenProgram.uniqueIDs_iff
PNP.DirectWire.WireOpenProgram.completeReferences_iff
PNP.DirectWire.WireOpenProgram.graph_dependency_iff
PNP.DirectWire.WireOpenProgram.OrderedEvents.order_complete
PNP.DirectWire.WireOpenProgram.OrderedEvents.order_nodup
PNP.DirectWire.WireOpenProgram.OrderedEvents.order_length
PNP.DirectWire.WireOpenProgram.OrderedEvents.identities_nodup
PNP.DirectWire.WireOpenProgram.orderEvents_success_iff
PNP.DirectWire.WireOpenProgram.orderEvents_failure_iff
PNP.DirectWire.WireOpenProgram.Transition.charged_eq
PNP.DirectWire.WireOpenProgram.Transition.removed_eq
PNP.DirectWire.WireOpenProgram.Transition.dischargeRecord_binding
PNP.DirectWire.WireOpenProgram.Transition.pending_persists_or_discharged
PNP.DirectWire.WireOpenProgram.Transition.created_pending
PNP.DirectWire.WireOpenProgram.Transition.causalInvariant
PNP.DirectWire.WireOpenProgram.execute_failed_tail
PNP.DirectWire.WireOpenProgram.Execution.total_charge
PNP.DirectWire.WireOpenProgram.Execution.total_removed
PNP.DirectWire.WireOpenProgram.Execution.record_identities
PNP.DirectWire.WireOpenProgram.Execution.pending_persists_or_discharged
PNP.DirectWire.WireOpenProgram.Execution.creationsClosed_of_finalClosed
PNP.DirectWire.WireOpenProgram.Execution.causalInvariant
PNP.DirectWire.WireOpenProgram.CompiledProgram.closed
PNP.DirectWire.WireOpenProgram.CompiledProgram.full_output
PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field
PNP.DirectWire.WireOpenProgram.CompiledProgram.gate_balance
PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle
PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_count
PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_identities_nodup
PNP.DirectWire.WireOpenProgram.CompiledProgram.dependency_before
PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant
PNP.DirectWire.WireOpenProgram.CompiledProgram.output_causal_bound
PNP.DirectWire.WireOpenProgram.CompiledProgram.field_causal_bound
PNP.DirectWire.WireOpenProgram.compile_exists_iff
PNP.DirectWire.WireOpenProgram.compile_none_iff
PNP.DirectWire.WireOpenSupportSplice.ownershipLift_original
PNP.DirectWire.WireOpenSupportSplice.ownershipLift_allocated
PNP.DirectWire.WireOpenSupportSplice.ownershipLift_injective
PNP.DirectWire.WireOpenSupportSplice.ownershipRawNode_exterior
PNP.DirectWire.WireOpenSupportSplice.ownershipRawNode_nested
PNP.DirectWire.WireOpenSupportSplice.ownership_compiled_position
PNP.DirectWire.WireOpenSupportSplice.ownership_partition
PNP.DirectWire.WireOpenSupportSplice.ownership_charged_origin
PNP.DirectWire.WireOpenSupportSplice.ownership_distinct
PNP.DirectWire.WireOpenSupportSplice.physical_ownership
PNP.DirectWire.WireOpenSupportSplice.Receipt.physical_ownership
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.allocations_nodup
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.advance_charged
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.advance_removed_length
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.advance_conservation
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.ledger_charged
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.ledger_removed_length
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.ledger_partition
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.physical_ownership
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.lift_injective
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.labelled_live
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.labelled_physical_ownership
PNP.DirectWire.WireOpenProgram.PrimitiveOwnership.labelled_charged_origin
PNP.DirectWire.WireOpenProgram.Transition.local_physical_ownership
PNP.DirectWire.WireOpenProgram.Transition.local_charged_origin
PNP.DirectWire.WireOpenProgram.bornBefore_mono
PNP.DirectWire.WireOpenProgram.ProgramOwnership.initial_wellFormed
PNP.DirectWire.WireOpenProgram.ProgramOwnership.accounted_before
PNP.DirectWire.WireOpenProgram.ProgramOwnership.origin_before
PNP.DirectWire.WireOpenProgram.ProgramOwnership.origin_injective
PNP.DirectWire.WireOpenProgram.ProgramOwnership.liftOrigin_original
PNP.DirectWire.WireOpenProgram.ProgramOwnership.liftOrigin_allocated
PNP.DirectWire.WireOpenProgram.ProgramOwnership.liftOrigin_injective
PNP.DirectWire.WireOpenProgram.ProgramOwnership.lift_originals
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_live
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_charged_length
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_removed_length
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_charge_origin
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_physical_position
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_support_compiled_position
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_partition
PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_wellFormed
PNP.DirectWire.WireOpenProgram.Execution.carryOwnership_wellFormed
PNP.DirectWire.WireOpenProgram.Execution.carryOwnership_charged_length
PNP.DirectWire.WireOpenProgram.Execution.carryOwnership_removed_length
PNP.DirectWire.WireOpenProgram.Execution.carryOwnership_charge_survives
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_wellFormed
PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_origin_injective
PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_charge_origin
PNP.DirectWire.WireOpenProgram.allocation_namespaces_disjoint
PNP.DirectWire.WireOpenProperSupport.program_equivalent
PNP.DirectWire.WireOpenProperSupport.program_causalInterfaceBound
PNP.DirectWire.WireOpenProperSupport.program_compiles
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.output
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.field
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.gateCount
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.charge_accounting
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.gain_iff_local_gain
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.gain_iff_net_charges
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.strictGain
PNP.DirectWire.WireOpenProperSupport.SplicedProgram.strictResidualDescent
PNP.DirectWire.WireOpenProperSupport.compile_complete
PNP.DirectWire.WireOpenProperSupport.compile_exists_iff
PNP.DirectWire.WireOpenProperSupport.compile_none_iff
PNP.DirectWire.WireOpenProperSupport.ownershipLift_original
PNP.DirectWire.WireOpenProperSupport.ownershipLift_allocated
PNP.DirectWire.WireOpenProperSupport.ownershipLift_injective
PNP.DirectWire.WireOpenProperSupport.ownershipRawNode_exterior
PNP.DirectWire.WireOpenProperSupport.ownershipRawNode_program
PNP.DirectWire.WireOpenProperSupport.ownership_compiled_position
PNP.DirectWire.WireOpenProperSupport.ownership_partition
PNP.DirectWire.WireOpenProperSupport.ownership_charged_origin
PNP.DirectWire.WireOpenProperSupport.ownership_distinct
PNP.DirectWire.WireOpenProperSupport.physical_ownership
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.proper_support
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.gateCount
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger
PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle
PNP.DirectWire.WireOpenCertificate.verify_complete
PNP.DirectWire.WireOpenCertificate.verify_exists_iff
PNP.DirectWire.WireOpenCertificate.verify_sound
PNP.DirectWire.WireOpenCertificate.verify_decode_none
PNP.DirectWire.WireOpenCertificate.verify_program_none
PNP.DirectWire.WireOpenCertificate.verify_not_proper
PNP.DirectWire.WireOpenCertificate.verify_no_gain

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-269: formal artefact coverage becomes 245 of 247; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Concrete machine and cost kernel

One literal finite four-stage pipeline handles every raw bitstring. The total framer uses exactly 4 work steps on empty input, 4 * k * k + 9 * k + 7 for complete two-bit cells, and 4 * k * k + 9 * k + 5 when the final cell is partial; its compiled raw cost is bounded by 6 * m * m + 39 * m + 75. Every supplied exact n-step target run lifts to exactly 3 * n work steps. PipelineCompiler preserves one raw target's verdict and ordinary output at an explicit external polynomial. PipelineSequentialCompiler composes two raw targets in one literal finite table, passes either first verdict onward, preserves the second verdict and output, retains stuck-first timeout, and proves R(m) = PipelineRaw(p)(m) + 6 + PipelineRaw(q)(m + p(m) + 1). PipelineRefinement recursively applies that compiler to every FunctionProgram composition and DecisionProgram precomposition node. Its 16 audited declarations have empty axiom closure, and PolynomialTimeDecider.compileToMachine exposes the complete tree as one raw polynomial-time machine.

This closes the concrete complexity machine-link blocker only. It does not construct a deterministic polynomial-time CNF-SAT decider or an NP-completeness reduction. CNF-SAT in P, NP-completeness, and P = NP are not established; PNP.Main.p_eq_np remains absent and the publication gate remains false.

Reviewed theorem interfaces (161)

PNP.Concrete.BitString.decodePair_pair
PNP.Concrete.DecisionProgram.RawRefinement.compile_haltsWithin
PNP.Concrete.DecisionProgram.RawRefinement.compile_verdict_eq
PNP.Concrete.FunctionProgram.RawRefinement.compile_haltsWithin
PNP.Concrete.FunctionProgram.RawRefinement.compile_output_eq
PNP.Concrete.NatPolynomial.eval_mono
PNP.Concrete.PipelineCompiler.acceptingSuppliedTrace_workRunExact_of_rawRunExact
PNP.Concrete.PipelineCompiler.outputBits_length_le_pipelineOutputSizeBound_of_rawRunExact
PNP.Concrete.PipelineCompiler.pipelineOutputSizeBound_eval
PNP.Concrete.PipelineCompiler.pipeline_accepts_iff
PNP.Concrete.PipelineCompiler.pipeline_boundedDecide_eq
PNP.Concrete.PipelineCompiler.pipeline_correct
PNP.Concrete.PipelineCompiler.pipeline_machineOutput_eq
PNP.Concrete.PipelineCompiler.pipeline_ne_timeout
PNP.Concrete.PipelineCompiler.pipeline_timeout_of_stuck_rawRunExact
PNP.Concrete.PipelineCompiler.rejectingSuppliedTrace_workRunExact_of_rawRunExact
PNP.Concrete.PipelineCompiler.run_pipeline_accept_at_bound_of_rawRunExact
PNP.Concrete.PipelineCompiler.run_pipeline_reject_at_bound_of_rawRunExact
PNP.Concrete.PipelineCompiler.suppliedTraceRawSteps_le_of_rawRunExact
PNP.Concrete.PipelineCompiler.suppliedTraceRawSteps_le_pipelineRawTimeBound
PNP.Concrete.PipelineCompiler.totalInputLaunch_workStep
PNP.Concrete.PipelineSequentialCompiler.acceptingSequentialTrace_workRunExact_of_rawRunExact
PNP.Concrete.PipelineSequentialCompiler.firstOutputSizeBound_eval
PNP.Concrete.PipelineSequentialCompiler.firstTraceAndLaunch_workRunExact_of_rawRunExact
PNP.Concrete.PipelineSequentialCompiler.rejectingSequentialTrace_workRunExact_of_rawRunExact
PNP.Concrete.PipelineSequentialCompiler.run_sequential_accept_at_bound_of_rawRunExact
PNP.Concrete.PipelineSequentialCompiler.run_sequential_reject_at_bound_of_rawRunExact
PNP.Concrete.PipelineSequentialCompiler.sequentialOutputSizeBound_eval
PNP.Concrete.PipelineSequentialCompiler.sequentialRawSteps_le_of_rawRunExact
PNP.Concrete.PipelineSequentialCompiler.sequentialRawSteps_le_sequentialRawTimeBound
PNP.Concrete.PipelineSequentialCompiler.sequential_accepts_iff
PNP.Concrete.PipelineSequentialCompiler.sequential_boundedDecide_eq
PNP.Concrete.PipelineSequentialCompiler.sequential_correct
PNP.Concrete.PipelineSequentialCompiler.sequential_machineOutput_eq
PNP.Concrete.PipelineSequentialCompiler.sequential_ne_timeout
PNP.Concrete.PipelineSequentialCompiler.sequential_timeout_of_stuck_first_rawRunExact
PNP.Concrete.PipelineSequentialStateNamespace.findWorkRule_sequential_first_of_some
PNP.Concrete.PipelineSequentialStateNamespace.findWorkRule_sequential_second_of_some
PNP.Concrete.PipelineSequentialStateNamespace.firstAcceptLaunch_workStep
PNP.Concrete.PipelineSequentialStateNamespace.firstPipelineState_ne_secondPipelineState
PNP.Concrete.PipelineSequentialStateNamespace.firstRejectLaunch_workStep
PNP.Concrete.PipelineSequentialStateNamespace.sequentialWorkMachine_acceptState_ne_rejectState
PNP.Concrete.PolynomialTimeDecider.compileToMachine_accepts_iff
PNP.Concrete.PipelineInputFramer.boundedDecide_compilePairedInputFramer_accept
PNP.Concrete.PipelineInputFramer.boundedDecide_compileTotalInputFramer_accept
PNP.Concrete.PipelineInputFramer.boundedDecide_compileTotalInputFramer_ne_timeout
PNP.Concrete.PipelineInputFramer.pairedInputFramerFinal_isHalted
PNP.Concrete.PipelineInputFramer.pairedInputFramerFinal_represents
PNP.Concrete.PipelineInputFramer.pairedInputFramerRawTimeBound_exact
PNP.Concrete.PipelineInputFramer.pairedInputFramer_workRunExact
PNP.Concrete.PipelineInputFramer.run_compilePairedInputFramer_rawTimeBound
PNP.Concrete.PipelineInputFramer.run_compileTotalInputFramer_encoded_rawTimeBound
PNP.Concrete.PipelineInputFramer.run_compileTotalInputFramer_rawTimeBound_blankEquivalent
PNP.Concrete.PipelineInputFramer.totalInputFramerFinal_isHalted
PNP.Concrete.PipelineInputFramer.totalInputFramerFinal_represents
PNP.Concrete.PipelineInputFramer.totalInputFramerRawTimeBound_le
PNP.Concrete.PipelineInputFramer.totalInputFramer_workRunExact
PNP.Concrete.PipelineMachineSimulation.findIndexedRawRuleFrom_map_snd
PNP.Concrete.PipelineMachineSimulation.find_liftMachine_entry
PNP.Concrete.PipelineMachineSimulation.liftMachine_isHalted_eq_of_representsConfiguration
PNP.Concrete.PipelineMachineSimulation.rawRunExact?_exists_le_run
PNP.Concrete.PipelineMachineSimulation.run_compileWorkMachine_eighteen_mul_of_rawRunExact
PNP.Concrete.PipelineMachineSimulation.run_compileWorkMachine_eighteen_mul_of_run_halted
PNP.Concrete.PipelineMachineSimulation.run_compileWorkMachine_eighteen_of_step
PNP.Concrete.PipelineMachineSimulation.workRunExact_three_mul_of_rawRunExact
PNP.Concrete.PipelineMachineSimulation.workRunExact_three_of_step
PNP.Concrete.PipelineMachineSimulation.workRun_three_mul_of_run_halted
PNP.Concrete.PipelineOutputHandoff.framedOutputHandoffFinal_isHalted
PNP.Concrete.PipelineOutputHandoff.framedOutputHandoffRawTimeBound_exact
PNP.Concrete.PipelineOutputHandoff.framedOutputHandoff_workRunExact_of_represents
PNP.Concrete.PipelineOutputHandoff.run_compileFramedOutputHandoff_of_represents
PNP.Concrete.PipelinePairedCompiler.machineOutput_length_le_input_add_fuel
PNP.Concrete.PipelinePairedCompiler.outputBits_length_le_pairedPipelineOutputSizeBound_of_rawRunExact
PNP.Concrete.PipelinePairedCompiler.pairedPipelineOutputSizeBound_eval
PNP.Concrete.PipelinePairedCompiler.pairedPipeline_accepts_iff
PNP.Concrete.PipelinePairedCompiler.pairedPipeline_boundedDecide_eq
PNP.Concrete.PipelinePairedCompiler.pairedPipeline_correct_on_pair
PNP.Concrete.PipelinePairedCompiler.pairedPipeline_machineOutput_eq
PNP.Concrete.PipelinePairedCompiler.pairedPipeline_ne_timeout
PNP.Concrete.PipelinePairedCompiler.run_pairedPipeline_accept_at_bound_of_rawRunExact
PNP.Concrete.PipelinePairedCompiler.run_pairedPipeline_reject_at_bound_of_rawRunExact
PNP.Concrete.PipelinePairedCompiler.suppliedTraceTerminalRawSteps_le_of_rawRunExact
PNP.Concrete.PipelinePairedCompiler.suppliedTraceTerminalRawSteps_le_pairedPipelineRawTimeBound
PNP.Concrete.PipelineStageBridges.acceptingHandoffState_ne_rejectingHandoffState
PNP.Concrete.PipelineStageBridges.acceptingLaunch_workStep
PNP.Concrete.PipelineStageBridges.bridgedAccept_workRunExact_of_rawRunExact
PNP.Concrete.PipelineStageBridges.bridgedReject_workRunExact_of_rawRunExact
PNP.Concrete.PipelineStageBridges.bridgedWorkSteps_eq
PNP.Concrete.PipelineStageBridges.findWorkRule_bridged_acceptingHandoff_of_some
PNP.Concrete.PipelineStageBridges.findWorkRule_bridged_input_of_some
PNP.Concrete.PipelineStageBridges.findWorkRule_bridged_rejectingHandoff_of_some
PNP.Concrete.PipelineStageBridges.findWorkRule_bridged_simulation_of_some
PNP.Concrete.PipelineStageBridges.inputLaunch_workStep
PNP.Concrete.PipelineStageBridges.rejectingLaunch_workStep
PNP.Concrete.PipelineStageBridges.run_compileBridgedMachine_accept_of_rawRunExact
PNP.Concrete.PipelineStageBridges.run_compileBridgedMachine_reject_of_rawRunExact
PNP.Concrete.PipelineStageBridges.workBoundedDecide_bridged_accept_of_rawRunExact
PNP.Concrete.PipelineStageBridges.workBoundedDecide_bridged_reject_of_rawRunExact
PNP.Concrete.PipelineStageBridges.workBoundedDecide_bridged_timeout_of_stuck_rawRunExact
PNP.Concrete.PipelineStateNamespace.findWorkRule_composedRules_handoff
PNP.Concrete.PipelineStateNamespace.findWorkRule_composedRules_input
PNP.Concrete.PipelineStateNamespace.findWorkRule_composedRules_simulation
PNP.Concrete.PipelineStateNamespace.findWorkRule_rename
PNP.Concrete.PipelineStateNamespace.renamedInputFramer_workRunExact
PNP.Concrete.PipelineStateNamespace.renamedLiftMachine_workRunExact_of_rawRunExact
PNP.Concrete.PipelineStateNamespace.renamedOutputHandoff_workRunExact_of_represents
PNP.Concrete.PipelineStateNamespace.stageState_injective
PNP.Concrete.PipelineStateNamespace.workBoundedDecide_rename
PNP.Concrete.PipelineStateNamespace.workRunExact?_rename
PNP.Concrete.PipelineTape.frameWithGarbage_represents
PNP.Concrete.PipelineTape.handoffTarget_withGarbage_represents
PNP.Concrete.PipelineTape.represents_expandLeft_of_nil
PNP.Concrete.PipelineTape.represents_expandRight_of_nil
PNP.Concrete.PipelineTape.represents_moveLeft_of_cons
PNP.Concrete.PipelineTape.represents_moveRight_of_cons
PNP.Concrete.PipelineTape.represents_write
PNP.Concrete.PipelineTerminalBridge.acceptingPackerLaunch_workStep
PNP.Concrete.PipelineTerminalBridge.acceptingSuppliedTrace_workRunExact_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.acceptingTerminalFinal_isHalted
PNP.Concrete.PipelineTerminalBridge.acceptingTerminal_workRunExact_of_represents
PNP.Concrete.PipelineTerminalBridge.bridged_workRunExact_of_exact
PNP.Concrete.PipelineTerminalBridge.bridged_workStep?_of_some
PNP.Concrete.PipelineTerminalBridge.findWorkRule_terminalBridge_acceptingPacker_of_some
PNP.Concrete.PipelineTerminalBridge.findWorkRule_terminalBridge_rejectingPacker_of_some
PNP.Concrete.PipelineTerminalBridge.machineOutput_compileTerminalBridge_accept_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.machineOutput_compileTerminalBridge_reject_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.outputBits_compileTerminalBridge_accepting_of_represents
PNP.Concrete.PipelineTerminalBridge.outputBits_compileTerminalBridge_rejecting_of_represents
PNP.Concrete.PipelineTerminalBridge.rejectingPackerLaunch_workStep
PNP.Concrete.PipelineTerminalBridge.rejectingSuppliedTrace_workRunExact_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.rejectingTerminalFinal_isHalted
PNP.Concrete.PipelineTerminalBridge.rejectingTerminal_workRunExact_of_represents
PNP.Concrete.PipelineTerminalBridge.run_compileTerminalBridge_accept_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.run_compileTerminalBridge_accepting_of_represents
PNP.Concrete.PipelineTerminalBridge.run_compileTerminalBridge_accepting_of_represents_at_bound
PNP.Concrete.PipelineTerminalBridge.run_compileTerminalBridge_reject_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.run_compileTerminalBridge_rejecting_of_represents
PNP.Concrete.PipelineTerminalBridge.run_compileTerminalBridge_rejecting_of_represents_at_bound
PNP.Concrete.PipelineTerminalBridge.simulationPrefix_terminalBridge_workBoundedDecide_timeout
PNP.Concrete.PipelineTerminalBridge.suppliedTraceTerminalWorkSteps_eq
PNP.Concrete.PipelineTerminalBridge.terminalBridgeMachine_acceptState_ne_rejectState
PNP.Concrete.PipelineTerminalBridge.terminalBridge_runtime_le
PNP.Concrete.PipelineTerminalBridge.workBoundedDecide_terminalBridge_accept_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.workBoundedDecide_terminalBridge_reject_of_rawRunExact
PNP.Concrete.PipelineTerminalBridge.workBoundedDecide_terminalBridge_timeout_of_stuck_rawRunExact
PNP.Concrete.PolynomialTimeMachine.verdict_accepts_iff
PNP.Concrete.PolynomialTimeMachine.verdict_ne_timeout
PNP.Concrete.Tape.outputBits_handoffTarget
PNP.Concrete.Tape.outputBits_moveRight_moveLeft
PNP.Concrete.Tape.outputBits_ofInput
PNP.Concrete.Tape.outputBits_right_append_blank
PNP.Concrete.TerminalOutputPacker.machineOutput_compileTerminalOutputPacker_eq
PNP.Concrete.TerminalOutputPacker.run_compileTerminalOutputPacker
PNP.Concrete.TerminalOutputPacker.run_compileTerminalOutputPacker_exact
PNP.Concrete.TerminalOutputPacker.terminalOutputPackerFinal_isHalted
PNP.Concrete.TerminalOutputPacker.terminalOutputPacker_one_step_short_timeout
PNP.Concrete.TerminalOutputPacker.terminalOutputPacker_output_eq
PNP.Concrete.TerminalOutputPacker.terminalOutputPacker_runtime_le
PNP.Concrete.TerminalOutputPacker.terminalOutputPacker_workRunExact
PNP.Concrete.run_succ
PNP.Concrete.run_zero

Concrete P, NP, and polynomial reductions

Bitstring languages, finite charged decision/verifier/function pipelines grounded in concrete machines, polynomial certificate/runtime/output bounds, recursively compiled exact raw-machine refinements, many-one reductions, and the NP-complete-in-P implication.

The recursive refinement compiler closes the charged-to-raw machine link, but it does not construct raw paired verifiers beyond the existing CNF-SAT membership witness, prove CNF-SAT is in P or NP-complete, or establish the publication root theorem.

Reviewed theorem interfaces (7)

PNP.Concrete.FunctionProgram.RawRefinement.output_size_le
PNP.Concrete.np_complete_in_p_implies_p_eq_np
PNP.Concrete.p_subset_np
PNP.Concrete.reduction_comp
PNP.Concrete.reduction_refl
PNP.Concrete.reduction_transports_p
PNP.Main.concretePEqualsNP_iff

Concrete universal CNF-SAT verifier

An unconditional formula-grammar outcome, universal bounded work outcome, exact accept/reject semantics, no-timeout theorem, literal finite-machine paired verifier, and CNF-SAT membership in NP.

This proves CNF-SAT membership in NP only; it does not prove CNF-SAT is in P, NP-completeness, or P = NP.

Reviewed theorem interfaces (8)

PNP.Concrete.FinalUniversalDesign.cnfCompiled_accept_iff_check
PNP.Concrete.FinalUniversalDesign.cnfCompiled_ne_timeout
PNP.Concrete.FinalUniversalDesign.cnfCompiled_reject_iff_check_false
PNP.Concrete.FinalUniversalDesign.cnfConcreteVerifier_decision
PNP.Concrete.FinalUniversalDesign.cnfConcreteVerifier_inputMode
PNP.Concrete.FinalUniversalDesign.cnfSATInNP
PNP.Concrete.FinalUniversalDesign.cnfUniversalWorkOutcome
PNP.Concrete.FinalUniversalDesign.formulaGrammarOutcome

Concrete Cook-Levin dimensions and variable layout

Fuel padding preserves designated halts and stuck timeouts; every literal machine state is below an explicit finite ceiling; the input, time, and tape dimensions are executable NatPolynomial expressions; and tape-symbol, head, state, certificate-bit, and certificate-length variables occupy proved disjoint in-range blocks. Elementary at-least-one and pair-exclusion CNF clauses have exact propositional semantics. All 20 reviewed theorems have empty axiom closure.

This is the finite layout substrate only. It does not yet construct a transition tableau, prove tableau soundness or completeness, compile a formula emitter, define a polynomial reduction to CNFSAT, or establish CNFSAT NP-completeness, CNFSAT in P, or P = NP.

Reviewed theorem interfaces (20)

PNP.Concrete.CookLevin.VariableLayout.certificateBitVariable_lt_variableCount
PNP.Concrete.CookLevin.VariableLayout.certificateBitVariable_ne_certificateLengthVariable
PNP.Concrete.CookLevin.VariableLayout.certificateLengthVariable_lt_variableCount
PNP.Concrete.CookLevin.VariableLayout.headVariable_lt_variableCount
PNP.Concrete.CookLevin.VariableLayout.headVariable_ne_stateVariable
PNP.Concrete.CookLevin.VariableLayout.stateVariable_lt_variableCount
PNP.Concrete.CookLevin.VariableLayout.stateVariable_ne_certificateBitVariable
PNP.Concrete.CookLevin.VariableLayout.symbolVariable_lt_variableCount
PNP.Concrete.CookLevin.VariableLayout.symbolVariable_ne_headVariable
PNP.Concrete.CookLevin.atLeastOneClause_satisfied_iff
PNP.Concrete.CookLevin.eval_encodedInputPolynomial
PNP.Concrete.CookLevin.eval_tapeWidthPolynomial
PNP.Concrete.CookLevin.excludePairClause_not_satisfied_of_both_true
PNP.Concrete.CookLevin.machine_acceptState_lt_bound
PNP.Concrete.CookLevin.machine_rejectState_lt_bound
PNP.Concrete.CookLevin.machine_startState_lt_bound
PNP.Concrete.CookLevin.rule_source_lt_machineStateBound
PNP.Concrete.CookLevin.rule_target_lt_machineStateBound
PNP.Concrete.CookLevin.run_pad_of_halted
PNP.Concrete.CookLevin.run_pad_of_stuck

Concrete fixed-certificate execution tableau

For one fixed source input, certificate, finite-rule machine, and fuel budget, the canonical raw execution trace has exactly fuel + 1 configurations. Intrinsic first-match transition validity is equivalent to equality with that trace, every valid endpoint equals the ordinary run endpoint, and accept/reject/timeout verdicts agree exactly with boundedDecide. All 30 declarations and eight reviewed theorem types have empty axiom closure.

This is the semantic fixed-certificate tableau only. It does not yet quantify a variable certificate, encode tape windows or tableau rows as CNF, compile a formula emitter, define a polynomial reduction to CNFSAT, or establish CNFSAT NP-completeness, CNFSAT in P, or P = NP.

Reviewed theorem interfaces (8)

PNP.Concrete.CookLevin.FixedTableauInstance.exists_accepting_iff_boundedDecide_accept
PNP.Concrete.CookLevin.FixedTableauInstance.tableauVerdict_of_valid
PNP.Concrete.CookLevin.FixedTableauInstance.valid_iff_eq_canonical
PNP.Concrete.CookLevin.canonicalTableau_valid
PNP.Concrete.CookLevin.run_succ_eq_run_advance
PNP.Concrete.CookLevin.tableauEndpoint_of_valid
PNP.Concrete.CookLevin.trace_length
PNP.Concrete.CookLevin.validTableau_iff_eq_trace

Uniform bounded verifier tableaux

For an arbitrary proof-bearing verifier in the concrete NP model and one source input, the complete finite decision pipeline is compiled to one raw machine. Every certificate inside the explicit certificate polynomial shares one answer-independent raw fuel obtained by evaluating the compiled raw-time polynomial at the maximum encoded input size. Per-certificate fuel is below that bound, padding follows a proved halt, exact verdicts are preserved, and language membership is equivalent to an existential bounded accepting semantic tableau. All 41 declarations and nine reviewed theorem types have empty axiom closure.

This is a uniform semantic verifier-tableau equivalence only. It does not encode configurations, transition windows, or variable-length certificates as Boolean clauses; emit CNF; prove emitter size or runtime polynomials; define a polynomial reduction to CNFSAT; or establish CNFSAT NP-completeness, CNFSAT in P, or P = NP.

Reviewed theorem interfaces (9)

PNP.Concrete.CookLevin.VerifierTableauProblem.actualFuel_le_uniformFuel
PNP.Concrete.CookLevin.VerifierTableauProblem.actualFuel_ne_timeout
PNP.Concrete.CookLevin.VerifierTableauProblem.dimensions_timeBound
PNP.Concrete.CookLevin.VerifierTableauProblem.exists_accepting_iff_program_accept
PNP.Concrete.CookLevin.VerifierTableauProblem.language_iff_exists_acceptingTableau
PNP.Concrete.CookLevin.VerifierTableauProblem.rawInput_size_le
PNP.Concrete.CookLevin.VerifierTableauProblem.tableauVerdict_eq_program_of_valid
PNP.Concrete.CookLevin.VerifierTableauProblem.uniformFuel_verdict_eq
PNP.Concrete.CookLevin.verifierEncodedInput_size_le

Finite local Cook-Levin CNF compiler

Width-indexed literals materialize exact Boolean assignments and compile to the concrete CNF semantics without out-of-range variables. Unit constraints, finite implications, and pairwise exactly-one groups have exact satisfaction equivalences; local programs have exact recursive clause counts, satisfiability reflection, and a proved well-scoped formula. All 75 declarations and nine reviewed theorem types have empty axiom closure.

This is a local clause compiler only. It does not enumerate the verifier tableau, encode initialization, transition windows, certificate length, or acceptance as a complete formula; prove an all-input emitter size/runtime polynomial; define a reduction to CNFSAT; or establish CNFSAT NP-completeness, CNFSAT in P, or P = NP.

Reviewed theorem interfaces (9)

PNP.Concrete.CookLevin.BoundedLiteral.emit_variable_lt
PNP.Concrete.CookLevin.LocalConstraint.emit_holds_iff
PNP.Concrete.CookLevin.LocalProgram.emitted_clause_count
PNP.Concrete.CookLevin.LocalProgram.toFormula_satisfiable_iff
PNP.Concrete.CookLevin.LocalProgram.toFormula_satisfied_iff
PNP.Concrete.CookLevin.assignmentAt_assignmentOf
PNP.Concrete.CookLevin.exactlyOneBoundedClauses_holds_iff
PNP.Concrete.CookLevin.implicationClauses_holds_iff
PNP.Concrete.CookLevin.localProgram_formula_wellScoped

Finite whole-tableau Cook-Levin CNF syntax

A uniform bounded verifier-tableau problem is compiled answer-independently into one finite, well-scoped concrete CNF formula. The program emits one-hot symbol/head/state rows, first-match control updates, untouched-cell preservation, exact input-only or symbolic paired-certificate initialization, and a designated final accept constraint. Canonical encoding/decoding, exact local satisfaction reflection, and exact emitted clause counting are proved. All 81 declarations and ten reviewed theorem types have empty axiom closure.

This is finite formula syntax and local-clause reflection only. It does not yet prove that formula satisfiability is equivalent to an accepting raw verifier execution, prove external encoded-output-size or construction-runtime polynomials, define a concrete polynomial reduction to CNFSAT, or establish CNFSAT NP-completeness, CNFSAT in P, or P = NP.

Reviewed theorem interfaces (10)

PNP.Concrete.CookLevin.VerifierTableauProblem.certificateBitWidth_eq_of_paired
PNP.Concrete.CookLevin.VerifierTableauProblem.certificateLengthWidth_eq_of_paired
PNP.Concrete.CookLevin.VerifierTableauProblem.decode_encodedFormula
PNP.Concrete.CookLevin.VerifierTableauProblem.dimensions_encodedInputLength
PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormula_mem_CNFSAT_iff
PNP.Concrete.CookLevin.VerifierTableauProblem.findRule_some_mem
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_clauseCount
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_satisfiable_iff
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_satisfied_iff
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_wellScoped

Finite whole-tableau Cook-Levin CNF semantics

Every satisfying assignment decodes to a unique-symbol, unique-head, unique-state finite row at each bounded time. The decoded initial row is exact in both verifier modes, each adjacent row is the literal deterministic first-match successor, and the final state is accepting. Conversely, every such intrinsic finite accepting tableau constructs a satisfying assignment. Formula satisfiability and concrete CNFSAT membership are therefore equivalent to this finite semantics. All 161 explicit declarations are axiom-audited; the six reviewed theorem types depend only on the permitted Lean standard axioms Quot.sound and propext, with no project axiom.

This milestone itself proves equivalence only with an intrinsic finite-row model; the following raw-tape milestone supplies the execution bridge. External encoded-output-size and construction-runtime polynomials, a concrete polynomial reduction to CNFSAT, CNFSAT NP-completeness, CNFSAT in P, and P = NP remain absent.

Reviewed theorem interfaces (6)

PNP.Concrete.CookLevin.VerifierTableauProblem.decodedInitialRow_eq_paired
PNP.Concrete.CookLevin.VerifierTableauProblem.decodedRow_next
PNP.Concrete.CookLevin.VerifierTableauProblem.decodedTableau_transitions
PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormula_mem_CNFSAT_iff_finiteAccepting
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_satisfiable_iff_finiteAccepting
PNP.Concrete.CookLevin.VerifierTableauProblem.tableauAssignment_transitionProgram_holds

Finite tableau to raw Tape semantics

The finite Cook-Levin rows are proved exactly equivalent to ordinary focused raw Tape execution. Absolute two-sided tape observations cover explicit and implicit blanks; the local successor matches designated halts, missing-rule stutter, and the literal first matching raw rule; a centered head invariant rules out finite-window clamping; and both verifier input modes have exact initial rows, including reversible bounded-certificate reconstruction. Formula satisfiability and concrete CNFSAT membership are therefore equivalent to the concrete verifier language. All 54 explicit declarations are axiom-audited, and the nine reviewed theorem types use only the permitted Lean standard axiom allowlist with no project axiom.

This proves exact semantic reduction correctness only. It does not yet prove external encoded-formula-size or formula-construction-runtime polynomials, package a concrete PolynomialReduction, establish CNFSAT NP-completeness, CNFSAT in P, or P = NP.

Reviewed theorem interfaces (9)

PNP.Concrete.Tape.symbolAt_moveLeft
PNP.Concrete.Tape.symbolAt_moveRight
PNP.Concrete.CookLevin.VerifierTableauProblem.FiniteRow.next_represents_advance
PNP.Concrete.CookLevin.VerifierTableauProblem.certificateOf_certificate
PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormula_mem_CNFSAT_iff_language
PNP.Concrete.CookLevin.VerifierTableauProblem.finiteRun_head_bounds
PNP.Concrete.CookLevin.VerifierTableauProblem.finiteRun_represents_run
PNP.Concrete.CookLevin.VerifierTableauProblem.hasFiniteAccepting_iff_language
PNP.Concrete.CookLevin.VerifierTableauProblem.pairedInitialRowFor_represents

External Cook-Levin encoded-formula size

The actual canonical unary-indexed CNF bitstring generated for a fixed concrete polynomial-time verifier is bounded by an explicit NatPolynomial evaluated only at the external source-input length. Exact codec lengths, both verifier input modes, every concrete tableau constraint family, program and emitted-clause counts, clause width, and the mode-sensitive exact formula-variable width polynomial are covered. All 110 explicit declarations are axiom-audited; the ten reviewed theorem types use only the permitted Lean standard axioms Quot.sound and propext, with no project axiom or choice axiom.

This does not implement or time a raw finite formula builder, package a concrete PolynomialReduction, establish CNFSAT NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (10)

PNP.Concrete.CookLevin.encodeCNF_size_exact
PNP.Concrete.CookLevin.encodeCNF_size_le
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaVariableCountPolynomial_eval
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaWidthPolynomial_eval
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaConstraintCountPolynomial_eval
PNP.Concrete.CookLevin.VerifierTableauProblem.program_length_le_formulaConstraintCountPolynomial
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_clauseCount_le_formulaClauseCountPolynomial
PNP.Concrete.CookLevin.VerifierTableauProblem.formula_clause_length_le
PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormulaSizePolynomial_eval
PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormula_size_le

Rectangular Cook-Levin formula schedule

For every concrete verifier-tableau problem, a finite answer-independent rectangular schedule allocates exact constraint, clause, token, and raw-bit slots. Removing empty slots in order reproduces the existing canonical local program, bounded clauses, CNF tokens, and encoded formula. The raw-bit schedule length is exactly the previously proved encodedFormulaSizePolynomial evaluated at external source-input length. All 79 explicit declarations are axiom-audited; the eight reviewed theorem types use only the permitted Lean standard axioms Quot.sound and propext, with no project axiom or choice axiom.

This is a pure schedule specification. It does not interpret a slot as a constant-time raw-machine action, implement or time a raw finite formula builder, construct a FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (8)

PNP.Concrete.CookLevin.VerifierTableauProblem.initialCellAtCoordinate_eq_initialCellAt
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaConstraintSchedule_emit_eq_program
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaConstraintSchedule_length
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaClauseSchedule_length
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaClauseSchedule_emit_eq_formulaClauses
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaTokenSchedule_length
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSchedule_length
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSchedule_emit_eq_encodedFormula

Direct Cook-Levin formula cursor

For every concrete verifier-tableau problem and natural coordinate, direct constraint, clause, token, and raw-bit decoders agree pointwise with the canonical rectangular schedules while preserving out-of-range, valid-padding, and populated states. Fuelled bit traversal proves exact bounded prefixes, complete traversal, one-step-short behavior, terminal behavior, excess-fuel stability, the external encoded-size polynomial, and canonical emitted output. A token-level specification cursor additionally exposes exact in-range, done, and terminal single-step laws. All 136 explicit declarations are axiom-audited; the 16 reviewed theorem types use only the permitted Lean standard axioms Quot.sound and propext, with no project axiom or choice axiom.

This is a Lean specification cursor. It does not prove constant-time raw slot interpretation, implement or time a raw finite formula builder, construct a FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (16)

PNP.Concrete.CookLevin.VerifierTableauProblem.formulaConstraintSlotDirect_eq
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaClauseSlotDirect_eq
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaTokenSlotDirect_eq
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSlotDirect_eq
PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSlotCountDirect_eq_polynomial
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_prefix
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_to_end
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_full
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.step_at_end
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_one_step_short
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.step_after_one_step_short
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_excess
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_full_emit_eq_encodedFormula
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaTokenCursor.step_at_end
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaTokenCursor.step_of_done
PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaTokenCursor.step_of_lt

Literal Cook-Levin builder input-length tally

A fixed 19-rule work machine starts at the proved all-input framer endpoint, preserves every external source bit, appends exactly one unary tally symbol per source bit in fresh right-side workspace, and returns to the source head. It accepts after exactly 2*n*n + 4*n + 2 work steps; the compiled raw machine reaches the encoded endpoint after exactly 12*n*n + 24*n + 12 steps. Malformed internal scan symbols and one-step-short fuel both time out. All 39 public declarations are axiom-audited; the ten reviewed theorem types use only the permitted Lean standard axioms Quot.sound and propext, with no project or choice axiom.

This is only the input-length preparation stage. It does not emit formula bits, interpret direct cursor slots as raw transitions, compose a complete raw formula builder, construct a FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (10)

PNP.Concrete.CookLevin.BuilderInputLength.finalTape_represents
PNP.Concrete.CookLevin.BuilderInputLength.inputTape_eq_totalInputFramerFinalTape
PNP.Concrete.CookLevin.BuilderInputLength.malformedScanSymbol_timeout
PNP.Concrete.CookLevin.BuilderInputLength.rawTimeBound_exact
PNP.Concrete.CookLevin.BuilderInputLength.run_compile
PNP.Concrete.CookLevin.BuilderInputLength.tallySizeBound_exact
PNP.Concrete.CookLevin.BuilderInputLength.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderInputLength.workRunExact
PNP.Concrete.CookLevin.BuilderInputLength.workRunExact_after_totalInputFramer
PNP.Concrete.CookLevin.BuilderInputLength.work_one_step_short_timeout

Executable Cook-Levin builder input prefix

One literal finite work machine contains collision-free renamed copies of the total all-input framer and fixed 19-rule unary tally, with a total nine-symbol tape/head-preserving launch between them. Every raw bitstring reaches the exact preserved-input tally endpoint in totalInputFramerWorkSteps(input) + 1 + 2*n*n + 4*n + 2 work transitions and within the external compiled polynomial 18*n*n + 63*n + 93. All 40 public declarations are axiom-audited: 29 have empty closure, one uses only propext, and ten use only propext and Quot.sound.

This is still only an executable input-preparation prefix. It emits no formula bit, performs no raw formula-cursor interpretation, supplies no complete formula builder or construction-time RawRefinement, packages no concrete PolynomialReduction, and establishes neither CNFSAT NP-completeness, CNFSAT in P, nor P = NP.

Reviewed theorem interfaces (14)

PNP.Concrete.CookLevin.BuilderInputPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderInputPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderInputPrefix.finalTape_tally_length
PNP.Concrete.CookLevin.BuilderInputPrefix.findWorkRule_framer_of_some
PNP.Concrete.CookLevin.BuilderInputPrefix.findWorkRule_tally_of_some
PNP.Concrete.CookLevin.BuilderInputPrefix.framerState_ne_tallyState
PNP.Concrete.CookLevin.BuilderInputPrefix.launch_workStep
PNP.Concrete.CookLevin.BuilderInputPrefix.malformedTallyScanSymbol_timeout
PNP.Concrete.CookLevin.BuilderInputPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderInputPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderInputPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderInputPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderInputPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderInputPrefix.work_one_step_short_timeout

Standalone Cook-Levin builder token appender

A fixed 59-rule work machine appends any of the four canonical two-bit CNF tokens selected only by its finite control state after a represented source word and exact unary input-length tally. For source length n and k existing tokens, it accepts at the exact endpoint after 2 * (max 1 n + n + k + 3) work steps. Its distinguished start state appends T, the first canonical formula header token, within the external compiled bound 24*n + 48; the two emitted bits are proved equal to the first two bits of every concrete verifier-tableau encoding. Malformed tally/output phases and one-step-short fuel remain timeouts. All 68 public declarations are axiom-audited: 42 have empty closure, 13 use only propext, and 13 use only propext and Quot.sound.

This milestone audits the token appender independently of its later composed use. It does not compute the remaining width header, interpret a dynamic formula cursor coordinate, emit a complete formula, construct a builder RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (17)

PNP.Concrete.CookLevin.BuilderTokenAppender.appendToken_workRunExact
PNP.Concrete.CookLevin.BuilderTokenAppender.firstHeaderToken_after_builderInputPrefix
PNP.Concrete.CookLevin.BuilderTokenAppender.firstHeaderToken_bits_eq_encodedFormula_take_two
PNP.Concrete.CookLevin.BuilderTokenAppender.firstHeaderToken_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderTokenAppender.firstHeaderToken_workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderTokenAppender.firstHeaderToken_workRunExact
PNP.Concrete.CookLevin.BuilderTokenAppender.firstTokenRawTimeBound_eval
PNP.Concrete.CookLevin.BuilderTokenAppender.firstTokenRawTimeBound_le
PNP.Concrete.CookLevin.BuilderTokenAppender.formulaBitSlotDirect_one
PNP.Concrete.CookLevin.BuilderTokenAppender.formulaBitSlotDirect_zero
PNP.Concrete.CookLevin.BuilderTokenAppender.malformedOutputSymbol_timeout
PNP.Concrete.CookLevin.BuilderTokenAppender.malformedTallySymbol_timeout
PNP.Concrete.CookLevin.BuilderTokenAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderTokenAppender.run_compile_firstHeaderToken_rawTimeBound
PNP.Concrete.CookLevin.BuilderTokenAppender.tokenSymbol_bits
PNP.Concrete.CookLevin.BuilderTokenAppender.workspaceTape_empty_eq_builderInputLength_finalTape
PNP.Concrete.CookLevin.BuilderTokenAppender.workspaceTape_represents

Composed Cook-Levin builder first-token prefix

One literal 184-rule finite work machine contains all 116 executable input-prefix rules, nine total symbol-preserving bridge rules, and all 59 token-appender rules under injective disjoint state renamings. Every raw bitstring runs through total framing, exact unary input tallying, the bridge, and the appender to preserve the workspace and emit exactly the first T header token. The exact all-input work trace compiles within 18*n*n + 87*n + 147 raw steps; the final two bits equal the first two bits of every canonical encoded verifier-tableau formula. Prefix-endpoint, malformed tally/output, and one-step-short negative cases time out. All 37 public declarations are axiom-audited: 21 have empty closure, three use only propext, and 13 use only propext and Quot.sound, with no project axiom or Classical.choice.

This emits exactly the fixed answer-independent first T token, hence only the first two canonical formula bits. It does not compute the remaining width header, implement a dynamic cursor, emit a complete formula, construct a builder RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (25)

PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.appenderState_injective
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.appender_workRunExact
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.finalTokenBits_eq_encodedFormula_take_two
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.findWorkRule_appender_of_some
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.findWorkRule_prefix_of_some
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.launch_workStep
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.malformedPrefixTally_timeout
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.prefixState_injective
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.prefixState_ne_appenderState
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.rules_length
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderFirstTokenPrefix.work_one_step_short_timeout

Composed Cook-Levin complete width header

For every fixed concrete polynomial-time verifier, one literal finite work machine contains the 184-rule raw-input/first-token prefix, a structurally generated unary NatPolynomial evaluator, a 16-rule unary-root controller, two complete 59-rule token appenders, and five total nine-symbol bridges under injective pairwise-disjoint state renamings. Its table has exactly 363 plus the evaluator rule count rules. Every raw input follows an exact all-input trace, evaluates the verifier's mode-sensitive formula width into unary scratch space without calling NatPolynomial.eval in executable rules, and emits exactly FormulaWidth copies of T followed by F. The resulting bits are the complete canonical encoded-formula width header, and an external NatPolynomial bounds the compiled raw run. The evaluator's 74 and composition's 84 public declarations are completely axiom-audited: every closure is empty or uses only propext and Quot.sound, with no project axiom or Classical.choice.

This endpoint is the complete answer-independent width header only. It does not implement the dynamic formula cursor or body emission, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (48)

PNP.Concrete.CookLevin.BuilderCompleteHeader.HeaderController.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderCompleteHeader.HeaderController.rules_length
PNP.Concrete.CookLevin.BuilderCompleteHeader.HeaderController.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderCompleteHeader.HeaderController.workRunExact
PNP.Concrete.CookLevin.BuilderCompleteHeader.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderCompleteHeader.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderCompleteHeader.controllerF_launch_workStep
PNP.Concrete.CookLevin.BuilderCompleteHeader.controllerState_injective
PNP.Concrete.CookLevin.BuilderCompleteHeader.controllerT_launch_workStep
PNP.Concrete.CookLevin.BuilderCompleteHeader.evaluatorController_launch_workStep
PNP.Concrete.CookLevin.BuilderCompleteHeader.evaluatorState_injective
PNP.Concrete.CookLevin.BuilderCompleteHeader.fAppenderState_injective
PNP.Concrete.CookLevin.BuilderCompleteHeader.finalTape_represents
PNP.Concrete.CookLevin.BuilderCompleteHeader.finalTokenBits_eq_encodedFormula_header
PNP.Concrete.CookLevin.BuilderCompleteHeader.findWorkRule_controller_of_some
PNP.Concrete.CookLevin.BuilderCompleteHeader.findWorkRule_evaluator_of_some
PNP.Concrete.CookLevin.BuilderCompleteHeader.findWorkRule_fAppender_of_some
PNP.Concrete.CookLevin.BuilderCompleteHeader.findWorkRule_prefix_of_some
PNP.Concrete.CookLevin.BuilderCompleteHeader.findWorkRule_tAppender_of_some
PNP.Concrete.CookLevin.BuilderCompleteHeader.headerTokens_eq_encodeUnaryTokens
PNP.Concrete.CookLevin.BuilderCompleteHeader.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderCompleteHeader.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderCompleteHeader.prefixEvaluator_launch_workStep
PNP.Concrete.CookLevin.BuilderCompleteHeader.prefixState_injective
PNP.Concrete.CookLevin.BuilderCompleteHeader.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderCompleteHeader.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderCompleteHeader.rules_length
PNP.Concrete.CookLevin.BuilderCompleteHeader.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderCompleteHeader.run_compile_exact
PNP.Concrete.CookLevin.BuilderCompleteHeader.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderCompleteHeader.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderCompleteHeader.tAppenderState_injective
PNP.Concrete.CookLevin.BuilderCompleteHeader.tController_launch_workStep
PNP.Concrete.CookLevin.BuilderCompleteHeader.width_eq_FormulaWidth
PNP.Concrete.CookLevin.BuilderCompleteHeader.width_positive
PNP.Concrete.CookLevin.BuilderCompleteHeader.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderCompleteHeader.workRunExact
PNP.Concrete.CookLevin.BuilderCompleteHeader.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.compilerStepsPolynomial_eval
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.root_prefix_length
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.root_register_length
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.rule_source_lt_acceptState
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.rules_length
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.scratchWord_symbol
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.workRunExact
PNP.Concrete.CookLevin.BuilderUnaryPolynomial.workTimePolynomial_eval

Composed Cook-Levin body-start prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine contains the complete width-header machine, a structurally generated unary evaluator for the next canonical token slot, one complete 59-rule token appender, and two total nine-symbol bridges under injective pairwise-disjoint state renamings. Its table has exactly 440 plus the width-evaluator and next-token-slot-evaluator rule counts. Every raw input follows an exact all-input trace, preserves the unary input tally and header workspace, retains next token coordinate FormulaVariableSlotBound + 2 and bit cursor twice that coordinate, and emits exactly FormulaWidth copies of T followed by F and Sep. The resulting bits are the canonical encoded-formula prefix through the first body separator; the compiled run is bounded by the complete-header bound plus 72, six times the unary next-slot evaluator work count, 24*n, and 12*width. All 60 public declarations are axiom-audited: 30 have empty closure, five use only propext, and 25 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed answer-independent body-opening separator after the complete width header and retains its coordinate as data. It does not implement a dynamic formula cursor or subsequent body emission, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (42)

PNP.Concrete.CookLevin.BuilderBodyStartPrefix.appenderState_injective
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.appender_workRunExact
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.bodyStartTokens_eq_canonical_prefix
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.cursorAppender_launch_workStep
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.cursorDeadState_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.cursorEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.cursorState_injective
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.cursorState_ne_appenderState
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.finalOutside_contains_nextTokenSlot
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.finalTokenBits_eq_encodedFormula_bodyStart
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.findWorkRule_appender_of_some
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.findWorkRule_cursor_of_some
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.findWorkRule_header_of_some
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.firstBodyTokenSlotDirect_eq_separator
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerRejectEndpoint_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerState_injective
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerState_ne_appenderState
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerState_ne_cursorState
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.header_workRunExact
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.nextBitCursor_nextSlot
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.nextTokenSlot_eq_formulaVariableSlotBound_add_two
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rule_source_ne_rejectState
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rules_length
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderBodyStartPrefix.work_one_step_short_timeout

Composed Cook-Levin first-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine contains the complete body-start-prefix machine, a structurally generated unary evaluator for token coordinate FormulaVariableSlotBound + 4, two complete 59-rule token appenders, and three total nine-symbol bridges under four injective pairwise-disjoint state renamings. Its table has exactly 585 plus the width, body-start next-slot, and first-literal next-slot evaluator rule counts. Every raw input follows an exact all-input trace, preserves the unary tally and earlier token workspace, retains the corresponding doubled bit cursor, and emits exactly FormulaWidth copies of T followed by F, Sep, T, and F. The final T/F pair is constructively pinned to the positive sign and unary-zero terminator of the first scheduled literal, positive variable zero, and all emitted bits equal encodedFormula.take (2 * (FormulaWidth + 4)). The compiled run is bounded by the body-start bound plus 174, six times the new unary evaluator work count, 48*n, and 24*width. All 74 current public declarations are axiom-audited: 21 have empty closure, three use only propext, and 50 use only propext and Quot.sound, with no project axiom or Classical.choice; the added halt-separation interface supports the reviewed first-clause composition.

This milestone emits only the first canonical literal after the body-opening separator and retains the following coordinate as data. It does not implement a dynamic formula cursor or remaining body emission, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (52)

PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluatorDeadState_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluatorEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluatorState_injective
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluatorState_ne_fAppenderState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluatorState_ne_tAppenderState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluatorT_launch_workStep
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.evaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.fAppenderState_injective
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.fAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.finalOutside_contains_nextTokenSlot
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_firstLiteral
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.findWorkRule_evaluator_of_some
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.findWorkRule_fAppender_of_some
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.findWorkRule_prefix_of_some
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.findWorkRule_tAppender_of_some
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.firstLiteralSignSlotDirect_eq_t
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.firstLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.firstLiteralTokens_eq_canonical_prefix
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.firstLiteralZeroTerminatorSlotDirect_eq_f
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.malformedFAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.malformedFAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.nextBitCursor_nextSlot
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.nextTokenSlot_eq_formulaVariableSlotBound_add_four
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixEvaluator_launch_workStep
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixRejectEndpoint_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixState_injective
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixState_ne_evaluatorState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixState_ne_fAppenderState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefixState_ne_tAppenderState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.tAppenderEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.tAppenderState_injective
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.tAppenderState_ne_fAppenderState
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.tAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.tF_launch_workStep
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.work_one_step_short_timeout

Composed Cook-Levin first-clause prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine contains the complete first-literal-prefix machine, a structurally generated unary evaluator for token coordinate FormulaVariableSlotBound + 12, and a fixed 535-rule tail made from eight complete 59-rule token appenders and seven total nine-symbol bridges under disjoint injective state renamings. Its table has exactly 1138 plus the width, body-start next-slot, first-literal next-slot, and first-clause next-slot evaluator rule counts. Every raw input follows an exact all-input trace, preserves the unary tally and earlier token workspace, retains the corresponding doubled bit cursor, and emits exactly FormulaWidth copies of T followed by F, Sep, T, F, T, T, F, T, T, T, F, and Finish. The final eight tokens are constructively pinned to the remainder of the complete positive at-least-one shape clause on variables zero, one, and two; the following direct token slot is proved to be valid padding. All emitted bits equal encodedFormula.take (2 * (FormulaWidth + 12)). The compiled run is bounded by the first-literal bound plus 1158, six times the new unary evaluator work count, 192*n, and 96*width. All 79 public declarations are axiom-audited: 38 have empty closure, 13 use only propext, and 28 use only propext and Quot.sound, with no project axiom or Classical.choice; the 80-line combined audit additionally covers the predecessor halt-separation theorem.

This milestone emits only the complete first canonical clause after the width header and retains the following coordinate as data. It does not implement a dynamic formula cursor or remaining formula-body emission, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (43)

PNP.Concrete.CookLevin.BuilderFirstClausePrefix.FirstClauseTailAppender.finalTape_represents
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.FirstClauseTailAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.FirstClauseTailAppender.rules_length
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.FirstClauseTailAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.FirstClauseTailAppender.tailTokens_length
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.FirstClauseTailAppender.workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.WorkChain.firstState_injective
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.WorkChain.firstState_ne_secondState
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.WorkChain.launch_workStep
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.WorkChain.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.WorkChain.secondState_injective
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.WorkChain.workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.evaluatorEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.evaluatorTail_launch_workStep
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.evaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.finalTokenBits_eq_encodedFormula_firstClause
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.firstClauseTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.firstClauseTokens_eq_canonical_prefix
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.launch_workStep
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.nextBitCursor_nextSlot
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.nextTokenSlot_eq_formulaVariableSlotBound_add_twelve
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.rules_length
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.tail_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.nextTokenSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFirstClausePrefix.rule_source_ne_acceptState

Literal Cook-Levin token-cursor padding step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete first-clause prefix with a total nine-symbol bridge and a fixed 45-rule cursor-advance table under disjoint nested state images. Its table has exactly 1192 plus the four inherited unary-evaluator rule counts. Every raw input follows an exact all-input trace, preserves the complete first-clause output, and advances the retained unary token coordinate from FormulaVariableSlotBound + 12 to FormulaVariableSlotBound + 13. The direct decoder proves that the consumed coordinate is the first in-range padding slot, so the token-level specification cursor advances without emitting a token. The cursor suffix takes exactly 2*cursorWord.length + 8 work steps including launch, and the compiled run is bounded by FirstClausePrefix.rawTimeBound + 48 + 12*cursorWord.length. All 47 public declarations, including two reviewed dead-state dispatch facts used downstream, are axiom-audited: 14 have empty closure, seven use only propext, and 26 use only propext and Quot.sound, with no project axiom or Classical.choice.

This is one fixed padding-coordinate transition after the complete first clause. It is not a general dynamic cursor loop or raw decoder for arbitrary schedule coordinates, emits no additional formula token, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (31)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.advance_workRunExact
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.rules_length
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.directOutcome_is_padding
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.finalTokenBits_eq_encodedFormula_firstClause
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.finalTokenSlot_eq_formulaVariableSlotBound_add_thirteen
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.launch_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.rules_length
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.specification_step
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.workRunExact
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.work_one_step_short_timeout

Cook-Levin first-clause remaining-padding run

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the preceding first-clause cursor step with structurally generated unary evaluators for D = (FormulaVariableSlotBound - 1) * (FormulaVariableSlotBound + 6) and the second-clause coordinate, plus one fixed 25-rule countdown controller. Its table has exactly 1244 plus the six inherited and generated evaluator rule counts. Every raw input follows an exact all-input trace, preserves the complete first-clause output, traverses all D remaining first-clause padding coordinates without emitting a token, and reaches FormulaVariableSlotBound + 1 + FormulaTokensPerClause, where direct schedule lookup is proved to return Sep. The recursive specification run agrees at every padding coordinate and the following specification step observes Sep. The compiled exact run has an explicit external input-size polynomial bound, accepts within that bound, and remains fail-closed for malformed countdown scratch/root states, the unlaunched prefix endpoint, and one-step-short fuel. All 83 public declarations plus one predecessor transport theorem are axiom-audited: 37 have empty closure, 11 use only propext, and 36 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone executes exactly the remaining first-clause padding block and identifies the second-clause separator boundary. It is not a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the second clause or remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (48)

PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopback_workStep
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.rules_length
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.countEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.countdownBoundPolynomial_eval
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.countdown_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.finalTape_represents
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.finalTokenBits_eq_encodedFormula_firstClause
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.finalTokenSlot_eq_secondClauseStart
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.formulaVariablePredecessorPolynomial_eval
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.formulaVariablePredecessorPolynomial_eval_add_one
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.formulaVariableSlotBound_at_least_three
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.launch_workStep
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.malformedCountdownRoot_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.malformedCountdownScratch_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.paddingSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.predecessorSlot_add_remainingPaddingCount
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.remainingPaddingCount_eq
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_twelve
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.remainingPaddingCount_positive
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.rules_length
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.run_compile_exact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.secondClauseStart_direct_eq_sep
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.secondClauseStart_eq
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.specification_padding_run
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.specification_target_step
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.workRunExact
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderCompleteHeader.HeaderController.workRunExact_of_unit_or_separator

Uniform Cook-Levin full-schedule cursor controller

For every concrete polynomial-time verifier and raw input, the exact polynomial body-opportunity count equals the complete token schedule after the padded unary header. A semantic cursor returns the full canonical schedule and emitted formula. One deterministic finite raw machine composes the complete header, generated count and terminal-coordinate evaluators, and a fixed positive countdown table. It consumes the arbitrary body count exactly, materializes the unique terminal coordinate, accepts within an explicit input-size polynomial bound, and remains fail-closed for malformed countdown geometry, the unlaunched header endpoint, and one-step-short fuel.

This milestone provides a uniform control scaffold for the complete input-dependent Cook-Levin token schedule, but the raw loop does not decode or emit the visited body entries. It is not the complete raw formula builder or its FunctionProgram.RawRefinement, does not package the concrete Cook-Levin PolynomialReduction, does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, does not close a global gate, and does not prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderFullScheduleCursorController.cook_levin_full_schedule_cursor_controller_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-208: formal artefact coverage becomes 184 of 186; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Uniform Cook-Levin arbitrary-slot header router

For every concrete polynomial-time verifier and every coordinate below its complete direct token schedule, one fixed 54-rule deterministic work machine compares the coordinate with the exact problem-derived first-body boundary. Its exact trace accepts precisely the header branch and rejects equality or the post-header branch. The semantic route is definitionally faithful to formulaTokenSlotDirect; the compiled execution is bounded by the verifier-derived polynomial 36 * terminalSlotPolynomial^2; one-step-short fuel and malformed symbols remain timeout. All 51 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone routes only the top-level header boundary. It does not decode the post-header quotient and remainder into a clause and within-clause token slot, does not emit a body token, and is not the complete raw formula builder or its FunctionProgram.RawRefinement. It does not package the concrete Cook-Levin PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a global gate, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderArbitrarySlotHeaderRouter.cook_levin_arbitrary_slot_header_router_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-209: formal artefact coverage becomes 185 of 187; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Uniform Cook-Levin arbitrary-slot post-header decoder

For every concrete polynomial-time verifier and every coordinate below its complete direct token schedule, the M209 outer route is refined by a structurally recursive all-coordinate post-header decoder. Every body result gives typed finite clause and within-clause coordinates that reconstruct the exact remainder; the unique Finish and out-of-range cases are characterized; and the interpreted route agrees with direct token lookup. A checked reader recovers the exact shifted remainder from every M209 raw comparison result while preserving M209's exact raw trace. All 22 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone adds an unbounded semantic clause/within-clause decoder and extracts the exact shifted remainder from M209's checked raw result. It does not implement raw division, raw body-token emission, the complete raw formula builder or its FunctionProgram.RawRefinement. It does not package the concrete Cook-Levin PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a global gate, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderArbitrarySlotPostHeaderDecoder.cook_levin_arbitrary_slot_post_header_decoder_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-210: formal artefact coverage becomes 186 of 188; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Fixed Cook-Levin post-header raw quotient/remainder divider

For every natural dividend and positive unary width, one fixed 99-rule deterministic work machine reaches the exact natural quotient and strict remainder tape, reconstructs the dividend, compiles with exactly six raw transitions per certified work step, times out one step short, and satisfies an explicit quadratic bound in the complete unary encoded input length. The zero-width dispatcher returns none. M210 body coordinates instantiate the same decoded quotient and remainder. All 57 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone proves a standalone fixed unary divider. It is not spliced onto M209's checked raw result, does not classify Finish or out-of-range routes, does not emit or append a Cook-Levin body token, and does not complete the raw formula builder or its FunctionProgram.RawRefinement. It does not package the concrete Cook-Levin PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a global gate, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPostHeaderRawDivider.cook_levin_builder_post_header_raw_divider_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-211: formal artefact coverage becomes 187 of 189; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-coordinate Cook-Levin post-header raw launch

For every concrete verifier tableau problem and every natural coordinate, executable Lean orchestration reads the exact shifted remainder from M209's checked raw terminal configuration and conditionally launches M211's fixed positive-width divider. The exact M209 and M211 traces are retained; every M210 body, Finish, and out-of-range result is recovered; every coordinate inside the complete token schedule excludes the out-of-range post-header branch; and the summed compiled work is bounded by one verifier-derived polynomial in the source-input length. All 24 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone composes M209's checked result reader and M211's exact divider through executable Lean orchestration. It is not a literal raw tape-to-tape bridge, does not preserve the complete builder workspace through such a rewrite, does not emit or append a Cook-Levin body or Finish token, and does not complete the raw formula builder or its FunctionProgram.RawRefinement. It does not package the concrete Cook-Levin PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a global gate, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPostHeaderRawLaunch.cook_levin_builder_post_header_raw_launch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-212: formal artefact coverage becomes 188 of 190; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Literal Cook-Levin post-header raw tape bridge

For every concrete verifier tableau problem, arbitrary exterior workspace, and in-range coordinate, one fixed collision-free 351-rule bridge consumes the exact M209 equality or greater-than terminal tape, derives zero or the exact positive shifted remainder, copies the positive problem width, and reaches a shielded M211 input. Exact bridge and divider traces preserve the complete exterior, recover the exact quotient and remainder, compile at six raw steps per work step, time out one step short, and fit one verifier-derived source-size polynomial. All 78 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone closes the literal M209-to-M211 physical tape handoff only. It does not select, emit, or append a Cook-Levin body or Finish token, iterate the complete token schedule, complete the raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPostHeaderRawTapeBridge.cook_levin_builder_post_header_raw_tape_bridge_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-213: formal artefact coverage becomes 189 of 191; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Literal Cook-Levin post-divider raw route classifier

For every concrete verifier tableau problem, arbitrary safe exterior prefix and builder workspace, and in-range coordinate, one fixed collision-free 180-rule bridge consumes the exact M213 equality or greater-than divider-terminal tape, copies the exact problem-derived clause count from a restored sidecar, preserves the complete exterior and remainder ledger, and constructs a shielded M209 comparison input from the literal quotient marks. Exact bridge and comparator traces cannot cross their boundaries, compile at six raw steps per work step, time out one step short, agree with every M210 body or Finish route, and fit one verifier-derived source-size polynomial. All 85 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone closes the literal post-divider body-versus-Finish route-classification handoff only. It does not inspect, select, emit, or append a Cook-Levin token, iterate the complete token schedule, complete the raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPostDividerRawRouteClassifier.cook_levin_builder_post_divider_raw_route_classifier_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-31-214: formal artefact coverage becomes 190 of 192; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-coordinate Cook-Levin selected-token launch

For every concrete verifier tableau problem and every post-header schedule coordinate, the canonical schedule alone derives padding, the exact body token, or the unique Finish token without a supplied route or token. M214's physical classifier contract is retained, every populated entry runs the existing fixed 59-rule appender to the exact next emitted prefix, exact work and compiled traces time out one step short, and the combined staged work fits one verifier-derived source-size polynomial. All 30 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone derives each canonical post-header padding, body-token, or Finish entry and launches the existing fixed token appender for populated entries through executable Lean orchestration. The selection handoff is not yet a literal raw tape rewrite. It does not iterate the complete token schedule, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPostDividerSelectedTokenLaunch.cook_levin_builder_post_divider_selected_token_launch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-31-215: formal artefact coverage becomes 191 of 193; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Complete semantic Cook-Levin schedule iteration

For every concrete verifier tableau problem, structural recursion consumes every verifier-derived post-header schedule opportunity without a supplied coordinate, token, route, trace, schedule, or precomputed formula. Every bounded run equals the canonical emitted prefix, the complete run equals encodeCNFTokens of the generated formula, every coordinate retains M215's exact classifier/appender evidence for arbitrary workspace, and the aggregate staged compiled work fits one source-size polynomial. All 12 public declarations are axiom-audited with only the approved Lean-standard closure and no project axiom or Classical.choice.

This milestone composes M215's proof-carrying per-coordinate stages through executable Lean recursion. It is not one literal raw-machine loop and does not prove a physical tape-to-tape handoff between successive stages, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderCompleteScheduleIteration.cook_levin_builder_complete_schedule_iteration_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-31-216: formal artefact coverage becomes 192 of 194; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Physical optional-token dispatch

For every raw input, arbitrary exterior workspace, emitted prefix, and optional token request, one fixed collision-free 64-rule machine reads one of five physical request symbols, restores the canonical builder left boundary, and either accepts without changing padding output or enters the existing renamed 59-rule token appender. Exact work and six-for-one compiled traces, one-step-short nonhalting, malformed blank-request timeout, canonical scheduleEntry specialization at every post-header coordinate, and one verifier-derived source-size polynomial are proved. All 49 public declarations are axiom-audited: 23 have empty closure, 13 use only propext, and 13 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone physically dispatches a supplied tape-resident padding or CNF-token request into the existing fixed appender. It does not derive that request from M214's raw coordinate classifier, connect the classifier output directly to this request cell, iterate one physical selector/dispatcher loop through the complete token schedule, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalOptionalTokenDispatch.cook_levin_builder_physical_optional_token_dispatch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-217: formal artefact coverage becomes 193 of 195; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-coordinate physical dispatch schedule

For every concrete verifier problem and every canonical post-header coordinate, a total recursion applies M217 optional-token semantics, agrees at every bounded prefix with the canonical emitted token stream, and reaches the complete encoded formula. Every coordinate and arbitrary exterior retains M217 exact work, compiled and one-step-short physical traces together with M214 classifier evidence. The sum of all exact dispatch costs is bounded by the problem-derived body-slot count times M217 uniform bound, one polynomial in encoded source-input length. All 16 public declarations are axiom-audited: two have empty closure and fourteen use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone composes exact physical dispatch traces over every canonical request, but each request is still constructed from the Lean schedule. It does not derive a request from M214 raw classifier cells, connect successive final and initial tapes, implement one literal raw-machine loop, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalDispatchSchedule.cook_levin_builder_physical_dispatch_schedule_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-218: formal artefact coverage becomes 194 of 196; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Physical Finish-request handoff

For every concrete verifier problem, the unique final post-header coordinate is derived internally and M214 proves its in-range equal-classifier result. The canonical builder workspace is protected beyond the comparator end marker; one fixed writer produces M217's tape-resident Finish request, and one collision-free 137-rule composition runs the comparator, writer and dispatcher. Exact work, six-for-one compiled and one-step-short traces hold for arbitrary classifier exterior, and one verifier-derived polynomial bounds compiled work. All 49 public declarations are axiom-audited: 23 have empty closure, six use only propext, and 20 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone physically derives only the unique canonical Finish request. It does not derive body-token or padding requests from raw coordinates, preserve the builder suffix through every preceding classifier stage, connect successive schedule configurations into one literal raw-machine loop, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalFinishRequest.cook_levin_builder_physical_finish_request_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-219: formal artefact coverage becomes 195 of 197; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-coordinate physical classifier pipeline

For every concrete verifier problem, every canonical post-header coordinate and arbitrary protected builder workspace, one fixed collision-free 711-rule machine composes M213's router-to-divider bridge, M211's divider, M214's divider-to-comparator bridge and comparator, and three fixed launch transitions. Three exact physical tape handoffs preserve the workspace suffix, the final raw state agrees with M214's typed body-or-Finish semantics, and exact work, six-for-one compiled execution, one-step-short nonhalting, component decomposition and one source-size polynomial bound are proved. All 63 public declarations are axiom-audited: 44 have empty closure, four use only propext, and 15 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone physically composes the complete suffix-preserving classifier pipeline for every canonical post-header coordinate. It does not derive body-token or padding request symbols, connect the resulting body or Finish classification to M217's request dispatcher, iterate one literal raw-machine schedule loop, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierPipeline.cook_levin_builder_physical_classifier_pipeline_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-220: formal artefact coverage becomes 196 of 198; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Full-classifier Finish-request cell

For every concrete verifier problem and arbitrary protected builder workspace, the canonical Finish coordinate is derived internally. M220's full 711-rule classifier has its terminal verdict names swapped without changing transition semantics, then is chained through one fixed launch table to M219's one-cell writer as a collision-free 721-rule machine. The classifier reaches the end marker, the writer changes exactly that focused cell to M217's Finish request while preserving the rest of the tape, and exact work, six-for-one compiled execution, one-step-short nonhalting and one source-size polynomial bound are proved. All 36 public declarations are axiom-audited: nine have empty closure, three use only propext, and 24 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone connects only the unique canonical Finish terminal of the full physical classifier to one literal M217-compatible request cell. It does not derive body-token or padding request symbols, orient the preserved workspace for the dispatcher, run M217 from the M220 endpoint, iterate one literal raw-machine schedule loop, construct the complete raw formula builder or its FunctionProgram.RawRefinement, or package the concrete Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierFinishRequest.cook_levin_builder_physical_classifier_finish_request_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-02-221: formal artefact coverage becomes 197 of 199; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Full-classifier Finish-workspace orientation

For every concrete verifier problem, M222 prepends one blank sentinel to the canonical builder workspace, derives the complete M220/M221 classifier prefix, proves that prefix contains no blank, and chains M221 to one fixed ten-rule left scanner. The resulting collision-free 740-rule machine crosses exactly the classifier prefix and halts at the sentinel with a tape equal to the spatial mirror of M217's canonical Finish request entry, retaining classifier evidence as exterior data. Exact work, six-for-one compiled execution, one-step-short nonhalting, a derived prefix-size bound and one source-input-size polynomial bound are proved. All 57 public declarations are axiom-audited: 27 have empty closure and 30 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone closes only the physical workspace-orientation edge for the unique full-classifier Finish path. Equality with a spatial mirror of M217's canonical request entry does not prove that M217's existing machine executes on the mirrored representation. It does not derive body-token or padding requests, run a mirrored dispatcher, connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierFinishWorkspaceOrientation.cook_levin_builder_physical_classifier_finish_workspace_orientation_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-02-222: formal artefact coverage becomes 198 of 200; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Full-classifier reflected Finish dispatch

For every concrete verifier problem, M223 reflects M217's fixed 64-rule dispatcher by exchanging left and right moves while preserving rule queries and states, and proves that reflection transports exact finite-machine execution. Chained after M222, the resulting collision-free 813-rule machine executes the complete classifier's unique Finish path from raw classifier entry through workspace orientation and the reflected dispatcher to an appender endpoint containing the complete canonical CNF token encoding. Exact work, six-for-one compiled execution, one-step-short nonhalting and one source-input-size polynomial bound are proved. All 51 public declarations are axiom-audited: 23 have empty closure, seven use only propext, and 21 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone closes only reflected M217 execution for the unique full-classifier Finish path. It does not derive body-token or padding request symbols, connect every classifier outcome to the dispatcher, connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierFinishMirroredDispatch.cook_levin_builder_physical_classifier_finish_mirrored_dispatch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-02-223: formal artefact coverage becomes 199 of 201; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

First-body separator physical dispatch

For every concrete verifier problem, M224 derives first-body coordinate zero and its canonical separator entry, runs the complete 711-rule classifier through the populated-body terminal, crosses the positive unary clause-count suffix with a fixed two-rule request writer, reorients the protected builder workspace with a fixed ten-rule scanner, and executes M223's reflected 64-rule dispatcher. One collision-free 814-rule machine reaches the exact canonical prefix ending in the first clause separator, with exact work, six-for-one compiled execution, one-step-short nonhalting and one source-input-size polynomial bound. All 121 public declarations are axiom-audited: 53 have empty closure, one uses only propext, and 67 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone closes only the first populated full-classifier body route. It does not select arbitrary body tokens, derive padding requests, connect every classifier outcome, connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierFirstBodySeparatorMirroredDispatch.cook_levin_builder_physical_classifier_first_body_separator_mirrored_dispatch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-03-224: formal artefact coverage becomes 200 of 202; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-body staged-request physical dispatch

For every concrete verifier problem and every coordinate in its complete clause-token body rectangle, M225 runs the complete 711-rule classifier while preserving an explicitly staged canonical optional-token request, relays that request through one fixed 14-rule scanner, and executes M223's reflected 64-rule dispatcher. One collision-free 807-rule composition covers populated and padding coordinates and reaches each exact next canonical emitted prefix, with exact work, six-for-one compiled execution, one-step-short nonhalting and one source-input-size polynomial bound. The current M227 audit covers all 82 public declarations: 33 have empty closure, nine use only propext, and 40 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone stages each canonical body or padding request explicitly on protected tape. It does not synthesize that request from raw classifier state, include the unique Finish route in the same machine, connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllBodyStagedRequestMirroredDispatch.cook_levin_builder_physical_classifier_all_body_staged_request_mirrored_dispatch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-03-225: formal artefact coverage becomes 201 of 203; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-route physical classifier terminal join

For every concrete verifier problem, every coordinate in its complete post-header schedule and arbitrary protected workspace, M226 injectively embeds M220's complete 711-rule classifier and adds one total nine-symbol, tape-preserving redirect from its unique Finish/reject terminal to the same continuation-ready accepting state reached by all body coordinates. The resulting collision-free 720-rule machine takes zero additional steps on body routes and exactly one redirect step on Finish, with exact work, six-for-one compiled execution, one-step-short nonhalting and one source-input-size polynomial bound. All 34 public declarations are axiom-audited: 22 have empty closure, three use only propext, and nine use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone normalizes only the complete physical classifier's terminal control flow. It does not synthesize, stage or dispatch a body-token request, connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierTerminalJoin.cook_levin_builder_physical_classifier_terminal_join_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-03-226: formal artefact coverage becomes 202 of 204; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Cook-Levin second-clause separator step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete first-clause padding run with a selected 59-rule Sep appender, two total nine-symbol bridges, and the existing fixed 45-rule cursor advance under collision-free nested state images. Its table has exactly 1366 plus the six inherited and generated unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical token prefix through the Sep beginning clause two, and advances the retained unary coordinate by one. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 13)), and direct schedule lookup proves that the following token is F. The compiled run is bounded by BuilderFirstClausePaddingRun.rawTimeBound + 246 + 24*n + 12*FormulaWidth + 12*cursorWord.length. Malformed appender tally/output, malformed cursor scratch, both unlaunched endpoints, and one-step-short total fuel remain timeout. All 54 new public declarations plus two reviewed predecessor dispatch facts are axiom-audited: 15 have empty closure, 11 use only propext, and 30 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed populated Sep transition beginning clause two and advances to the following F coordinate. It is not a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit that F or the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.finalTokenBits_eq_encodedFormula_secondClauseStart
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.finalTokenSlot_eq_secondClauseStart_add_one
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.prefixSeparator_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.secondClauseStartTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.separatorCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.specification_separator_step
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead

Cook-Levin second-clause first-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-clause-separator prefix with two selected 59-rule F appenders, four total symbol-preserving bridges, and two copies of the existing 45-rule cursor advance under collision-free nested state images. One F/cursor component has 113 rules, the two-component suffix has 235 rules, and the global table has exactly 1610 plus the six inherited and generated unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical prefix through the complete negative literal on variable zero in clause two, and retains the negative-sign coordinate on variable one. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 15)); direct schedule lookup proves the sign, unary-zero terminator, and following sign are all F. The compiled run is bounded by BuilderSecondClauseSeparatorStep.rawTimeBound + 564 + 48*n + 24*FormulaWidth + 24*cursorWord.length. All four pre-launch endpoints, malformed tally/output in both appenders, malformed scratch in both cursors, and one-step-short fuel remain timeout. All 85 new public declarations plus two reviewed cursor dead-loop facts are axiom-audited: 25 have empty closure, 18 use only propext, and 44 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed negative literal on variable zero in clause two and advances to the following negative-sign coordinate. It does not complete clause two, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (58)

PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_secondClauseFirstLiteral
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.finalTokenSlot_eq_secondClauseStart_add_three
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstCursorEndpoint_before_secondAppender_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstFalseTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstFalseTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstLiteralSignSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstLiteralSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.firstLiteralZeroTerminatorSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.malformedFirstAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.malformedFirstAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.malformedFirstCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.malformedSecondAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.malformedSecondAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.malformedSecondCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.prefixFirstLiteral_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondClauseFirstLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondFalseTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondFalseTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.specification_firstLiteral_sign_step
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead

Cook-Levin second-clause second-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete clause-two first-literal prefix with selected 59-rule F, T, and F appenders, six total symbol-preserving bridges, and three copies of the existing 45-rule cursor advance under collision-free nested state images. The selected T/cursor component has 113 rules, the T/F tail has 235 rules, the complete three-token suffix has 357 rules, and the global table has exactly 1976 plus the six inherited and generated unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical prefix through the complete negative literal on variable one in clause two, and retains the following Finish coordinate. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 18)); direct schedule lookup proves the sign F, unary unit T, terminator F, and following Finish. The compiled run is bounded by BuilderSecondClauseFirstLiteralPrefix.rawTimeBound + 1026 + 72*n + 36*FormulaWidth + 36*cursorWord.length. All six pre-launch endpoints, malformed tally/output in all three appenders, malformed scratch in all three cursors, and one-step-short fuel remain timeout. All 113 new public declarations plus two reviewed cursor dead-loop facts are axiom-audited: 34 have empty closure, 25 use only propext, and 56 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed negative literal on variable one in clause two and advances to the following Finish coordinate. It does not emit the clause terminator, complete clause two, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (75)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalTokenBits_eq_encodedFormula_secondClauseSecondLiteral
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalTokenSlot_eq_secondClauseStart_add_six
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.firstAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.firstCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedSignAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedSignAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedSignCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedTerminatorAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedTerminatorAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedTerminatorCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedUnaryAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedUnaryAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedUnaryCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.nextTokenSlot_direct_eq_finish
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.prefixSecondLiteral_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondClauseSecondLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralSignSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralTerminatorSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralUnaryUnitSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.signAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.signAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.signCursorEndpoint_before_unary_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.signTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_secondLiteral_sign_step
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_secondLiteral_terminator_step
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_secondLiteral_unaryUnit_step
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.terminatorAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.terminatorAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.terminatorTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.thirdAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.thirdCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.trueFalseSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.trueFalseSuffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryCursorEndpoint_before_terminator_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.work_one_step_short_timeout

Cook-Levin complete second-clause prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete clause-two second-literal prefix with a selected 59-rule Finish appender, two total symbol-preserving bridges, and one copy of the existing 45-rule cursor advance under collision-free state images. The fixed suffix has exactly 113 rules and the global table has exactly 2098 plus the six inherited and generated unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical prefix through the complete second clause, and retains its first in-range padding coordinate. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 19)); direct schedule lookup proves the executed opportunity is Finish and the retained next opportunity is padding. The compiled run is bounded by BuilderSecondClauseSecondLiteralPrefix.rawTimeBound + 390 + 24*n + 12*FormulaWidth + 12*cursorWord.length. Both pre-launch endpoints, malformed appender tally/output, malformed cursor scratch, and one-step-short fuel remain timeout. All 55 new public declarations plus two reviewed cursor dead-loop facts are axiom-audited: 15 have empty closure, 10 use only propext, and 32 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed Finish terminator that completes clause two and advances to its first padding coordinate. It does not traverse clause-two padding, reach clause three, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (41)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.clauseTerminatorSlot_direct_eq_finish
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTokenBits_eq_encodedFormula_secondClause
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTokenSlot_eq_secondClauseStart_add_seven
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finishTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.nextTokenSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.prefixFinish_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.secondClauseTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.specification_terminator_step
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePrefix.work_one_step_short_timeout

Cook-Levin second-clause remaining-padding run

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-clause prefix with structurally generated unary evaluators for D = (FormulaVariableSlotBound - 1) * (FormulaVariableSlotBound + 6) + 5 and the third-clause coordinate, plus the reused fixed 25-rule PaddingCountdown controller. Three total symbol-preserving WorkChain bridges yield a table with exactly 2150 plus the six inherited/generated predecessor evaluator rule counts and the two new evaluator rule counts. Every raw input follows an exact all-input trace, preserves the complete second-clause output, traverses all D = FormulaTokensPerClause - 7 remaining second-clause padding coordinates without emitting a token, and reaches FormulaVariableSlotBound + 1 + 2 * FormulaTokensPerClause, where direct schedule lookup is proved to return Sep. The recursive specification run agrees at every padding coordinate and the following specification step observes Sep. The emitted bits remain encodedFormula.take (2 * (FormulaWidth + 19)). The compiled exact run is bounded by BuilderSecondClausePrefix.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps, accepts within that external input-size polynomial, and remains fail-closed for malformed countdown scratch/root states, the unlaunched prefix endpoint, and one-step-short fuel. All 65 new public declarations plus the three reviewed reused-countdown declarations are axiom-audited: 26 have empty closure, 9 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone executes exactly the remaining second-clause padding block and identifies the third-clause separator boundary without emitting a token. It reaches clause three only as a retained coordinate. It is not a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the third-clause separator or remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (39)

PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.countEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.countdownBoundPolynomial_eval
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.countdown_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalTokenBits_eq_encodedFormula_secondClause
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalTokenSlot_eq_thirdClauseStart
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.launch_workStep
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.malformedCountdownRoot_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.malformedCountdownScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.paddingSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.predecessorSlot_add_remainingPaddingCount
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.remainingPaddingCount_eq
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_seven
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.remainingPaddingCount_positive
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rules_length
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.specification_padding_run
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.specification_target_step
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.thirdClauseStart_direct_eq_sep
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.thirdClauseStart_eq
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.workRunExact
PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.work_one_step_short_timeout

Cook-Levin third-clause separator step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-clause padding run with the reused selected 59-rule Sep appender, two total nine-symbol bridges, and the existing fixed 45-rule cursor advance under collision-free nested state images. Its table has exactly 2272 plus eight inherited unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical token prefix through the Sep beginning clause three, and advances the retained unary coordinate by one. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 20)), and direct schedule lookup proves that the following token is F. The compiled run is bounded by BuilderSecondClausePaddingRun.rawTimeBound + 330 + 24*n + 12*FormulaWidth + 12*cursorWord.length. All 48 new public declarations plus eight reviewed suffix interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed populated Sep transition beginning clause three and advances to the following F coordinate. It is not a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit that F or the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTokenBits_eq_encodedFormula_thirdClauseStart
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTokenSlot_eq_thirdClauseStart_add_one
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.prefixSeparator_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.separatorCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.specification_next_step
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.specification_separator_step
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.thirdClauseStartTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.work_one_step_short_timeout

Cook-Levin third-clause first-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete third-clause-separator prefix with the reused 235-rule two-F appender/cursor suffix behind one total nine-symbol bridge under collision-free nested state images. One F/cursor component has 113 rules, the two-component suffix has 235 rules, and the global table has exactly 2516 plus the eight inherited and generated unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical prefix through the complete negative literal on variable zero in clause three, and retains the negative-sign coordinate on variable two. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 22)); direct schedule lookup proves the sign, unary-zero terminator, and following sign are all F, with the third excluded pair constructively identified as variables zero and two. The compiled run is bounded by BuilderThirdClauseSeparatorStep.rawTimeBound + 732 + 48*n + 24*FormulaWidth + 24*cursorWord.length. All four pre-launch endpoints, malformed tally/output in both appenders, malformed scratch in both cursors, and one-step-short fuel remain timeout. All 74 new public declarations plus eleven reviewed suffix declarations and two reviewed cursor dead-loop facts are axiom-audited: 24 have empty closure, 18 use only propext, and 45 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed negative literal on variable zero in clause three and advances to the following negative-sign coordinate. It does not emit that following F, complete clause three, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (58)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_thirdClauseFirstLiteral
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTokenSlot_eq_thirdClauseStart_add_three
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstAppender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstCursorEndpoint_before_secondAppender_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstFalseTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstFalseTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralSignSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralZeroTerminatorSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefixFirstLiteral_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondAppender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondFalseTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondFalseTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_firstLiteral_sign_step
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.thirdClauseFirstLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.work_one_step_short_timeout

Cook-Levin third-clause second-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete third-clause-first-literal prefix with a fixed 479-rule F/T/T/F appender/cursor suffix behind one total nine-symbol bridge under collision-free nested state images. The nested component tables have 113, 235, 357, and 479 rules, and the global table has exactly 3004 plus the eight inherited and generated unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical prefix through the complete negative literal on variable two in clause three, and retains the following Finish coordinate. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 26)); direct schedule lookup proves the sign F, both unary units T, the terminator F, and the following Finish. The compiled run is bounded by BuilderThirdClauseFirstLiteralPrefix.rawTimeBound + 1752 + 96*n + 48*FormulaWidth + 48*cursorWord.length. All eight pre-launch endpoints, malformed tally/output in all four appenders, malformed scratch in all four cursors, and one-step-short fuel remain timeout. All 145 public declarations are axiom-audited: 46 have empty closure, 32 use only propext, and 67 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed negative literal on variable two in clause three and advances to the following Finish coordinate. It does not emit the following Finish, complete clause three, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (92)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.finalTokenBits_eq_encodedFormula_thirdClauseSecondLiteral
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.finalTokenSlot_eq_thirdClauseStart_add_seven
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.firstAppender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.firstCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.firstUnaryAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.firstUnaryCursorEndpoint_before_secondUnary_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.fourthAppender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.fourthCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedFirstUnaryAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedFirstUnaryAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedFirstUnaryCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSecondUnaryAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSecondUnaryAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSecondUnaryCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSignAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSignAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSignCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedTerminatorAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedTerminatorAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedTerminatorCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.nextTokenSlot_direct_eq_finish
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.prefixSecondLiteral_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondAppender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondLiteralFirstUnaryUnitSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondLiteralSecondUnaryUnitSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondLiteralSignSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondLiteralSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondLiteralTerminatorSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondUnaryAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondUnaryAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondUnaryCursorEndpoint_before_terminator_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondUnaryTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.signAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.signAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.signCursorEndpoint_before_firstUnary_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.signTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.specification_secondLiteral_secondUnaryUnit_step
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.specification_secondLiteral_sign_step
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.specification_secondLiteral_terminator_step
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.specification_secondLiteral_unaryUnit_step
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.terminatorAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.terminatorAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.terminatorTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.thirdAppender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.thirdClauseSecondLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.thirdCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.trueFalseSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.trueFalseSuffix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.trueTrueFalseSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.trueTrueFalseSuffix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.unaryAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.unaryTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.work_one_step_short_timeout

Cook-Levin complete third-clause prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete clause-three second-literal prefix with a selected 59-rule Finish appender, two total symbol-preserving bridges, and one copy of the existing 45-rule cursor advance under collision-free state images. The fixed suffix has exactly 113 rules and the global table has exactly 3126 plus the eight inherited unary-evaluator rule counts. Every raw input follows an exact all-input trace, emits the canonical prefix through the complete third clause, and retains its first in-range padding coordinate. The emitted bits equal encodedFormula.take (2 * (FormulaWidth + 27)); direct schedule lookup proves the executed opportunity is Finish and the retained next opportunity is padding. The compiled run is bounded by BuilderThirdClauseSecondLiteralPrefix.rawTimeBound + 498 + 24*n + 12*FormulaWidth + 12*BuilderThirdClauseSeparatorStep.cursorWord.length. Both pre-launch endpoints, malformed appender tally/output, malformed cursor scratch, and one-step-short fuel remain timeout. All 55 new public declarations plus two reviewed cursor dead-loop facts are axiom-audited: 14 have empty closure, 10 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits only the fixed Finish terminator that completes clause three and advances to its first padding coordinate. It does not traverse clause-three padding, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (41)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.appender_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.clauseTerminatorSlot_direct_eq_finish
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTokenBits_eq_encodedFormula_thirdClause
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTokenSlot_eq_thirdClauseStart_add_eight
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finishTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.nextTokenSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefixFinish_launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.specification_terminator_step
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.thirdClauseTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePrefix.work_one_step_short_timeout

Cook-Levin third-clause remaining-padding run

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete third-clause prefix with structurally generated unary evaluators for D = (FormulaVariableSlotBound - 1) * (FormulaVariableSlotBound + 6) + 4 and the fourth-clause coordinate, plus the reused fixed 25-rule PaddingCountdown controller. Three total symbol-preserving WorkChain bridges yield a table with exactly 3178 plus the eight inherited/generated predecessor evaluator rule counts and the two new evaluator rule counts. Every raw input follows an exact all-input trace, preserves the complete third-clause output, traverses all D = FormulaTokensPerClause - 8 remaining third-clause padding coordinates without emitting a token, and reaches FormulaVariableSlotBound + 1 + 3 * FormulaTokensPerClause, where direct schedule lookup is proved to return Sep. The recursive specification run agrees at every padding coordinate and the following specification step observes Sep. The emitted bits remain encodedFormula.take (2 * (FormulaWidth + 27)). The compiled exact run is bounded by BuilderThirdClausePrefix.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps, accepts within that external input-size polynomial, and remains fail-closed for malformed countdown scratch/root states, the unlaunched prefix endpoint, and one-step-short fuel. All 65 new public declarations plus the three reviewed reused-countdown declarations are axiom-audited: 26 have empty closure, 9 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone executes exactly the remaining third-clause padding block and identifies the fourth-clause separator boundary without emitting a token. It reaches clause four only as a retained coordinate. It is not a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the fourth-clause separator or remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (39)

PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.countEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.countdownBoundPolynomial_eval
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.countdown_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTape_represents
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTokenBits_eq_encodedFormula_thirdClause
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTokenSlot_eq_fourthClauseStart
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.fourthClauseStart_direct_eq_sep
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.fourthClauseStart_eq
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.launch_workStep
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.malformedCountdownRoot_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.malformedCountdownScratch_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.paddingSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.predecessorSlot_add_remainingPaddingCount
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_eq
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_eight
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_positive
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rules_length
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_exact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.specification_padding_run
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.specification_target_step
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.workRunExact
PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.work_one_step_short_timeout

Cook-Levin fourth-clause separator step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete third-clause padding run with the reused selected 59-rule Sep appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 3300 plus the ten inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the fourth-clause Sep; preserves encodedFormula.take (2 * (FormulaWidth + 28)); and retains coordinate FormulaVariableSlotBound + 1 + 3 * FormulaTokensPerClause + 1, whose direct next schedule token is F. The external compiled bound evaluates to BuilderThirdClausePaddingRun.rawTimeBound + 426 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused separator/cursor interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the fixed Sep that starts clause four. It observes but does not emit the following F, does not complete clause four, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalTokenBits_eq_encodedFormula_fourthClauseStart
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalTokenSlot_eq_fourthClauseStart_add_one
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.fourthClauseStartTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.prefixSeparator_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rules_length
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.separatorCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.specification_next_step
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.specification_separator_step
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_pairwise_query_distinct

Cook-Levin fourth-clause first-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete fourth-clause separator prefix with the reused 357-rule F/T/F appender/cursor suffix through one outer total nine-symbol WorkChain bridge. The global table has exactly 3666 plus the ten inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits the complete first negative literal on variable one in clause four; preserves encodedFormula.take (2 * (FormulaWidth + 31)); and retains coordinate FormulaVariableSlotBound + 1 + 3 * FormulaTokensPerClause + 4, whose direct next schedule token is F. The external compiled bound evaluates to BuilderFourthClauseSeparatorStep.rawTimeBound + 1422 + 72 * n + 36 * FormulaWidth + 36 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, all six unlaunched-endpoint, and one-step-short results are proved. All 97 new public declarations, 16 reviewed reused suffix interfaces, and two cursor dead-state facts are axiom-audited: 33 have empty closure, 25 use only propext, and 57 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly the fixed first negative literal on variable one in clause four. It observes but does not emit the following second-literal F, does not complete clause four, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (75)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_fourthClauseFirstLiteral
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalTokenSlot_eq_fourthClauseStart_add_four
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralSignSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralTerminatorSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralUnaryUnitSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.fourthClauseFirstLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedSignAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedSignAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedSignCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedTerminatorAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedTerminatorAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedTerminatorCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedUnaryAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedUnaryAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedUnaryCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.prefixFirstLiteral_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.secondAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.secondCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.signAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.signAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.signCursorEndpoint_before_unary_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.signTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_firstLiteral_sign_step
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_firstLiteral_unaryUnit_step
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.terminatorAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.terminatorAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.terminatorTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.thirdAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.thirdCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.trueFalseSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.trueFalseSuffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.unaryAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.unaryAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.unaryCursorEndpoint_before_terminator_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.unaryTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct

Cook-Levin fourth-clause second-literal prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete fourth-clause first-literal prefix with the reused 479-rule F/T/T/F appender/cursor suffix through one outer total nine-symbol WorkChain bridge. The global table has exactly 4154 plus the ten inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits the complete second negative literal on variable two in clause four; preserves encodedFormula.take (2 * (FormulaWidth + 35)); and retains coordinate FormulaVariableSlotBound + 1 + 3 * FormulaTokensPerClause + 8, whose direct next schedule token is Finish. The external compiled bound evaluates to BuilderFourthClauseFirstLiteralPrefix.rawTimeBound + 2232 + 96 * n + 48 * FormulaWidth + 48 * BuilderFourthClauseSeparatorStep.cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, all eight unlaunched-endpoint, and one-step-short results are proved. All 124 new public declarations, 21 reviewed reused suffix interfaces, and two cursor dead-state facts are axiom-audited: 46 have empty closure, 32 use only propext, and 69 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly the fixed second negative literal on variable two in clause four. It observes but does not emit the following Finish, does not complete clause four, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (92)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalTokenBits_eq_encodedFormula_fourthClauseSecondLiteral
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalTokenSlot_eq_fourthClauseStart_add_eight
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.firstAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.firstCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.firstUnaryAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.firstUnaryCursorEndpoint_before_secondUnary_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.fourthAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.fourthClauseSecondLiteralTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.fourthCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedFirstUnaryAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedFirstUnaryAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedFirstUnaryCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSecondUnaryAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSecondUnaryAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSecondUnaryCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSignAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSignAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSignCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedTerminatorAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedTerminatorAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedTerminatorCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.nextTokenSlot_direct_eq_finish
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.prefixSecondLiteral_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.rules_length
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondLiteralFirstUnaryUnitSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondLiteralSecondUnaryUnitSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondLiteralSignSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondLiteralSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondLiteralTerminatorSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondUnaryAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondUnaryAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondUnaryCursorEndpoint_before_terminator_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.secondUnaryTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.signAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.signAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.signCursorEndpoint_before_firstUnary_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.signTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_secondLiteral_secondUnaryUnit_step
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_secondLiteral_sign_step
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_secondLiteral_terminator_step
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_secondLiteral_unaryUnit_step
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.terminatorAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.terminatorAppenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.terminatorTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.thirdAppender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.thirdCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.trueFalseSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.trueFalseSuffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.trueTrueFalseSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.trueTrueFalseSuffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.unaryAppenderCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.unaryTokenCursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.workRunExact
PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rules_length
PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rules_pairwise_query_distinct

Cook-Levin complete fourth-clause prefix

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the fourth-clause second-literal prefix with a selected 59-rule Finish appender, one existing 45-rule cursor advance, and two total nine-symbol WorkChain bridges. The selected suffix has exactly 113 rules and the global table has exactly 4276 plus the ten inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits the Finish that completes clause four; preserves encodedFormula.take (2 * (FormulaWidth + 36)); and retains coordinate FormulaVariableSlotBound + 1 + 3 * FormulaTokensPerClause + 9, whose direct next schedule token is padding. The external compiled bound evaluates to BuilderFourthClauseSecondLiteralPrefix.rawTimeBound + 618 + 24 * n + 12 * FormulaWidth + 12 * BuilderFourthClauseSeparatorStep.cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 55 new public declarations and two cursor dead-state facts are axiom-audited: 14 have empty closure, 10 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly the fixed Finish terminator that completes clause four and advances to its first padding coordinate. It does not traverse clause-four padding, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (41)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.appender_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.clauseTerminatorSlot_direct_eq_finish
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTape_represents
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTokenBits_eq_encodedFormula_fourthClause
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTokenSlot_eq_fourthClauseStart_add_nine
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finishTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.fourthClauseTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.nextTokenSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefixFinish_launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rules_length
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_exact
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.specification_next_step
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.specification_terminator_step
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePrefix.work_one_step_short_timeout

Cook-Levin fourth-clause remaining-padding run

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete fourth-clause prefix with two structurally generated unary evaluators, the reused 25-rule PaddingCountdown machine, and three total nine-symbol WorkChain bridges. Its table has exactly 4328 plus twelve inherited/generated unary-evaluator rule counts. For every raw bitstring it traverses exactly FormulaTokensPerClause - 9 padding opportunities without emitting a token, preserves encodedFormula.take (2 * (FormulaWidth + 36)), and retains coordinate FormulaVariableSlotBound + 1 + 4 * FormulaTokensPerClause. Direct schedule lookup and the specification cursor both prove that this first opportunity in the intentionally empty fifth fixed-width clause slot is padding. The external compiled bound is BuilderFourthClausePrefix.rawTimeBound + 18 + six times the count-evaluator work, countdown bound, and target-evaluator work. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-countdown, unlaunched-predecessor, and one-step-short results are proved. All 65 new public declarations and three reused countdown interfaces are axiom-audited: 26 have empty closure, 9 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone traverses only the remaining padding in clause four and retains the first opportunity in the intentionally empty fifth clause rectangle. It does not traverse that empty rectangle, reach the next constraint, emit another token, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (39)

PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.countEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.countdownBoundPolynomial_eval
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.countdown_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.fifthClauseSlotStart_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.fifthClauseSlotStart_eq
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTape_represents
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTokenBits_eq_encodedFormula_fourthClause
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTokenSlot_eq_fifthClauseSlotStart
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.launch_workStep
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.malformedCountdownRoot_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.malformedCountdownScratch_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.paddingSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.predecessorSlot_add_remainingPaddingCount
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_eq
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_nine
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_positive
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rules_length
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_exact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.specification_padding_run
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.specification_target_step
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.workRunExact
PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.work_one_step_short_timeout

Cook-Levin empty fifth-clause padding run

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the fourth-clause padding predecessor with two structurally generated unary evaluators, the reused 25-rule PaddingCountdown machine, and three total nine-symbol WorkChain bridges. Its table has exactly 4380 plus fourteen inherited/generated unary-evaluator rule counts. For every raw bitstring it traverses exactly FormulaTokensPerClause padding opportunities in the intentionally empty fifth fixed-width clause rectangle without emitting a token, preserves encodedFormula.take (2 * (FormulaWidth + 36)), and retains coordinate FormulaVariableSlotBound + 1 + 5 * FormulaTokensPerClause. Direct schedule lookup and the specification cursor prove that every traversed fifth-slot opportunity and the first opportunity in the intentionally empty sixth slot are padding. The external compiled bound is BuilderFourthClausePaddingRun.rawTimeBound + 18 + six times the count-evaluator work, countdown bound, and target-evaluator work. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-countdown, unlaunched-predecessor, and one-step-short results are proved. All 65 new public declarations and three reused countdown interfaces are axiom-audited: 28 have empty closure, 9 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone traverses only the intentionally empty fifth clause rectangle and retains the first opportunity in the intentionally empty sixth clause rectangle. It does not traverse that sixth rectangle, reach the next constraint, emit another token, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (39)

PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.countEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.countdownBoundPolynomial_eval
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.countdown_workRunExact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.sixthClauseSlotStart_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.sixthClauseSlotStart_eq
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTape_represents
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTokenBits_eq_encodedFormula_fourthClause
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTokenSlot_eq_sixthClauseSlotStart
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.launch_workStep
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.malformedCountdownRoot_timeout
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.malformedCountdownScratch_timeout
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.predecessorSlot_add_paddingCount
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_eq
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_eq_formulaTokensPerClause
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_positive
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rules_length
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_exact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.specification_padding_run
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.specification_target_step
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.workRunExact
PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.work_one_step_short_timeout

Cook-Levin remaining first-constraint padding run

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the fifth-clause padding predecessor with two structurally generated unary evaluators, the reused 25-rule PaddingCountdown machine, and three total nine-symbol WorkChain bridges. Its table has exactly 4432 plus sixteen inherited/generated unary-evaluator rule counts. For every raw bitstring it traverses exactly (FormulaVariableSlotBound - 2) * (FormulaVariableSlotBound + 2) * FormulaTokensPerClause = (FormulaClauseSlotsPerConstraint - 5) * FormulaTokensPerClause remaining empty token opportunities of the first scheduled constraint without emitting a token, preserves encodedFormula.take (2 * (FormulaWidth + 36)), and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause. Direct schedule lookup and the specification cursor prove that every traversed opportunity is padding and the endpoint is the Sep beginning the second scheduled constraint. The external compiled bound is BuilderFifthClausePaddingRun.rawTimeBound + 18 + six times the count-evaluator work, countdown bound, and target-evaluator work. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-countdown, unlaunched-predecessor, and one-step-short results are proved. All 65 new public declarations and three reused countdown interfaces are axiom-audited: 26 have empty closure, 9 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone traverses only the remaining empty clause rectangles of the first scheduled constraint and retains the Sep beginning the second scheduled constraint. It observes but does not emit that separator, does not emit the next constraint's first literal, implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, emit the remaining formula body, construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (39)

PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le
PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.countEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.countdownBoundPolynomial_eval
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.countdown_workRunExact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.secondConstraintStart_direct_eq_sep
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.secondConstraintStart_eq
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTape_represents
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTokenBits_eq_encodedFormula_fourthClause
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTokenSlot_eq_secondConstraintStart
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.launch_workStep
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.malformedCountdownRoot_timeout
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.malformedCountdownScratch_timeout
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingSlot_direct_eq_padding
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.predecessorSlot_add_paddingCount
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_eq
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_eq_remaining_first_constraint
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_positive
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rules_length
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_exact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.specification_padding_run
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.specification_target_step
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.workRunExact
PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.work_one_step_short_timeout

Cook-Levin second-constraint separator step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete first-constraint padding run with the reused selected 59-rule Sep appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 4554 plus the sixteen inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the Sep beginning the second scheduled constraint; preserves encodedFormula.take (2 * (FormulaWidth + 37)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 1, whose direct next schedule token is T. The external compiled bound evaluates to BuilderFirstConstraintPaddingRun.rawTimeBound + 534 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused separator/cursor interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the fixed Sep that starts the second scheduled constraint. It observes but does not emit the following T, does not emit the first literal or traverse the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalTokenBits_eq_encodedFormula_secondConstraintStart
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalTokenSlot_eq_secondConstraintStart_add_one
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.nextTokenSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefixSeparator_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.secondConstraintStartTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.separatorCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.specification_separator_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.work_one_step_short_timeout

Cook-Levin second-constraint first-literal sign step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint separator step with the reused selected 59-rule T appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 4676 plus the sixteen inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the positive sign beginning the second scheduled constraint's first literal; preserves encodedFormula.take (2 * (FormulaWidth + 38)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 2, whose direct next schedule token is the first unary T of a nonzero variable index. The external compiled bound evaluates to BuilderSecondConstraintSeparatorStep.rawTimeBound + 546 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused true-token/cursor interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the fixed positive T sign that begins the second scheduled constraint's first literal. It observes but does not emit the following unary T, does not complete that literal or traverse the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSign
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalTokenSlot_eq_secondConstraintStart_add_two
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.nextTokenSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefixSign_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.secondConstraintFirstLiteralSignTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.specification_sign_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.trueTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.work_one_step_short_timeout

Cook-Levin second-constraint first-literal first unary-unit step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint first-literal sign step with the reused selected 59-rule T appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 4798 plus the sixteen inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the first unary T of the second scheduled constraint's first variable index; preserves encodedFormula.take (2 * (FormulaWidth + 39)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 3. A constructive schedule proof establishes that the index is at least three, so the direct next schedule token is the second unary T. The external compiled bound evaluates to BuilderSecondConstraintFirstLiteralSignStep.rawTimeBound + 558 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused true-token/cursor interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the first unary T of the second scheduled constraint's first variable index. It observes but does not emit the following second unary T, does not complete that literal or traverse the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralFirstUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalTokenSlot_eq_secondConstraintStart_add_three
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.nextTokenSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.prefixFirstUnaryUnit_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.secondConstraintFirstLiteralFirstUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.specification_firstUnaryUnit_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.trueTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.work_one_step_short_timeout

Cook-Levin second-constraint first-literal second unary-unit step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint first-literal first-unary-unit step with the reused selected 59-rule T appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 4920 plus the sixteen inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the second unary T of the second scheduled constraint's first variable index; preserves encodedFormula.take (2 * (FormulaWidth + 40)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 4. A constructive schedule proof establishes that the index is at least three, so the direct next schedule token is the third unary T. The external compiled bound evaluates to BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rawTimeBound + 570 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused true-token/cursor interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the second unary T of the second scheduled constraint's first variable index. It observes but does not emit the following third unary T, does not complete that literal or traverse the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSecondUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalTokenSlot_eq_secondConstraintStart_add_four
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.nextTokenSlot_direct_eq_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.prefixSecondUnaryUnit_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.secondConstraintFirstLiteralSecondUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.specification_secondUnaryUnit_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.trueTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.work_one_step_short_timeout

Cook-Levin second-constraint first-literal third unary-unit step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint first-literal second-unary-unit step with the reused selected 59-rule T appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 5042 plus the sixteen inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the third and final unary T of the second scheduled constraint's first variable index; preserves encodedFormula.take (2 * (FormulaWidth + 41)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 5. A constructive schedule case split proves the selected variable index is exactly three in both the width-one head-variable and wider position-one blank-symbol branches, so the direct next schedule token is the terminating F. The external compiled bound evaluates to BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rawTimeBound + 582 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused true-token/cursor interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the third and final unary T of the second scheduled constraint's first variable index. It observes but does not emit the following terminating F, does not complete that literal or traverse the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralThirdUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalTokenSlot_eq_secondConstraintStart_add_five
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.nextTokenSlot_direct_eq_f
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.prefixThirdUnaryUnit_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.secondConstraintFirstLiteralThirdUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.specification_thirdUnaryUnit_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.trueTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.work_one_step_short_timeout

Cook-Levin second-constraint first-literal terminator step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint first-literal third-unary-unit step with the reused selected 59-rule F appender and 45-rule cursor advance through one outer total nine-symbol WorkChain bridge. The global table has exactly 5164 plus the sixteen inherited/generated unary-evaluator rule counts. Every raw input follows exact prefix, appender, cursor, bridge, suffix, and combined traces; emits exactly the terminating F of the second scheduled constraint's first literal; preserves encodedFormula.take (2 * (FormulaWidth + 42)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 6. A constructive schedule case split proves the direct next schedule token is Finish when tapeWidth is one and the positive T beginning the next literal at wider widths. The external compiled bound evaluates to BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rawTimeBound + 594 + 24 * n + 12 * FormulaWidth + 12 * cursorWord.length. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, malformed-workspace, both unlaunched-endpoint, and one-step-short results are proved. All 48 new public declarations plus eight reviewed reused false-token/cursor and dead-state interfaces are axiom-audited: 14 have empty closure, 11 use only propext, and 31 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one token: the terminating F of the second scheduled constraint's first literal. It observes but does not emit the following Finish in the width-one case or the following positive T in wider cases, does not emit the remainder of the second constraint or traverse that constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep
PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_length
PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.appenderEndpoint_before_cursor_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.appender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.cursor_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.falseTokenCursor_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralTerminator
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalTokenSlot_eq_secondConstraintStart_add_six
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.malformedAppenderOutput_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.malformedAppenderTally_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.malformedCursorScratch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.nextTokenSlot_direct_eq_finish_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.prefixTerminator_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.secondConstraintFirstLiteralTerminatorTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.specification_next_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.specification_terminator_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.work_one_step_short_timeout

Cook-Levin second-constraint first-literal successor token step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint first-literal terminator with the represented-width unary evaluator, one 93-rule finite width branch that enters a single reused 59-rule token appender at either Finish or T, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 5284 plus the eighteen inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, branch/appender, retained-coordinate, bridge, suffix, and combined traces; emits Finish exactly when tapeWidth is one and T at every wider width; preserves encodedFormula.take (2 * (FormulaWidth + 43)); and retains coordinate FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 7. Direct lookup and the specification cursor prove the following opportunity is padding at width one and unary T at wider widths. The external compiled bound evaluates to BuilderSecondConstraintFirstLiteralTerminatorStep.rawTimeBound + 600 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. All 80 new public declarations plus two strengthened predecessor boundary lemmas are axiom-audited: 37 have empty closure, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone emits exactly one width-selected token after the terminating F of the second scheduled constraint's first literal: Finish at width one or positive T at wider widths. It observes but does not emit the following padding opportunity at width one or unary T at wider widths, does not emit the remainder of the second constraint or traverse that constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.branchAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSuccessor
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTokenSlot_eq_secondConstraintStart_add_seven
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.secondConstraintFirstLiteralSuccessorTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.specification_successor_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlot_eq_secondConstraintStart_add_seven
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.work_one_step_short_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.followingTokenSlot_direct_eq_padding_or_t

Cook-Levin second-constraint padding-or-unary opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second-constraint first-literal successor-token predecessor with the represented-width unary evaluator, one 93-rule finite optional-appender table, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 5404 plus the twenty inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width T-appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the first unary T of the second literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 1)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 8. Direct lookup and the specification cursor prove the following slot is again padding at width one and the second unary T at wider widths. The external compiled bound evaluates to BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rawTimeBound + 612 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. All 80 new public declarations plus two strengthened schedule lemmas are axiom-audited: 37 have empty closure, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one width-selected schedule opportunity after the second scheduled constraint first literal: padding with no emitted token at width one or the first unary T of the second literal at wider widths. It observes but does not consume the following padding opportunity at width one or second unary T at wider widths, does not complete the second literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_optional_unary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.secondFollowingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintPaddingOrUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_eight
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_eight
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.secondConstraintPaddingOrUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.work_one_step_short_timeout

Cook-Levin second-constraint second padding-or-unary opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete first padding-or-unary-opportunity predecessor with the represented-width unary evaluator, the same reviewed 93-rule finite optional-appender table, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 5524 plus the twenty-two inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width T-appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the second unary T of the second literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 2)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 9. Direct lookup and the specification cursor prove the following slot is again padding at width one and the third unary T at wider widths. The external compiled bound evaluates to BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rawTimeBound + 624 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. All 66 new public declarations, fourteen reused optional-appender interfaces, and two strengthened schedule lemmas are axiom-audited: 37 have empty closure, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one additional width-selected schedule opportunity after the second scheduled constraint first literal: padding with no emitted token at width one or the second unary T of the second literal at wider widths. It observes but does not consume the following padding opportunity at width one or third unary T at wider widths, does not complete the second literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_two_optional_unary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.thirdFollowingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintSecondPaddingOrUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_nine
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_nine
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.secondConstraintSecondPaddingOrUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.work_one_step_short_timeout

Cook-Levin second-constraint third padding-or-unary opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete second padding-or-unary-opportunity predecessor with the represented-width unary evaluator, the same reviewed 93-rule finite optional-appender table, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 5644 plus the twenty-four inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width T-appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the third unary T of the second literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 3)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 10. Direct lookup and the specification cursor prove the following slot is again padding at width one and the fourth unary T at wider widths. The external compiled bound evaluates to BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rawTimeBound + 636 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. All 66 new public declarations, fourteen reused optional-appender interfaces, and two strengthened schedule lemmas are axiom-audited: 37 have empty closure, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one additional width-selected schedule opportunity after the second scheduled constraint first literal: padding with no emitted token at width one or the third unary T of the second literal at wider widths. It observes but does not consume the following padding opportunity at width one or fourth unary T at wider widths, does not complete the second literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_three_optional_unary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.fourthFollowingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintThirdPaddingOrUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_ten
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_ten
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.secondConstraintThirdPaddingOrUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.work_one_step_short_timeout

Cook-Levin second-constraint fourth padding-or-unary opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete third padding-or-unary-opportunity predecessor with the represented-width unary evaluator, the same reviewed 93-rule finite optional-appender table, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 5764 plus the twenty-six inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width T-appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the fourth unary T of the second literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 4)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 11. Direct lookup and the specification cursor prove the following slot is padding at width one and the terminating F at wider widths. The external compiled bound evaluates to BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rawTimeBound + 648 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. All 66 new public declarations, fourteen reused optional-appender interfaces, and two strengthened schedule lemmas are axiom-audited: 37 have empty closure, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one additional width-selected schedule opportunity after the second scheduled constraint first literal: padding with no emitted token at width one or the fourth unary T of the second literal at wider widths. It observes but does not consume the following padding opportunity at width one or terminating F at wider widths, does not complete the second literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.fifthFollowingTokenSlot_direct_eq_padding_or_f
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintFourthPaddingOrUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_eleven
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_f
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_eleven
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.secondConstraintFourthPaddingOrUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.work_one_step_short_timeout

Cook-Levin second-constraint fifth padding-or-terminator opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete fourth padding-or-unary-opportunity predecessor with the represented-width unary evaluator, a new reviewed 93-rule finite optional-terminator table over the audited token-appender rules, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 5884 plus the twenty-eight inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width F-appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the terminating F of the second literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 5)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 12. Direct lookup and the specification cursor prove the following slot is padding at width one and the opening unary T of the following literal at wider widths. The external compiled bound evaluates to BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rawTimeBound + 660 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. The measured audit covers all 66 new public outer declarations, fourteen new optional-terminator interfaces, and two strengthened schedule lemmas: 37 closures are empty, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one additional width-selected schedule opportunity after the second scheduled constraint first literal: padding with no emitted token at width one or the terminating F of the second literal at wider widths. It observes but does not consume the following padding opportunity at width one or opening unary T at wider widths, does not complete the following literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary_and_optional_terminator
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.sixthFollowingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintFifthPaddingOrTerminator
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_twelve
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_twelve
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.secondConstraintFifthPaddingOrTerminatorTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.work_one_step_short_timeout

Cook-Levin second-constraint sixth padding-or-opening-unary opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete fifth padding-or-terminator-opportunity predecessor with the represented-width unary evaluator, the reviewed 93-rule finite optional-appender table, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 6004 plus the thirty inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width opening-T appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the opening positive T of the following literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 6)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 13. Direct lookup and the specification cursor prove the following slot is padding at width one and the first unary-index T of the following literal at wider widths. The external compiled bound evaluates to BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rawTimeBound + 672 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. The measured audit covers all 66 new public declarations, fourteen reused optional-appender interfaces, and two strengthened schedule lemmas: 37 closures are empty, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one additional width-selected schedule opportunity after the second scheduled constraint second literal: padding with no emitted token at width one or the opening positive T of the following literal at wider widths. It observes but does not consume the following padding opportunity at width one or first unary-index T at wider widths, does not complete the following literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary_and_optional_terminator_and_optional_opening_unary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.seventhFollowingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintSixthPaddingOrOpeningUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_thirteen
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_thirteen
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.secondConstraintSixthPaddingOrOpeningUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.work_one_step_short_timeout

Cook-Levin second-constraint seventh padding-or-unary opportunity step

For every fixed concrete polynomial-time verifier, one literal finite work machine composes the complete sixth padding-or-opening-unary-opportunity predecessor with the represented-width unary evaluator, the reviewed 93-rule finite optional-appender table, and the retained-coordinate unary evaluator through three total nine-symbol WorkChain bridges. The global table has exactly 6124 plus the thirty-two inherited/generated unary-evaluator rule counts. Every raw input follows exact predecessor, width-evaluator, width-one skip or wider-width first-unary-index-T appender, retained-coordinate, bridge, suffix, and combined traces. At tapeWidth one it consumes padding and emits no token; at every wider width it appends exactly the first unary-index T of the following literal. The output equals encodedFormula.take (2 * (FormulaWidth + 43 + if tapeWidth = 1 then 0 else 7)) and the retained coordinate is FormulaVariableSlotBound + 1 + FormulaClauseSlotsPerConstraint * FormulaTokensPerClause + 14. Direct lookup and the specification cursor prove the following slot is padding at width one and the second unary-index T of the following literal at wider widths. The external compiled bound evaluates to BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rawTimeBound + 684 + 24 * n + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps. Compiled exact, bounded, blank-equivalent, accepting, non-timeout, predecessor-unlaunched-endpoint, and one-step-short results are proved while component malformed-workspace behavior remains fail-closed. The measured audit covers all 66 new public declarations, fourteen reused optional-appender interfaces, and two strengthened schedule lemmas: 37 closures are empty, 12 use only propext, and 33 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone consumes exactly one additional width-selected schedule opportunity after the second scheduled constraint following literal opening: padding with no emitted token at width one or the first unary-index T of the following literal at wider widths. It observes but does not consume the following padding opportunity at width one or second unary-index T at wider widths, does not complete the following literal or traverse the remainder of the second constraint, does not implement a general dynamic formula cursor or raw decoder for arbitrary schedule coordinates, does not emit the remaining formula body, and does not construct a complete formula builder or FunctionProgram.RawRefinement, package a concrete PolynomialReduction, establish CNFSAT NP-hardness or NP-completeness, establish CNFSAT in P, or prove P = NP.

Reviewed theorem interfaces (40)

PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary_and_optional_terminator_and_optional_opening_unary_and_optional_first_unary
PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.eighthFollowingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalConfiguration_state
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalOutside_contains_finalTokenSlot
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalTape_represents
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintSeventhPaddingOrUnary
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_fourteen
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_fourteen
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rawTimeBound_eval
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rawTimeBound_le
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rules_length
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_exact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.secondConstraintSeventhPaddingOrUnaryTokens_eq_canonical_formula_prefix
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.specification_following_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.specification_opportunity_step
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.suffix_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.width_eq_tapeWidth
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.width_positive
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.workBoundedDecide_accept
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.workRunExact
PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.work_one_step_short_timeout

Typed direct-wire NAND semantics

Typed topological Boolean NAND programs and ordered multi-output direct-wire semantics.

This does not establish circuit minimization, SAT, or P = NP.

Reviewed theorem interfaces (3)

PNP.DirectWire.Equivalent.trans
PNP.DirectWire.andCircuit_spec
PNP.DirectWire.nandCircuit_spec

Finite enumeration, equivalence, and reference minimum

Exhaustive finite Boolean direct-wire search under the empty-profile reference model.

No polynomial-runtime result is obtained from this exhaustive reference search.

Reviewed theorem interfaces (4)

PNP.DirectWire.equivalentBool_eq_true_iff
PNP.DirectWire.exactWidthEnumeration_complete
PNP.DirectWire.referenceMinimum_invariant
PNP.DirectWire.residualSlack_eq_zero_iff_minimum

Concrete framed replacement and slack

The concrete serial framed context with support outputs and explicit bypass wires.

This is not an arbitrary-support replacement theorem for the report's global family.

Reviewed theorem interfaces (2)

PNP.DirectWire.compatibleReplacement_framed
PNP.DirectWire.framedGlobalSlackLaw

Locked-NAND local candidates and baseline accounting

Typed local macro candidates, source-derived counts, and five finite local square baselines.

Local minima are not a global BaselineDistinct or locked-NAND threshold theorem.

Reviewed theorem interfaces (6)

PNP.DirectWire.equalityDirect_referenceMinimum
PNP.DirectWire.lockedBaselineCount_report_formula
PNP.DirectWire.constantOneDirect_referenceMinimum
PNP.DirectWire.constantZeroDirect_referenceMinimum
PNP.DirectWire.prefixAndDirect_referenceMinimum
PNP.DirectWire.traceDirect_referenceMinimum

Locked-NAND global carrier and trace equivalence

Exact X/T/O/R/L/z carrier separation and both trace-equivalence directions for arbitrary finite topological NAND circuits.

Carrier/trace equivalence does not assemble the complete exposed candidates, prove cross-instance BaselineDistinct or final-output laws, construct the uniform polynomial builder, or establish the locked-NAND threshold.

Reviewed theorem interfaces (8)

PNP.DirectWire.LockedNANDTrace.carrierSeparation
PNP.DirectWire.LockedNANDTrace.finalLock_fresh
PNP.DirectWire.LockedNANDTrace.distinguishedChecks_length
PNP.DirectWire.LockedNANDTrace.tracePredicate_coherentExtension
PNP.DirectWire.LockedNANDTrace.trace_sound_of_predicate_true
PNP.DirectWire.LockedNANDTrace.traceEquivalence
PNP.DirectWire.LockedNANDTrace.satisfiable_iff_trace_extension
PNP.DirectWire.LockedNANDTrace.exists_coherent_trace

Locked-NAND global baseline and four-gate candidate assembly

Exact source-derived B/B baseline and B+4/B+1 extension for arbitrary finite topological NAND circuits.

Candidate assembly alone does not prove global BaselineDistinct, either conditional final-output branch law, the locked-NAND threshold, residual slack at most four, or a uniform polynomial bitstring builder.

Reviewed theorem interfaces (11)

PNP.DirectWire.LockedNANDGlobalCandidates.macroGateCount_report_formula
PNP.DirectWire.LockedNANDGlobalCandidates.nonemptyPrefixCandidate_semantics
PNP.DirectWire.LockedNANDGlobalCandidates.rawBaselineGateCount_eq_lockedBaselineCount
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_size
PNP.DirectWire.LockedNANDGlobalCandidates.baselinePrefixSource_semantics
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_size
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_initial_semantics
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_final_semantics
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_no_internal_constants
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_no_internal_constants
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_finalLock_irrelevant

Locked-NAND global baseline distinctness

All exposed baseline outputs are nonconstant, nonprojections, pairwise semantically distinct, and have exact exhaustive reference minimum B for arbitrary finite topological NAND circuits.

BaselineDistinct does not prove either whole-carrier final-output branch law, instantiate the complete threshold premise package, establish the locked-NAND threshold or global residual-slack bound, or construct the uniform polynomial bitstring builder.

Reviewed theorem interfaces (5)

PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_outputNonconstant
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_outputNotPositiveProjection
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_outputPairwiseDistinct
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_outputConditions
PNP.DirectWire.LockedNANDGlobalCandidates.baselineCandidate_referenceMinimum

Locked-NAND global unsatisfiable final-zero branch

For every finite topologically ordered NAND circuit, unsatisfiability makes the full final coordinate identically false on the whole carrier and fixes the exhaustive reference minimum at B.

This does not prove satisfiable FinalLockSeparation, instantiate the complete threshold package, establish the global locked-NAND threshold or residual-slack bound, or construct the uniform polynomial builder.

Reviewed theorem interfaces (2)

PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_final_eq_false_of_unsatisfiable
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_referenceMinimum_eq_baseline_of_unsatisfiable

Locked-NAND satisfiable separation and typed semantic threshold

For every finite topologically ordered NAND circuit, one answer-independent full candidate instantiates all six semantic premises, has residual slack at most four, and crosses the exact source-derived minimum threshold exactly when the source circuit is satisfiable.

This typed semantic theorem does not construct or compile the report's encoded polynomial-time SAT-to-locked-NAND builder, establish CNFSAT in P, prove NP-hardness transport, discharge the abstract locked-NAND threshold axiom, or prove P = NP.

Reviewed theorem interfaces (8)

PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_final_nonconstant_of_satisfiable
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_final_notPositiveProjection_of_satisfiable
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_final_distinctFromBaseline_of_satisfiable
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_satisfiableFinalConditions
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_referenceMinimum_bounds_of_satisfiable
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_residualSlack_le_four
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_satisfiable_iff_referenceMinimum_ge_succ
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_referenceMinimum_eq_baseline_of_unsatisfiable

Encoded locked-NAND semantic boundary

A strict version-zero bit grammar round-trips normalized NAND circuits and complete locked-NAND candidates; the pure all-bitstring transformation is fail-closed and preserves source satisfiability at the exact target threshold.

This is not a parser/validator machine, emitter machine, RawRefinement, PolynomialReduction, construction-runtime or output-size bound, abstract locked-NAND threshold discharge, CNFSAT-in-P result, or P = NP.

Reviewed theorem interfaces (11)

PNP.Concrete.LockedNAND.RawCircuit.normalize_idempotent
PNP.Concrete.LockedNAND.RawCircuit.normalize_eval
PNP.Concrete.LockedNAND.RawCircuit.elaborate_ofCircuit
PNP.Concrete.LockedNAND.RawCandidate.elaborate_ofCandidate
PNP.Concrete.LockedNAND.RawLockedInstance.elaborate_ofCandidate
PNP.Concrete.LockedNAND.decodeTokens_encodeTokens
PNP.Concrete.LockedNAND.decodeCircuit_encodeCircuit
PNP.Concrete.LockedNAND.decodeLockedInstance_encodeLockedInstance
PNP.Concrete.LockedNAND.decodeElaboratedCircuit_encodeCircuit_ofCircuit
PNP.Concrete.LockedNAND.encoded_fullCandidate_threshold_iff_satisfiable
PNP.Concrete.LockedNAND.buildLockedNANDInstance_correct

Concrete strict-v0 locked-NAND source parser

One literal nine-symbol finite work machine validates every strict version-zero source bitstring: it accepts exactly ValidEncodedCircuit, preserves valid bytes, clears invalid bytes, cannot time out within the proved compiled cubic bound, and supplies polynomial-time machine/function witnesses plus the validator's exact leaf RawRefinement.

This source parser alone does not emit the locked-NAND target or establish the source-to-target PolynomialReduction. The downstream emitter now supplies its own runtime/output bounds and strict composition, but the abstract locked-NAND threshold assumption, CNFSAT-in-P result, NP-hardness or NP-completeness transport, and P = NP remain absent.

Reviewed theorem interfaces (20)

PNP.Concrete.LockedNAND.SourceParser.acceptedTape_outputBits
PNP.Concrete.LockedNAND.SourceParser.allInput_exact
PNP.Concrete.LockedNAND.SourceParser.canonicalSteps_le_validWorkBound
PNP.Concrete.LockedNAND.SourceParser.compiledBoundedDecide_accept_iff
PNP.Concrete.LockedNAND.SourceParser.compiledBoundedDecide_ne_timeout
PNP.Concrete.LockedNAND.SourceParser.compiledMachineOutput_eq_validatedSourceBytes
PNP.Concrete.LockedNAND.SourceParser.compiledStart_blankEquivalent
PNP.Concrete.LockedNAND.SourceParser.decodeCircuitTokens_eq_none_iff_failure
PNP.Concrete.LockedNAND.SourceParser.illFormed_exact
PNP.Concrete.LockedNAND.SourceParser.machine_acceptState_ne_rejectState
PNP.Concrete.LockedNAND.SourceParser.malformed_exact
PNP.Concrete.LockedNAND.SourceParser.rules_length
PNP.Concrete.LockedNAND.SourceParser.rules_pairwise_query_distinct
PNP.Concrete.LockedNAND.SourceParser.statePrograms_length
PNP.Concrete.LockedNAND.SourceParser.validFinalConfiguration_isHalted
PNP.Concrete.LockedNAND.SourceParser.validFinalConfiguration_state
PNP.Concrete.LockedNAND.SourceParser.validRawBound_eq
PNP.Concrete.LockedNAND.SourceParser.validRawTimePolynomial_eval
PNP.Concrete.LockedNAND.SourceParser.validatedSourceBytesPolynomialTimeFunction_output
PNP.Concrete.LockedNAND.SourceParser.wellFormed_exact

Concrete strict-v0 locked-NAND target emitter

One literal 1,387,921-rule grammar-only controller emits the exact direct locked-NAND target on every grammar-decoded circuit, rejects malformed grammar with empty output, cannot time out within an explicit all-input polynomial, has an explicit quadratic output-size bound, and supplies compiled polynomial-time machine/function witnesses, exact leaf RawRefinement, and strict parser/emitter composition computing buildLockedNANDInstance.

The standalone emitter intentionally accepts every grammar-decoded raw circuit, including intrinsically invalid references; strict fail-closed semantics come from parser composition. The standalone emitter does not itself package the language equivalence as PolynomialReduction; the downstream concrete reduction milestone now does. The abstract locked-NAND threshold assumption, CNFSAT-in-P result, NP-hardness transport, and P = NP remain absent.

Reviewed theorem interfaces (22)

PNP.Concrete.LockedNAND.RawBuilder.rawLockedInstance_of_elaborate
PNP.Concrete.LockedNAND.RawBuilder.targetBytes_of_elaborated
PNP.Concrete.LockedNAND.TargetEmitterSpec.targetBytes_validatedSourceBytes_eq_buildLockedNANDInstance
PNP.Concrete.LockedNAND.TargetEmitterSpec.targetBytes_size_le
PNP.Concrete.LockedNAND.TargetEmitterController.rules_length_literal
PNP.Concrete.LockedNAND.TargetEmitterController.rules_pairwise
PNP.Concrete.LockedNAND.TargetEmitterController.machine_accept_ne_reject
PNP.Concrete.LockedNAND.TargetEmitterController.graph_wellFormed
PNP.Concrete.LockedNAND.TargetEmitterControllerTotalTrace.malformed_bounded_exact
PNP.Concrete.LockedNAND.TargetEmitterControllerTotalTrace.decoded_bounded_exact
PNP.Concrete.LockedNAND.TargetEmitterControllerTotalTrace.allInput_bounded_exact
PNP.Concrete.LockedNAND.TargetEmitterControllerPolynomialBound.controllerWorkTimePolynomial_eval
PNP.Concrete.LockedNAND.TargetEmitterControllerPolynomialBound.allInputWorkTimePolynomial_eval
PNP.Concrete.LockedNAND.TargetEmitterControllerPolynomialBound.compiledRawTimePolynomial_eval
PNP.Concrete.LockedNAND.TargetEmitterControllerPolynomialBound.controller_complete_path_polynomial
PNP.Concrete.LockedNAND.TargetEmitterControllerPolynomialBound.controllerUniformEnvelope_le_workBound
PNP.Concrete.LockedNAND.TargetEmitterControllerCompiled.compiledStart_blankEquivalent
PNP.Concrete.LockedNAND.TargetEmitterControllerCompiled.compiledMachineOutput_eq_targetBytes
PNP.Concrete.LockedNAND.TargetEmitterControllerCompiled.compiledBoundedDecide_accept_iff
PNP.Concrete.LockedNAND.TargetEmitterControllerCompiled.compiledBoundedDecide_ne_timeout
PNP.Concrete.LockedNAND.TargetEmitterControllerCompiled.rawTargetBytesPolynomialTimeFunction_output
PNP.Concrete.LockedNAND.TargetEmitterControllerCompiled.strictLockedNANDPolynomialTimeFunction_output

Concrete strict-v0 locked-NAND polynomial reduction

The existing strict parser/emitter composition is packaged as a concrete polynomial many-one reduction from EncodedNANDSAT to EncodedLockedNANDThreshold, with exact function identity, exact output, all-bitstring language equivalence, a ReducesTo witness, and recursive raw-machine refinement.

The downstream all-input CNF compiler now identifies CNFSAT with this concrete source language through a fixed finite machine and a direct polynomial reduction, then composes with this reduction. This milestone does not discharge the abstract target-language assumption, prove the report-level locked-NAND threshold theorem, put CNFSAT in P, complete residual minimization or ZeroSlack, or prove P = NP.

Reviewed theorem interfaces (5)

PNP.Concrete.LockedNAND.strictLockedNANDPolynomialReduction_function
PNP.Concrete.LockedNAND.strictLockedNANDPolynomialReduction_output
PNP.Concrete.LockedNAND.strictLockedNANDPolynomialReduction_correct
PNP.Concrete.LockedNAND.encodedNANDSAT_reducesTo_encodedLockedNANDThreshold
PNP.Concrete.LockedNAND.strictLockedNANDPolynomialReduction_hasRawRefinement

Concrete CNF-to-NAND semantic compiler

A total answer-independent compiler transforms every strict canonical CNF formula into an intrinsically topological well-formed NAND circuit, preserves satisfiability exactly, proves the exact gate count and a quadratic serialized-output bound, fails closed on every malformed bitstring, and composes semantically with the concrete locked-NAND threshold builder.

This milestone is the pure semantic and size-bound layer; the subsequent all-input milestone supplies the finite-machine, PolynomialTimeFunction, RawRefinement, and PolynomialReduction interfaces. Neither layer decides CNF-SAT, proves CNFSAT is in deterministic polynomial time, discharges the abstract report-level locked-NAND premise, completes ZeroSlack/PCCMin, or proves P = NP.

Reviewed theorem interfaces (18)

PNP.Concrete.CNFToNAND.encodeCNF_of_decodeEncodedCNF
PNP.Concrete.CNFToNAND.compileFormula_inputCount
PNP.Concrete.CNFToNAND.compileFormula_output_is_gate
PNP.Concrete.CNFToNAND.compileFormula_wellFormed
PNP.Concrete.CNFToNAND.decodeValidCircuit_encode_compileFormula
PNP.Concrete.CNFToNAND.compiledFormulaCircuit_eval_eq_true_iff
PNP.Concrete.CNFToNAND.compiledFormulaCircuit_satisfiable_iff
PNP.Concrete.CNFToNAND.compileFormula_satisfiable_iff
PNP.Concrete.CNFToNAND.formula_satisfiable_iff_encoded_compileFormula
PNP.Concrete.CNFToNAND.compileFormula_gateCount_exact
PNP.Concrete.CNFToNAND.compileFormula_gateCount_le
PNP.Concrete.CNFToNAND.cnfToNANDOutputSizePolynomial_eval
PNP.Concrete.CNFToNAND.compileEncodedCNFToNAND_of_decoded
PNP.Concrete.CNFToNAND.compileEncodedCNFToNAND_of_malformed
PNP.Concrete.CNFToNAND.compileEncodedCNFToNAND_size_le
PNP.Concrete.CNFToNAND.empty_not_encodedNANDSAT
PNP.Concrete.CNFToNAND.compileEncodedCNFToNAND_correct
PNP.Concrete.CNFToNAND.buildLockedNANDFromCNF_correct

Concrete all-input CNF-to-NAND polynomial reduction

One fixed 135,070-rule three-node parser/carrier/controller work graph halts on every bitstring, rejects malformed CNF words with empty output, emits exactly compileEncodedCNFToNAND on every valid source, has one external encoded-input polynomial, compiles to a non-timeout PolynomialTimeFunction, retains literal RawRefinement, packages a direct PolynomialReduction from CNFSAT to EncodedNANDSAT, and composes it with the strict locked-NAND reduction to EncodedLockedNANDThreshold.

This syntax-directed compiler does not itself decide CNF-SAT, put CNFSAT in deterministic polynomial time, establish SAT NP-hardness or CNFSAT NP-completeness, connect the concrete locked-NAND target to the abstract report-level threshold theorem, complete residual minimization or ZeroSlack/PCCMin, discharge any project assumption, or prove P = NP.

Reviewed theorem interfaces (28)

PNP.Concrete.CNFSourceParser.allInput_exact
PNP.Concrete.CNFSourceParser.compiledMachineOutput_eq_validatedCNFBytes
PNP.Concrete.CNFSourceParser.compiledBoundedDecide_ne_timeout
PNP.Concrete.CNFToNANDCarrierEncoder.canonical_exact
PNP.Concrete.CNFToNANDCarrierEncoder.canonicalWorkSteps_polynomial_bound
PNP.Concrete.CNFToNANDWorkspace.exact_execution_output
PNP.Concrete.CNFToNANDController.rules_length_literal
PNP.Concrete.CNFToNANDControllerTotalTrace.canonical_path
PNP.Concrete.CNFToNANDControllerTotalTrace.canonical_bounded_exact
PNP.Concrete.CNFToNANDCompilerMachine.rules_length_literal
PNP.Concrete.CNFToNANDCompilerTotalTrace.malformed_bounded_exact
PNP.Concrete.CNFToNANDCompilerTotalTrace.decoded_bounded_exact
PNP.Concrete.CNFToNANDCompilerTotalTrace.allInput_bounded_exact
PNP.Concrete.CNFToNANDCompilerPolynomialBound.allInputWorkTimePolynomial_eval
PNP.Concrete.CNFToNANDCompilerPolynomialBound.compiledRawTimePolynomial_eval
PNP.Concrete.CNFToNANDCompilerCompiled.compiledMachineOutput_eq_compileEncodedCNFToNAND
PNP.Concrete.CNFToNANDCompilerCompiled.compiledBoundedDecide_accept_iff
PNP.Concrete.CNFToNANDCompilerCompiled.compiledBoundedDecide_ne_timeout
PNP.Concrete.CNFToNANDCompilerCompiled.cnfToNANDPolynomialTimeFunction_output
PNP.Concrete.CNFToNAND.cnfToNANDPolynomialReduction_function
PNP.Concrete.CNFToNAND.cnfToNANDPolynomialReduction_output
PNP.Concrete.CNFToNAND.cnfToNANDPolynomialReduction_correct
PNP.Concrete.CNFToNAND.cnfSAT_reducesTo_encodedNANDSAT
PNP.Concrete.CNFToNAND.cnfToNANDPolynomialReduction_hasRawRefinement
PNP.Concrete.CNFToNAND.cnfToLockedNANDPolynomialReduction_output
PNP.Concrete.CNFToNAND.cnfToLockedNANDPolynomialReduction_correct
PNP.Concrete.CNFToNAND.cnfSAT_reducesTo_encodedLockedNANDThreshold
PNP.Concrete.CNFToNAND.cnfToLockedNANDPolynomialReduction_hasRawRefinement

Conditional locked-NAND threshold boundary

A proof-bearing six-premise candidate boundary for an arbitrary satisfiable proposition.

The premises are not instantiated by a uniform SAT-to-locked-NAND builder.

Reviewed theorem interfaces (2)

PNP.DirectWire.ConditionalThresholdBoundaryPremises.fullResidualSlack_le_four
PNP.DirectWire.ConditionalThresholdBoundaryPremises.satisfiable_iff_minimum_ge_succ

Fail-closed explicit-list residual routes

Executable strict-gain search over a caller-supplied finite implementation list.

Unresolved excludes no gain outside the supplied list and cannot imply ZeroSlack.

Reviewed theorem interfaces (5)

PNP.DirectWire.StrictEquivalentGain.strictResidualDescent
PNP.DirectWire.strictEquivalentGainBool_complete
PNP.DirectWire.firstListedGain_sound
PNP.DirectWire.firstListedGain_none_no_listed_gain
PNP.DirectWire.unresolved_positiveSlack_regression

Universal verified residual-gain chain bound

Every finite proof-bearing or executably verified chain of adjacent strict equivalent gains preserves semantics and the exhaustive reference minimum, while its endpoint residual slack plus its length is at most its starting residual slack. For the complete locked-NAND candidate, the existing residual-slack-at-most-four theorem specializes this to at most four verified gain steps.

This milestone bounds only a disclosed, independently verified sequence. It does not find the next gain, prove route or candidate-list completeness, justify stopping after fewer than the bound, construct ZeroSlack, compute an exact minimizer, establish polynomial checker or PCCMin runtime, put SAT in P, discharge a project assumption, or prove P = NP.

Reviewed theorem interfaces (14)

PNP.DirectWire.StrictEquivalentGain.strictResidualDescent
PNP.DirectWire.strictGainChainBool_eq_true_iff
PNP.DirectWire.StrictGainChain.end_equivalent
PNP.DirectWire.StrictGainChain.end_referenceMinimum_eq
PNP.DirectWire.StrictGainChain.end_residualSlack_add_length_le
PNP.DirectWire.StrictGainChain.length_le_residualSlack
PNP.DirectWire.strictGainChainBool_length_le_residualSlack
PNP.DirectWire.strictGainChainBool_length_le_of_residualSlack_le
PNP.DirectWire.StrictGainChain.eq_nil_of_residualSlack_eq_zero
PNP.DirectWire.strictGainChainBool_eq_nil_of_residualSlack_eq_zero
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_residualSlack_le_four
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidateImplementation_residualSlack_le_four
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_strictGainChain_length_le_four
PNP.DirectWire.LockedNANDGlobalCandidates.fullCandidate_strictGainChainBool_length_le_four

Global strict-gain stopping specification

For every finite direct-wire implementation, positive exhaustive-reference residual slack is equivalent to the existence of some strictly smaller semantically equivalent implementation; zero slack and semantic minimality are each equivalent to global absence of such an implementation. A verified chain endpoint with separately proved global no-gain evidence therefore has zero slack and packages an exact minimum result.

This is a semantic stopping criterion, not a stopping algorithm. It uses the exhaustive reference minimum as a mathematical witness and requires a proof quantifying over every finite implementation at the endpoint. It does not derive global absence from a finite scan, generate a route, prove candidate-list or route completeness, construct the manuscript's ZeroSlack certificate, establish polynomial checking or PCCMin runtime, put SAT in P, discharge a project assumption, or prove P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.referenceMinimumImplementation_gateCount_eq_referenceMinimum
PNP.DirectWire.referenceMinimumImplementation_equivalent
PNP.DirectWire.referenceMinimumImplementation_isSemanticallyMinimum
PNP.DirectWire.referenceMinimumImplementation_residualSlack_eq_zero
PNP.DirectWire.referenceMinimumImplementation_strictEquivalentGain_of_residualSlack_pos
PNP.DirectWire.residualSlack_pos_iff_exists_strictEquivalentGain
PNP.DirectWire.residualSlack_eq_zero_iff_forall_not_strictEquivalentGain
PNP.DirectWire.isSemanticallyMinimum_iff_forall_not_strictEquivalentGain
PNP.DirectWire.StrictGainChain.end_residualSlack_eq_zero_of_no_strictEquivalentGain
PNP.DirectWire.strictGainChainBool_end_residualSlack_eq_zero_of_no_strictEquivalentGain

Terminal full-carrier residual bridge

For every finite direct-wire implementation, terminalization preserves the exact whole implementation, gate count, and semantics at every input/output coordinate. An independently stated terminal minimum is attained, universally lower-bounds every complete terminal realization, and equals the exhaustive semantic reference minimum. Positive residual slack is equivalent to a cheaper whole-span full realization, every such realization gives strict residual descent, and zero slack is equivalent to absence of one.

This is the direct-wire terminal full-mode specialization of the manuscript bridge. It does not formalize the quotient carrier or quotient-to-full firewall, proper or governed supports, SaturatePositive, BCEL/BN2-BN6, packet or selector completeness, route generation, the ZeroSlack certificate, PCCMin, polynomial minimum search or checking, SAT in P, discharge a project assumption, or prove P = NP.

Reviewed theorem interfaces (13)

PNP.DirectWire.terminalize_implementation
PNP.DirectWire.terminalize_gateCount
PNP.DirectWire.TerminalFullRealization.realize_equivalent
PNP.DirectWire.TerminalFullRealization.realize_semantics
PNP.DirectWire.referenceMinimumTerminalFullRealization_gateCount
PNP.DirectWire.terminalFullMinimum_eq_referenceMinimum
PNP.DirectWire.terminalFullMinimum_spec
PNP.DirectWire.isTerminalFullMinimum_iff_eq_terminalFullMinimum
PNP.DirectWire.isTerminalFullMinimum_iff_eq_referenceMinimum
PNP.DirectWire.WholeSpanResidualWitness.strictResidualDescent
PNP.DirectWire.residualSlack_pos_iff_exists_wholeSpanResidualWitness
PNP.DirectWire.residualSlack_eq_zero_iff_no_wholeSpanResidualWitness
PNP.DirectWire.StrictEquivalentGain.strictResidualDescent

Terminal quotient/full mode firewall

For every finite direct-wire implementation, a computed finite profile observer records the ten terminal carrier roles and an explicit forgetful projection selects the quotient coordinates. Projection retains the exact implementation, gate count, and complete multi-output Boolean semantics. A quotient comparison has a checked full lift exactly when every forgotten profile coordinate agrees, lossless projections lift directly, and obligation discharge transports across a checked lift.

This is a terminal comparison/lifting firewall only. It supplies no proper or governed supports, arbitrary quotient construction, support or projection-defect minimum, saturation, Package E, BCEL/BN2-BN6, packet or selector completeness, global residual route, ZeroSlack certificate, PCCMin exactness or polynomial runtime, SAT-in-P result, discharged project assumption, or proof that P = NP.

Reviewed theorem interfaces (12)

PNP.DirectWire.TerminalFullCarrierRealization.project_realization
PNP.DirectWire.TerminalFullCarrierRealization.project_implementation
PNP.DirectWire.TerminalFullCarrierRealization.project_gateCount
PNP.DirectWire.TerminalFullCarrierRealization.project_equivalent
PNP.DirectWire.TerminalFullCarrierRealization.project_semantics
PNP.DirectWire.TerminalCheckedFullLift.fullRealization_realization
PNP.DirectWire.TerminalCheckedFullLift.fullRealization_profileEqual
PNP.DirectWire.terminalCheckedFullLift_iff_fullProfileEqual
PNP.DirectWire.TerminalQuotientComparison.checkedFullLift_of_keepsAll
PNP.DirectWire.TerminalFullCarrierRealization.obligationsDischarged
PNP.DirectWire.TerminalCheckedFullLift.obligationsDischarged
PNP.DirectWire.terminalQuotientEqualityNotConstructive

Terminal full/quotient projection minima

For every finite direct-wire implementation, computed finite terminal-profile observer, and explicit forgetful projection, complete enumeration through the current gate count computes an attained full-profile minimum and an attained quotient-profile minimum. Both minima universally lower-bound every matching realization, forgetting coordinates cannot increase the minimum, the full minimum decomposes as the quotient minimum plus a nonnegative projection defect, and that defect is zero exactly when an attained quotient minimum has a checked full lift.

These are exhaustive finite reference minima through the supplied implementation size. This milestone proves no polynomial runtime, proper or governed support construction, arbitrary manuscript quotient carrier, SaturatePositive, Package E, BCEL/BN2-BN6, complete residual routing, ZeroSlack certificate, PCCMin exactness, SAT-in-P result, discharged project assumption, or proof that P = NP.

Reviewed theorem interfaces (14)

PNP.DirectWire.terminalFullProfileMatchBool_complete
PNP.DirectWire.terminalQuotientProfileMatchBool_complete
PNP.DirectWire.terminalFullProfileMinimumRealization_gateCount
PNP.DirectWire.terminalQuotientProfileMinimumComparison_gateCount
PNP.DirectWire.terminalFullProfileMinimum_le
PNP.DirectWire.terminalQuotientProfileMinimum_le
PNP.DirectWire.terminalFullProfileMinimum_spec
PNP.DirectWire.terminalQuotientProfileMinimum_spec
PNP.DirectWire.terminalProjectionMinimum_mono
PNP.DirectWire.terminalQuotientMinimum_add_projectionDefect
PNP.DirectWire.terminalProjectionDefect_eq_zero_iff_minima_eq
PNP.DirectWire.terminalProjectionDefect_eq_zero_iff_exists_checkedFullLiftAtMinimum
PNP.DirectWire.terminalProfileMinima_eq_of_keepsAll
PNP.DirectWire.terminalProjectionDefect_pos_no_checkedFullLiftAtMinimum

Terminal projection transfer identity

For every finite direct-wire four-corner terminal-profile family sharing one computed observer and one explicit projection, signed full and quotient minimum deltas obey the exact Section 5.2 transfer identity. The projection excess is the quotient delta minus the full delta; if meet and both side defects are zero while the join defect is D, the excess equals D and is positive whenever D is positive.

This is signed arithmetic over four supplied corners. It does not construct or certify a proper governed support square, prove SaturatePositive, discharge Package E or BCEL/BN2-BN6, generate a complete residual route, prove ZeroSlack or PCCMin, establish polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (4)

PNP.DirectWire.terminalProjectionDefect_int
PNP.DirectWire.TerminalProjectionFourCorners.transferIdentity
PNP.DirectWire.TerminalProjectionFourCorners.constantCutEquation_of_defects
PNP.DirectWire.TerminalProjectionFourCorners.projectionExcess_pos_of_constantCut

Terminal saturation closure

For every finite terminal primitive-record universe and every explicit Boolean dependency system tagged by the manuscript's ten closure mechanisms, the generated reflexive transitive closure contains the seed, is dependency-closed, is least among closed supersets, is monotone and idempotent, and has exactly the closed supports as fixed points.

This closure theorem does not derive the dependency relation from an arbitrary circuit, construct proper support, prove support completion or square legitimacy, instantiate a projection-compatible square, prove SaturatePositive or BCELReady, discharge Package E or BCEL/BN2-BN6, generate a complete residual route, prove ZeroSlack or PCCMin, establish polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.mem_allTerminalPrimitiveRecords
PNP.DirectWire.terminalSaturate_extensive
PNP.DirectWire.terminalSaturate_closed
PNP.DirectWire.terminalSaturate_least
PNP.DirectWire.terminalSaturate_monotone
PNP.DirectWire.terminalSaturate_idempotent
PNP.DirectWire.terminalSaturate_fixed_iff_closed

Terminal executable and physical support completion

For every finite direct-wire candidate, explicit terminal dependency system, and finite seed list, a deterministic finite work list computes exactly the inductive saturation, then the actual program computes canonically ordered incoming boundary and outgoing interface wires. Lean proves no crossing wire is omitted or added and the composed physical support is compatible.

The terminal dependency system remains explicit data rather than an extracted profile frontier. This milestone does not construct proper positive support, prove support completion in the manuscript's full sense or square legitimacy, instantiate the required projection square, prove SaturatePositive, discharge Package E or BCEL/BN2-BN6, generate a complete residual route, prove ZeroSlack or PCCMin, establish polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (14)

PNP.DirectWire.mem_allTerminalSaturationRuleKinds
PNP.DirectWire.terminalSaturationEdge_eq_true_iff
PNP.DirectWire.terminalSaturateRecords_extensive
PNP.DirectWire.terminalSaturateRecords_sound
PNP.DirectWire.terminalSaturateRecords_closed
PNP.DirectWire.mem_terminalSaturateRecords_iff
PNP.DirectWire.mem_allTerminalSupportWires
PNP.DirectWire.mem_terminalBoundaryPorts_iff
PNP.DirectWire.mem_terminalInterfacePorts_iff
PNP.DirectWire.completeTerminalPhysicalSupport_incoming_complete
PNP.DirectWire.completeTerminalPhysicalSupport_outgoing_complete
PNP.DirectWire.completeTerminalPhysicalSupport_compatible
PNP.DirectWire.completeSaturatedTerminalPhysicalSupport_records
PNP.DirectWire.completeSaturatedTerminalPhysicalSupport_compatible

Arbitrary terminal support extraction

For every finite direct-wire candidate and finite terminal record list, including noncontiguous selections, the actual program is structurally extracted over its exact canonical incoming boundary and ordered outgoing interface. The extracted candidate equals an independently defined open-support function for every boundary valuation and recovers the original interface values on whole-circuit-induced boundaries; the construction also composes with executable terminal saturation.

The record list and terminal dependency system remain explicit inputs rather than the manuscript's derived profile frontier. This milestone does not construct a proper positive support, prove full governed support completion or square legitimacy, instantiate the required projection square, prove SaturatePositive, discharge Package E or BCEL/BN2-BN6, generate a complete residual route, prove ZeroSlack or PCCMin, establish polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (21)

PNP.DirectWire.mem_terminalSelectedGateIndices_iff
PNP.DirectWire.mem_terminalSelectedGates_iff
PNP.DirectWire.terminalSelectedGateIndices_nodup
PNP.DirectWire.terminalSelectedGates_nodup
PNP.DirectWire.extractTerminalSupport_records
PNP.DirectWire.extractTerminalSupport_boundary
PNP.DirectWire.extractTerminalSupport_selectedGates
PNP.DirectWire.extractTerminalSupport_interface
PNP.DirectWire.extractTerminalSupport_gateCount
PNP.DirectWire.terminalOpenGateEvaluation_induced_selected
PNP.DirectWire.terminalOpenSupportSemantics_induced
PNP.DirectWire.extractTerminalSupport_semantics
PNP.DirectWire.extractTerminalSupport_induced
PNP.DirectWire.extractSaturatedTerminalSupport_records
PNP.DirectWire.extractSaturatedTerminalSupport_gateCount
PNP.DirectWire.extractSaturatedTerminalSupport_semantics
PNP.DirectWire.extractSaturatedTerminalSupport_induced
PNP.DirectWire.mem_terminalSaturateRecords_iff
PNP.DirectWire.completeTerminalPhysicalSupport_incoming_complete
PNP.DirectWire.completeTerminalPhysicalSupport_compatible
PNP.DirectWire.completeSaturatedTerminalPhysicalSupport_compatible

Governed proper-positive terminal support search

For every finite direct-wire candidate and explicit terminal dependency system, Lean enumerates the complete canonical finite universe of primitive-record seeds, saturates and physically completes each seed, extracts its exact open support, and computes exact local gain from the exhaustive semantic reference minimum. The search returns a proof-bearing nonempty proper support with positive gain whenever one exists in that canonical seed universe, and its none result is equivalent to the absence of such a seed.

The terminal dependency system remains explicit input rather than a profile frontier derived from the circuit, and the search is exhaustive reference computation rather than a polynomial algorithm. This milestone does not prove global gain completeness, full manuscript support completion or square legitimacy, instantiate a projection-compatible square, prove SaturatePositive or BCELReady, discharge Package E or BCEL/BN2-BN6, generate a complete residual route, prove ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (22)

PNP.DirectWire.canonicalTerminalSupportSeed_mem
PNP.DirectWire.mem_canonicalTerminalSupportSeed_iff
PNP.DirectWire.terminalProperPositiveSupportBool_eq_true_iff
PNP.DirectWire.findTerminalProperPositiveSupport_sound
PNP.DirectWire.findTerminalProperPositiveSupport_exists_of_seed
PNP.DirectWire.findTerminalProperPositiveSupport_eq_none_iff
PNP.DirectWire.findTerminalProperPositiveSupport_unique
PNP.DirectWire.TerminalProperPositiveSupport.saturatedRecords_closed
PNP.DirectWire.TerminalProperPositiveSupport.physically_compatible
PNP.DirectWire.TerminalProperPositiveSupport.gateCount_bounds
PNP.DirectWire.TerminalProperPositiveSupport.extracted_semantics
PNP.DirectWire.TerminalProperPositiveSupport.extracted_induced
PNP.DirectWire.TerminalProperPositiveSupport.minimumReplacement_equivalent
PNP.DirectWire.TerminalProperPositiveSupport.referenceMinimum_lt_gateCount
PNP.DirectWire.TerminalProperPositiveSupport.minimumReplacement_size_lt
PNP.DirectWire.mem_terminalSaturateRecords_iff
PNP.DirectWire.completeSaturatedTerminalPhysicalSupport_compatible
PNP.DirectWire.extractSaturatedTerminalSupport_gateCount
PNP.DirectWire.extractSaturatedTerminalSupport_semantics
PNP.DirectWire.extractSaturatedTerminalSupport_induced
PNP.DirectWire.Candidate.referenceMinimumReplacement_equivalent
PNP.DirectWire.Candidate.referenceMinimumReplacement_size

Saturated terminal support-square closure

For every finite direct-wire candidate, every explicit terminal dependency system, and every pair of finite terminal seeds, Lean computes saturated left and right corners, their canonical closed meet, and their closed saturated-union join. It proves the exact greatest-lower-bound and least-upper-bound laws, seed extensionality, computed physical compatibility, exact gate count, open-support semantics, and induced whole-circuit recovery for all four corners.

The terminal dependency system remains explicit input rather than a profile frontier derived from the circuit. This milestone proves finite closed-corner algebra and computed physical extraction, not the manuscript's obstruction routing, frontier pushout, projection-compatible square, side-tight four-corner minima, BN2 square legitimacy, SaturatePositive, Package E, BCEL/BN2-BN6, complete residual routing, ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (23)

PNP.DirectWire.TerminalSaturatedSupportSquare.mem_meetRecords_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.leftRecords_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.rightRecords_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.meetRecords_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.mem_joinRecords_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.joinRecords_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.records_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.meetRecords_subset_left
PNP.DirectWire.TerminalSaturatedSupportSquare.meetRecords_subset_right
PNP.DirectWire.TerminalSaturatedSupportSquare.leftRecords_subset_join
PNP.DirectWire.TerminalSaturatedSupportSquare.rightRecords_subset_join
PNP.DirectWire.TerminalSaturatedSupportSquare.meetRecords_greatest
PNP.DirectWire.TerminalSaturatedSupportSquare.joinRecords_least
PNP.DirectWire.terminalSaturateRecords_mem_congr
PNP.DirectWire.TerminalSaturatedSupportSquare.records_congr
PNP.DirectWire.TerminalSaturatedSupportSquare.physically_compatible
PNP.DirectWire.TerminalSaturatedSupportSquare.extracted_gateCount
PNP.DirectWire.TerminalSaturatedSupportSquare.extracted_semantics
PNP.DirectWire.TerminalSaturatedSupportSquare.extracted_induced
PNP.DirectWire.mem_terminalSaturateRecords_iff
PNP.DirectWire.completeTerminalPhysicalSupport_compatible
PNP.DirectWire.extractTerminalSupport_semantics
PNP.DirectWire.extractTerminalSupport_induced

Governed terminal support completion

For every finite direct-wire candidate, explicit terminal dependency system, finite seed list, and computed saturated support-square corner, Lean computes the exact physical boundary, ordered interface, and partition of selected profile coordinates among all ten terminal profile roles. It proves exact membership, no duplicates, pairwise disjointness, record coverage, dependency closure, physical compatibility, and retention of each exact corner.

The terminal dependency system remains explicit input rather than a profile frontier derived from the circuit. This milestone computes a governed finite completion of each saturated support-square corner, not the manuscript's obstruction routing, frontier pushout, projection-compatible square, side-tight four-corner minima, BN2 square legitimacy, SaturatePositive, Package E, BCEL/BN2-BN6, complete residual routing, ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (26)

PNP.DirectWire.mem_allTerminalProfileRoles
PNP.DirectWire.mem_terminalProfileCoordinatesForRole_iff
PNP.DirectWire.terminalProfileCoordinatesForRole_nodup
PNP.DirectWire.completeTerminalGovernedSupport_records
PNP.DirectWire.TerminalGovernedCompletedSupport.frontier_boundary
PNP.DirectWire.TerminalGovernedCompletedSupport.frontier_interface
PNP.DirectWire.TerminalGovernedCompletedSupport.mem_profileCoordinates_iff
PNP.DirectWire.TerminalGovernedCompletedSupport.profileCoordinates_nodup
PNP.DirectWire.TerminalGovernedCompletedSupport.mem_own_profile_role_iff
PNP.DirectWire.TerminalGovernedCompletedSupport.profile_role_unique
PNP.DirectWire.TerminalGovernedCompletedSupport.profileCoordinates_disjoint
PNP.DirectWire.TerminalGovernedCompletedSupport.profile_record_covered_iff
PNP.DirectWire.TerminalGovernedCompletedSupport.required_mem
PNP.DirectWire.TerminalGovernedCompletedSupport.required_profile_mem
PNP.DirectWire.completeSaturatedTerminalGovernedSupport_records
PNP.DirectWire.completeSaturatedTerminalGovernedSupport_compatible
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_records
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_compatible
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_required_mem
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_required_profile_mem
PNP.DirectWire.completeTerminalPhysicalSupport_compatible
PNP.DirectWire.terminalSaturateRecords_closed
PNP.DirectWire.mem_terminalSaturateRecords_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.records_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.physically_compatible

Governed terminal frontier pushout

For every finite direct-wire candidate, explicit terminal dependency system, and computed saturated support square, Lean constructs the governed boundary, interface, and role-preserving profile pushout from the two side completions alone. The independently completed join frontier equals that gluing, the meet profile is the exact shared overlap, and every side physical coordinate is either retained externally or witnessed as internalized.

The terminal dependency system remains explicit input rather than a profile frontier derived from the circuit. This milestone proves exact frontier gluing for computed saturated support squares, not projection compatibility, side-tight four-corner minima, BN2 square legitimacy, SaturatePositive, Package E, BCEL/BN2-BN6, complete obstruction routing, ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (28)

PNP.DirectWire.allTerminalSupportWires_nodup
PNP.DirectWire.TerminalGovernedFrontier.extensionality
PNP.DirectWire.mem_terminalBoundaryFrontierPushout_iff
PNP.DirectWire.mem_terminalInterfaceFrontierPushout_iff
PNP.DirectWire.mem_terminalProfileFrontierPushout_iff
PNP.DirectWire.terminalBoundaryFrontierPushout_nodup
PNP.DirectWire.terminalInterfaceFrontierPushout_nodup
PNP.DirectWire.terminalProfileFrontierPushout_nodup
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_boundary_eq_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_interface_eq_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_meet_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_profile_eq_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.side_profile_mem_join
PNP.DirectWire.TerminalSaturatedSupportSquare.left_boundary_disposition
PNP.DirectWire.TerminalSaturatedSupportSquare.right_boundary_disposition
PNP.DirectWire.TerminalSaturatedSupportSquare.side_interface_disposition
PNP.DirectWire.TerminalSaturatedSupportSquare.governed_frontier_pushout
PNP.DirectWire.terminalGateSelected_eq_true_iff
PNP.DirectWire.terminalWireExternal_eq_true_iff
PNP.DirectWire.terminalBoundaryWire_eq_true_iff
PNP.DirectWire.terminalGateHasExternalConsumer_eq_true_iff
PNP.DirectWire.terminalInterfaceGate_eq_true_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.mem_meetRecords_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.mem_joinRecords_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.records_closed
PNP.DirectWire.TerminalSaturatedSupportSquare.physically_compatible
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_profile_iff

Governed terminal projection square

For every finite direct-wire candidate, explicit terminal dependency system, computed saturated support square, and every forgetful terminal projection, Lean retains the exact physical frontier, filters all ten role profiles exactly, proves projected meet is the shared side overlap, and proves projected join is the side-only projected pushout without reading the join corner.

The terminal dependency system remains explicit input rather than a profile frontier derived from the circuit. This milestone proves structural projection commutation for computed saturated support squares, not side-tight four-corner minima, BN2 square legitimacy, SaturatePositive, Package E, BCEL/BN2-BN6, complete obstruction routing, ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (23)

PNP.DirectWire.TerminalGovernedFrontier.project_boundary
PNP.DirectWire.TerminalGovernedFrontier.project_interface
PNP.DirectWire.TerminalGovernedFrontier.mem_project_profiles_iff
PNP.DirectWire.TerminalGovernedFrontier.project_profiles_nodup
PNP.DirectWire.TerminalGovernedFrontier.project_idempotent
PNP.DirectWire.mem_terminalProjectedGovernedFrontierPushout_profiles_iff
PNP.DirectWire.TerminalGovernedFrontier.project_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.projectedFrontier_boundary
PNP.DirectWire.TerminalSaturatedSupportSquare.projectedFrontier_interface
PNP.DirectWire.TerminalSaturatedSupportSquare.mem_projectedFrontier_profiles_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.projectedFrontier_profiles_nodup
PNP.DirectWire.TerminalSaturatedSupportSquare.forgotten_not_mem_projectedFrontier
PNP.DirectWire.TerminalSaturatedSupportSquare.projected_meet_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.projected_join_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.projected_join_eq_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.governed_projection_compatible
PNP.DirectWire.TerminalGovernedFrontier.extensionality
PNP.DirectWire.mem_terminalProfileFrontierPushout_iff
PNP.DirectWire.terminalProfileFrontierPushout_nodup
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_meet_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.governed_frontier_pushout

Side-tight four-corner minimum arithmetic

For every finite terminal projection four-corner family and every independently attained typed full or quotient basis, Lean proves componentwise minimum bounds and the exact signed four-slack identity. A fail-closed Boolean and Option gate returns the corresponding existing delta only when meet, left, right, and join all attain their exact minima; both canonical independently attained minimum bases pass.

The canonical corner minima are independently attained. This milestone proves numerical arithmetic and fail-closed exactness, not construction of one coherent four-corner basis, coherent completion, maximization over a finite tight family, BN2 square legitimacy, SaturatePositive, Package E, BCELReady or BCEL/BN2-BN6, complete obstruction routing, ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (24)

PNP.DirectWire.TerminalFourCornerSizes.componentwiseLE_refl
PNP.DirectWire.TerminalFourCornerSizes.numericallySideTight_iff_eq
PNP.DirectWire.TerminalFourCornerSizes.sideTightBool_eq_true_iff
PNP.DirectWire.TerminalFourCornerSizes.tightValue?_eq_some_iff
PNP.DirectWire.TerminalFourCornerSizes.tightValue?_sound
PNP.DirectWire.TerminalFourCornerSizes.tightValue?_complete
PNP.DirectWire.TerminalFourCornerSizes.incidenceValue_eq_minimum_add_slacks
PNP.DirectWire.TerminalProjectionFourCorners.fullMinimumSizes_incidenceValue
PNP.DirectWire.TerminalFullFourCornerBasis.minimum_componentwiseLE_sizes
PNP.DirectWire.TerminalFullFourCornerBasis.incidenceValue_eq_fullDelta_add_slacks
PNP.DirectWire.TerminalProjectionFourCorners.canonicalFullBasis_sizes
PNP.DirectWire.TerminalProjectionFourCorners.canonicalFullBasis_numericallySideTight
PNP.DirectWire.TerminalProjectionFourCorners.canonicalFullBasis_tightValue?
PNP.DirectWire.TerminalProjectionFourCorners.quotientMinimumSizes_incidenceValue
PNP.DirectWire.TerminalQuotientFourCornerBasis.minimum_componentwiseLE_sizes
PNP.DirectWire.TerminalQuotientFourCornerBasis.incidenceValue_eq_quotientDelta_add_slacks
PNP.DirectWire.TerminalProjectionFourCorners.canonicalQuotientBasis_sizes
PNP.DirectWire.TerminalProjectionFourCorners.canonicalQuotientBasis_numericallySideTight
PNP.DirectWire.TerminalProjectionFourCorners.canonicalQuotientBasis_tightValue?
PNP.DirectWire.TerminalProjectionFourCorners.canonical_numericallySideTight_values
PNP.DirectWire.terminalFullProfileMinimumRealization_gateCount
PNP.DirectWire.terminalQuotientProfileMinimumComparison_gateCount
PNP.DirectWire.terminalFullProfileMinimum_le
PNP.DirectWire.terminalQuotientProfileMinimum_le

Checked four-corner carrier transport

For every finite computed saturated terminal support square, direct-wire candidate, and forgetful terminal projection, Lean derives all four exact governed and extracted endpoints in common ambient coordinates, proves duplicate-free boundary, interface, and profile lists, transports meet and join profiles exactly, and classifies each present side physical coordinate as identically retained or constructively internalized through fail-closed queries.

This milestone supplies a checked common ambient carrier for the computed square. It does not transport four optimum realizers, prove the full four-corner optimum carrier-compatibility obligation, construct a coherent four-corner optimum, prove side-tight completion or BN2 square legitimacy, establish SaturatePositive, Package E, BCELReady or BCEL/BN2-BN6, complete obstruction routing, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (27)

PNP.DirectWire.TerminalFourCornerCarrier.boundaryDisposition?_eq_some_iff
PNP.DirectWire.TerminalFourCornerCarrier.interfaceDisposition?_eq_some_iff
PNP.DirectWire.TerminalFourCornerCarrier.boundary_nodup
PNP.DirectWire.TerminalFourCornerCarrier.interface_nodup
PNP.DirectWire.TerminalFourCornerCarrier.profile_nodup
PNP.DirectWire.TerminalFourCornerCarrier.extracted_boundary
PNP.DirectWire.TerminalFourCornerCarrier.extracted_interface
PNP.DirectWire.TerminalFourCornerCarrier.corner_compatible
PNP.DirectWire.TerminalFourCornerCarrier.meet_profile_transport
PNP.DirectWire.TerminalFourCornerCarrier.side_profile_transport
PNP.DirectWire.TerminalFourCornerCarrier.join_profile_transport
PNP.DirectWire.TerminalFourCornerCarrier.boundary_retained
PNP.DirectWire.TerminalFourCornerCarrier.boundary_internalized
PNP.DirectWire.TerminalFourCornerCarrier.interface_retained
PNP.DirectWire.TerminalFourCornerCarrier.interface_internalized
PNP.DirectWire.TerminalFourCornerCarrier.projection_compatible
PNP.DirectWire.TerminalFourCornerCarrier.complete_transport
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_compatible
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_meet_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.side_profile_mem_join
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_profile_iff
PNP.DirectWire.TerminalSaturatedSupportSquare.left_boundary_disposition
PNP.DirectWire.TerminalSaturatedSupportSquare.right_boundary_disposition
PNP.DirectWire.TerminalSaturatedSupportSquare.side_interface_disposition
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_boundary_eq_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.governedCompleted_join_interface_eq_pushout
PNP.DirectWire.TerminalSaturatedSupportSquare.governed_projection_compatible

Four-corner optimum carrier compatibility

For every finite computed saturated terminal support square and every explicit observer, Lean embeds all four exact corner candidates into one common ambient carrier, proves reversible semantic and gate-count preservation, proves exact ambient and corner reference minima agree, and localizes canonical full and quotient optima from one shared observer and projection without changing their exact minimum counts.

This milestone compares independently attained full and quotient optima on one reversible common carrier. It does not prove coherent transport along the square legs, construct a coherent four-corner optimum, prove sideTightCompletionExists or BN2 square legitimacy, derive the terminal dependency system, establish SaturatePositive, Package E, BCELReady or BCEL/BN2-BN6, complete obstruction routing, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (30)

PNP.DirectWire.terminalSupportWireAt_ambientIndex
PNP.DirectWire.TerminalSupportWire.ambientIndex_terminalSupportWireAt
PNP.DirectWire.TerminalSupportWire.ambientIndex_injective
PNP.DirectWire.TerminalFourCornerCarrier.boundaryIndex?_eq_some_iff
PNP.DirectWire.TerminalFourCornerCarrier.interfaceIndex?_eq_some_iff
PNP.DirectWire.TerminalFourCornerCarrier.boundaryIndex?_ambient_get
PNP.DirectWire.TerminalFourCornerCarrier.interfaceIndex?_get
PNP.DirectWire.TerminalFourCornerCarrier.boundaryAdapter_semantics_get
PNP.DirectWire.TerminalFourCornerCarrier.ambientizeCandidate_semantics_present
PNP.DirectWire.TerminalFourCornerCarrier.ambientizeCandidate_semantics_absent
PNP.DirectWire.TerminalFourCornerCarrier.localizeCandidate_semantics
PNP.DirectWire.TerminalFourCornerCarrier.localize_ambientize_semantics
PNP.DirectWire.TerminalFourCornerCarrier.ambientizeCandidate_gateCount
PNP.DirectWire.TerminalFourCornerCarrier.localizeCandidate_gateCount
PNP.DirectWire.TerminalFourCornerCarrier.ambientizeCandidate_equivalent
PNP.DirectWire.TerminalFourCornerCarrier.localizeCandidate_equivalent
PNP.DirectWire.TerminalFourCornerCarrier.localize_ambientize_equivalent
PNP.DirectWire.TerminalFourCornerCarrier.localizeImplementation_gateCount
PNP.DirectWire.TerminalFourCornerCarrier.ambient_referenceMinimum_eq_corner
PNP.DirectWire.TerminalFourCornerCarrier.optimizationCorners_at
PNP.DirectWire.TerminalFourCornerCarrier.optimizationCorners_role
PNP.DirectWire.TerminalFourCornerCarrier.optimizationCorners_projection
PNP.DirectWire.TerminalFourCornerCarrier.localizeRealization_gateCount
PNP.DirectWire.TerminalFourCornerCarrier.fourCornerOptimaCarrierCompatible
PNP.DirectWire.TerminalFourCornerCarrier.complete_transport
PNP.DirectWire.TerminalProjectionFourCorners.canonicalFullBasis_sizes
PNP.DirectWire.TerminalProjectionFourCorners.canonicalQuotientBasis_sizes
PNP.DirectWire.terminalFullProfileMinimumRealization_gateCount
PNP.DirectWire.terminalQuotientProfileMinimumComparison_gateCount
PNP.DirectWire.referenceMinimum_le_of_equivalent

Four-corner optimum coherence dichotomy

For every finite computed terminal support square, every explicit observer, every terminal projection, and either full or quotient coherence mode, Lean checks the four square legs in a deterministic order and returns either one coherent canonical optimum tuple with exact transport, side-tight, and incidence facts or the exact deterministic first failure.

This milestone classifies coherent transport or its exact first failure. It does not prove that every square is coherent, construct the later no-outcome route, prove sideTightCompletionExists or BN2 square legitimacy, establish SaturatePositive, Package E, BCELReady or BCEL/BN2-BN6, complete obstruction routing, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, removal of a project assumption, or P = NP.

Reviewed theorem interfaces (19)

PNP.DirectWire.TerminalOptimumLegTransport.recordsSubset
PNP.DirectWire.TerminalOptimumLegTransport.profileTransport
PNP.DirectWire.TerminalOptimumLegTransport.ambientCoordinate_exact
PNP.DirectWire.TerminalOptimumLegTransport.retainedOutput?_eq_some_iff
PNP.DirectWire.TerminalOptimumLegTransport.retained_or_internalized
PNP.DirectWire.TerminalFourCornerCarrier.optimumTransportTheta
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumCoherenceFailure?_sound
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumModeMismatch?_sound
PNP.DirectWire.TerminalFourCornerCarrier.noFailure_iff_coherentOptimumTuple
PNP.DirectWire.TerminalFourCornerCarrier.classifyOptimumCoherence_exhaustive
PNP.DirectWire.TerminalFourCornerCarrier.fourCornerOptimumCoherenceDichotomy
PNP.DirectWire.TerminalFourCornerCarrier.fourCornerOptimaCarrierCompatible
PNP.DirectWire.TerminalFourCornerCarrier.complete_transport
PNP.DirectWire.TerminalFourCornerCarrier.meet_profile_transport
PNP.DirectWire.TerminalFourCornerCarrier.side_profile_transport
PNP.DirectWire.TerminalFourCornerCarrier.interfaceIndex?_eq_some_iff
PNP.DirectWire.TerminalProjectionFourCorners.canonicalFullBasis_numericallySideTight
PNP.DirectWire.TerminalProjectionFourCorners.canonicalQuotientBasis_numericallySideTight
PNP.DirectWire.TerminalProjectionFourCorners.canonical_numericallySideTight_values

Four-corner side-tight completion under local route silence

For every finite computed terminal support square, every explicit observer, and either full or quotient coherence mode, the exact first local coherence query returns a proof-bearing sound route or, under computed local route silence, Lean supplies the complete checked side-tight coherent optimum tuple with exact minimum incidence value while retaining the separate quotient-promotion firewall.

This milestone closes only the local completion edge under computed local route silence. It does not prove universal route silence, connect a local obstruction to the complete global no-outcome route system, prove BN2 square legitimacy, derive the terminal dependency system, enumerate or maximize the complete tight-basis family, establish SaturatePositive, Package E, BCELReady or BCEL/BN2-BN6, complete obstruction routing, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (20)

PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumRoute?_coherence
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumRoute?_quotientPromotion
PNP.DirectWire.TerminalFourCornerOptimumRoutedFailure.sound
PNP.DirectWire.TerminalFourCornerCarrier.noOptimumCoherenceRoute_iff_noFailure
PNP.DirectWire.TerminalFourCornerCarrier.noOptimumPromotionRoute_iff_noModeMismatch
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumRoute?_sound
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletionOrFirstRoute
PNP.DirectWire.TerminalFourCornerOptimumRoutedFailure.excludesCoherentOptimum
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletionExists
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletionExistsEachMode
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletion_fullValue
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletion_quotientValue
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumCoherenceFailure?_sound
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumModeMismatch?_sound
PNP.DirectWire.TerminalFourCornerCarrier.noFailure_iff_coherentOptimumTuple
PNP.DirectWire.TerminalFourCornerCarrier.fourCornerOptimaCarrierCompatible
PNP.DirectWire.TerminalFourCornerCarrier.optimumTransportTheta
PNP.DirectWire.TerminalProjectionFourCorners.canonicalFullBasis_numericallySideTight
PNP.DirectWire.TerminalProjectionFourCorners.canonicalQuotientBasis_numericallySideTight
PNP.DirectWire.TerminalProjectionFourCorners.canonical_numericallySideTight_values

Complete four-corner BN2 tight-basis maximum

For every finite computed terminal support square, every explicit observer, and either full or quotient mode, Lean enumerates the complete finite tight-basis family, retains every exact profile-constrained minimum implementation at each corner, filters the full Cartesian product with the arbitrary-family coherence query, and proves under exact local route silence that the signed maximum equals the selected delta.

This milestone closes the remaining local BN2 tight-basis maximum under computed local route silence. It does not prove universal route silence, connect a local obstruction to the complete global no-outcome route system, prove BN2 square legitimacy, derive the terminal dependency system, establish SaturatePositive, Package E, BCELReady or BCEL/BN2-BN6, complete obstruction routing, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (28)

PNP.DirectWire.TerminalOptimumCoherenceMode.minimumAt_le_current
PNP.DirectWire.TerminalProjectionFourCorners.mem_minimumImplementationsAt_sound
PNP.DirectWire.TerminalProjectionFourCorners.mem_minimumImplementationsAt_complete
PNP.DirectWire.TerminalProjectionFourCorners.mem_minimumImplementationsAt_iff
PNP.DirectWire.TerminalProjectionFourCorners.mem_minimumImplementationBases_iff
PNP.DirectWire.TerminalFourCornerCarrier.tightBasisBool_eq_true_iff
PNP.DirectWire.TerminalFourCornerCarrier.mem_tightBasisFamily_sound
PNP.DirectWire.TerminalFourCornerCarrier.mem_tightBasisFamily_complete
PNP.DirectWire.TerminalFourCornerCarrier.mem_tightBasisFamily_iff
PNP.DirectWire.TerminalFourCornerCarrier.canonicalImplementationBasis_at
PNP.DirectWire.TerminalFourCornerCarrier.canonicalImplementationBasis_sizes
PNP.DirectWire.TerminalFourCornerCarrier.canonicalImplementationBasis_isTightCoherent
PNP.DirectWire.TerminalFourCornerCarrier.canonicalImplementationBasis_mem_tightFamily
PNP.DirectWire.TerminalFourCornerCarrier.tightBasis_incidenceValue_eq_delta
PNP.DirectWire.TerminalFourCornerCarrier.mem_tightBasisValues_eq_delta
PNP.DirectWire.TerminalFourCornerCarrier.tightBasisMaximum?_eq_delta
PNP.DirectWire.TerminalFourCornerCarrier.tightBasisMaximum?_full
PNP.DirectWire.TerminalFourCornerCarrier.tightBasisMaximum?_quotient
PNP.DirectWire.TerminalFourCornerCarrier.firstBasisCoherenceFailure?_sound
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumCoherenceFailure?_eq_basis
PNP.DirectWire.mem_allBoundedCandidates
PNP.DirectWire.terminalFullProfileMatchBool_complete
PNP.DirectWire.terminalQuotientProfileMatchBool_complete
PNP.DirectWire.terminalFullProfileMinimum_le
PNP.DirectWire.terminalQuotientProfileMinimum_le
PNP.DirectWire.TerminalFourCornerSizes.numericallySideTight_iff_eq
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumCoherenceFailure?_sound
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletionExists

Computed terminal BN2 square legitimacy

For every finite computed terminal support square built from two finite seeds under one explicit terminal dependency system, direct-wire candidate, observer, and forgetful projection, Lean constructs the exact compatible governed frontier and projection square, keeps full and quotient minimum quantities on the same carrier, and returns either the complete local conclusion under exact local route silence or the deterministic full-then-quotient proof-bearing first coherence route.

This milestone packages computed structural legitimacy and the exact local no-route conclusion. It does not derive the terminal dependency system from an arbitrary circuit, prove universal route silence, connect a local failure to the complete global no-outcome route system, identify a BCEL anchor square, establish SaturatePositive, Package E, BCELReady or later BCEL/BN2-BN6 conclusions, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (20)

PNP.DirectWire.TerminalComputedBN2SquareLegitimate.cornerCompatible
PNP.DirectWire.TerminalComputedBN2SquareLegitimate.meetProfile
PNP.DirectWire.TerminalComputedBN2SquareLegitimate.joinProfile
PNP.DirectWire.TerminalComputedBN2SquareLegitimate.projectionCompatible
PNP.DirectWire.TerminalFourCornerCarrier.computedBN2SquareLegitimate
PNP.DirectWire.TerminalComputedBN2SquareQuantities.sharedRole
PNP.DirectWire.TerminalComputedBN2SquareQuantities.sharedProjection
PNP.DirectWire.TerminalComputedBN2SquareQuantities.referenceMinimumPreserved
PNP.DirectWire.TerminalComputedBN2SquareQuantities.transferIdentity
PNP.DirectWire.TerminalFourCornerCarrier.computedBN2SquareQuantities
PNP.DirectWire.TerminalFourCornerCarrier.computedBN2LocalConclusion
PNP.DirectWire.TerminalFourCornerCarrier.computedBN2LocalConclusionOrFirstRoute
PNP.DirectWire.TerminalFourCornerCarrier.complete_transport
PNP.DirectWire.TerminalSaturatedSupportSquare.governed_frontier_pushout
PNP.DirectWire.TerminalFourCornerCarrier.fourCornerOptimaCarrierCompatible
PNP.DirectWire.TerminalFourCornerCarrier.sideTightCompletionExistsEachMode
PNP.DirectWire.TerminalFourCornerCarrier.tightBasisMaximum?_full
PNP.DirectWire.TerminalFourCornerCarrier.tightBasisMaximum?_quotient
PNP.DirectWire.TerminalFourCornerOptimumRoutedFailure.sound
PNP.DirectWire.TerminalProjectionFourCorners.transferIdentity

Computed terminal BCEL anchor nucleus and cut-square dichotomy

For every finite direct-wire candidate, explicit terminal dependency system, computed governed proper-positive support, forgetful projection, executable ambient observer, and positive whole-support projection defect, Lean computes the canonical minimum-cardinality positive anchor nucleus and returns either an insufficient nucleus, the exact first anchor-algebra mismatch, the exact first proper-cut defect mismatch, the proof-bearing first full-before-quotient local route, or exact constant-cut and local BN2 conclusions for every proper cut.

This milestone assumes a positive whole-support projection defect and an explicit terminal dependency system. It does not derive either premise, identify manuscript activation or charge equivalence classes absent from the terminal model, connect a local failure to the complete global no-outcome route system, establish SaturatePositive, Package E, BCELReady or later BCEL/BN2-BN6 conclusions, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (36)

PNP.DirectWire.TerminalBCELAnchorProblem.mem_anchorRecords_iff
PNP.DirectWire.TerminalBCELAnchorProblem.anchorRecords_nodup
PNP.DirectWire.TerminalBCELAnchorProblem.anchorRecords_mem_allAnchorSubfamilies
PNP.DirectWire.findTerminalPositiveAnchorNucleus_sound
PNP.DirectWire.findTerminalPositiveAnchorNucleus_eq_none_iff
PNP.DirectWire.findTerminalPositiveAnchorNucleus_exists_of_whole_positive
PNP.DirectWire.findTerminalPositiveAnchorNucleus_unique
PNP.DirectWire.TerminalBCELAnchorAlgebraCheck.disagrees_eq_true_iff
PNP.DirectWire.terminalBCELAnchorAlgebraCheck_mem
PNP.DirectWire.mem_allTerminalBCELAnchorAlgebraChecks_governed
PNP.DirectWire.firstTerminalBCELAnchorAlgebraMismatch?_sound
PNP.DirectWire.firstTerminalBCELAnchorAlgebraMismatch?_eq_none_iff
PNP.DirectWire.terminalBCELProperCutSeedBool_eq_true_iff
PNP.DirectWire.mem_allTerminalBCELProperCutSeeds_iff
PNP.DirectWire.TerminalBCELCutDefectCheck.disagrees_eq_true_iff
PNP.DirectWire.terminalBCELCutDefectCheck_mem
PNP.DirectWire.mem_allTerminalBCELCutDefectChecks_proper
PNP.DirectWire.firstTerminalBCELCutDefectMismatch?_sound
PNP.DirectWire.firstTerminalBCELCutDefectMismatch?_eq_none_all
PNP.DirectWire.firstTerminalBCELCutRoute?_sound
PNP.DirectWire.firstTerminalBCELCutRoute?_eq_none_noRoutes
PNP.DirectWire.computedBCELCutConclusionOfNoFailures
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.strictSubfamily_defect_zero
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.anchorSizeAtLeastTwo
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.properCutConstantEquation
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.properCutLocalConclusion
PNP.DirectWire.classifyTerminalBCELAnchorNucleus_exhaustive
PNP.DirectWire.allTerminalPrimitiveRecords_nodup
PNP.DirectWire.filter_mem_terminalListSubsets
PNP.DirectWire.mem_allTerminalPrimitiveRecords
PNP.DirectWire.TerminalFourCornerCarrier.firstOptimumRoute?_sound
PNP.DirectWire.TerminalFourCornerOptimumRoutedFailure.sound
PNP.DirectWire.TerminalFourCornerCarrier.computedBN2SquareLegitimate
PNP.DirectWire.TerminalFourCornerCarrier.computedBN2LocalConclusion
PNP.DirectWire.TerminalProjectionFourCorners.constantCutEquation_of_defects
PNP.DirectWire.TerminalProjectionFourCorners.projectionExcess_pos_of_constantCut

Computed terminal saturation-positivity firewall

For every finite direct-wire candidate, explicit terminal dependency system, computed governed proper-positive support, forgetful projection, and executable ambient observer, Lean computes the whole-support defect: zero projection defect returns an attained quotient minimum with a checked full lift, while positive defect delegates exactly to the existing fail-closed BCEL anchor-nucleus classifier.

This closes only projectionPositivityNotLostSilently in the current finite terminal model. It assumes an explicit terminal dependency system and an already computed governed proper-positive support. It does not discharge transparentSaturationCostBalanced, interfaceExposureRoutesToE, originKernelObligationClosureRouted, or firstNontransparentStepRecorded; establish full SaturatePositive, Package E, BCELReady or later BCEL/BN2-BN6 conclusions; prove ZeroSlack, PCCMin, polynomial runtime, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (12)

PNP.DirectWire.TerminalBCELAnchorProblem.wholeCorners_projectionDefect
PNP.DirectWire.TerminalProjectionPositivityLoss.minima_eq
PNP.DirectWire.classifyTerminalSaturationPositivity_loss_of_zero
PNP.DirectWire.classifyTerminalSaturationPositivity_bcel_of_positive
PNP.DirectWire.terminalSaturationPositivity_no_checkedFullLiftAtMinimum
PNP.DirectWire.classifyTerminalSaturationPositivity_exhaustive
PNP.DirectWire.terminalProjectionDefect_eq_zero_iff_minima_eq
PNP.DirectWire.terminalFullProfileMinimumRealization_gateCount
PNP.DirectWire.terminalProjectionDefect_pos_no_checkedFullLiftAtMinimum
PNP.DirectWire.TerminalProperPositiveSupport.saturatedRecords_closed
PNP.DirectWire.TerminalProperPositiveSupport.physically_compatible
PNP.DirectWire.TerminalProperPositiveSupport.extracted_semantics

Candidate-derived terminal saturation cost balance

For every finite direct-wire candidate, executable ambient observer, forgetful projection, and finite terminal seed, Lean computes the candidate-derived dependency system and deterministic rule-labelled saturation trace, then returns proof that every event is exactly cost-balanced with preserved full slack and nondecreasing projection defect, or records the exact first nontransparent event and complete transparent prefix.

This closes only the finite terminal forms of transparentSaturationCostBalanced and firstNontransparentStepRecorded. The executable observer and forgetful projection remain explicit model inputs, and a nontransparent event is recorded rather than routed. It does not discharge interfaceExposureRoutesToE or originKernelObligationClosureRouted; establish full SaturatePositive, Package E, BCELReady or later BCEL/BN2-BN6 conclusions; prove ZeroSlack, PCCMin, polynomial runtime, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (17)

PNP.DirectWire.terminalSaturateTrace_eventsLinked
PNP.DirectWire.terminalSaturateTrace_records
PNP.DirectWire.terminalCandidateSaturationSystem_profileSystem
PNP.DirectWire.TerminalTransparentSaturationStep.uniqueMaterializerOwner
PNP.DirectWire.TerminalTransparentSaturationStep.supportCostBalanced
PNP.DirectWire.TerminalTransparentSaturationStep.fullCostBalanced
PNP.DirectWire.TerminalTransparentSaturationStep.quotientCostBounded
PNP.DirectWire.TerminalTransparentSaturationStep.fullSlack_preserved
PNP.DirectWire.TerminalTransparentSaturationStep.projectionDefect_mono
PNP.DirectWire.TerminalTransparentSaturationStep.fullPositive_preserved
PNP.DirectWire.TerminalSaturationEventsLinked.fullSlack_preserved
PNP.DirectWire.TerminalSaturationEventsLinked.projectionDefect_mono
PNP.DirectWire.TerminalSaturationEventsLinked.fullPositive_preserved
PNP.DirectWire.TerminalSaturationBalanceOutcome.balanced_event
PNP.DirectWire.TerminalSaturationBalanceOutcome.balanced_fullSlack_preserved
PNP.DirectWire.TerminalSaturationBalanceOutcome.balanced_projectionDefect_mono
PNP.DirectWire.TerminalSaturationBalanceOutcome.balanced_fullPositive_preserved

Finite terminal interface-exposure routing

For every finite direct-wire candidate, executable ambient observer, forgetful projection, and finite terminal seed, Lean recognizes only an exact candidate-derived interface-consumer edge. Each recognized event is transparently cost-balanced or produces a proof-bearing local E-route; the production trace result records the exact first nontransparent event and complete transparent prefix, while non-interface first failures remain fail-closed.

This closes only the finite local form of interfaceExposureRoutesToE. The proof-bearing local E-route is an exposure-obligation coordinate, not a full Package E VerifyDW acceptance, a verified global gain, or global route completeness. The executable observer and forgetful projection remain explicit model inputs. It does not discharge originKernelObligationClosureRouted; establish full SaturatePositive, Package E, BCELReady or later BCEL/BN2-BN6 conclusions; prove ZeroSlack, PCCMin, polynomial runtime, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.terminalInterfaceExposureCoordinate?_sound
PNP.DirectWire.terminalCandidateInterfaceExposureCoordinate?_shape
PNP.DirectWire.terminalCandidateInterfaceExposureCoordinate?_edge
PNP.DirectWire.terminalInterfaceOutgoingCoordinate_eventCost_zero
PNP.DirectWire.TerminalInterfaceExposureERoute.sound
PNP.DirectWire.TerminalInterfaceExposureZeroCostRetract.eventCost_zero
PNP.DirectWire.TerminalInterfaceExposureZeroCostRetract.fullSlack_preserved
PNP.DirectWire.terminalInterfaceExposure_transparent_or_eRoute
PNP.DirectWire.TerminalFirstInterfaceExposureRoute.sound
PNP.DirectWire.classifyTerminalSaturationInterfaceRouting_exhaustive

Finite terminal SaturatePositive composition

For every finite direct-wire candidate, executable ambient observer, forgetful projection, and proof-bearing candidate BCEL anchor problem whose normalized seed has positive full slack, Lean recognizes exact candidate-derived origin, kernel, and obligation closures in both gate/profile orientations; checks cost transparency, obligation discharge, and forgotten-profile stability; preserves positive full slack across an all-safe trace into the checked-lift or BCEL firewall; or returns the exact first interface, closure, or other fail-closed nontransparent route with its complete safe prefix.

This closes the finite local form of originKernelObligationClosureRouted and composes the five reconstructed terminal sub-obligations only for an explicit proof-bearing problem. A local route is not a complete global outcome, Package E VerifyDW acceptance, verified gain, or global route-completeness result. The positive initial full-slack premise remains explicit. It does not establish manuscript-wide SaturatePositive, BCELReady, RankWF, ZeroSlack, PCCMin, polynomial runtime, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (9)

PNP.DirectWire.terminalOriginKernelObligationCoordinate?_sound
PNP.DirectWire.terminalCandidateOriginKernelObligationCoordinate?_shape
PNP.DirectWire.terminalCandidateOriginKernelObligationCoordinate?_edge
PNP.DirectWire.TerminalOriginKernelObligationClosureRoute.sound
PNP.DirectWire.terminalOriginKernelObligation_safe_or_route
PNP.DirectWire.TerminalSaturationClosureSafeStep.transparent
PNP.DirectWire.classifyTerminalSaturationClosureRouting_exhaustive
PNP.DirectWire.TerminalFiniteSaturatePositiveOutcome.sound
PNP.DirectWire.classifyTerminalFiniteSaturatePositive_exhaustive

Checked finite SaturatePositive-to-BCEL-ready composition

For every finite direct-wire candidate, executable terminal saturation model, and proof-bearing candidate BCEL anchor problem with explicit initial positive full slack, Lean reruns the recomputed finite SaturatePositive classifier and accepts only its positive-projection branch with a computed BCEL-ready anchor nucleus. The certificate retains the exact classifier equality, complete safe trace, positive final slack, positive whole-support defect, at-least-two anchor bound, exact constant-cut equation, and local full/quotient BN2 conclusion for every proper cut.

The terminal candidate, executable model, candidate-derived anchor problem, and initial positive full-slack premise remain explicit. Rejection of another finite branch is not a mapping into the complete global route system. This does not derive positivity from residual slack, construct BN3--BN6 data or a grouped family, derive constant activation, establish manuscript-wide SaturatePositive or BCELReady, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (4)

PNP.DirectWire.terminal_finite_saturate_positive_bcel_ready_checked_complete
PNP.DirectWire.TerminalFiniteBCELReadyCertificate.anchorSizeAtLeastTwo
PNP.DirectWire.TerminalFiniteBCELReadyCertificate.properCutConstantEquation
PNP.DirectWire.TerminalFiniteBCELReadyCertificate.properCutLocalConclusion

Same-candidate finite BCEL-ready and Packet carrier coherence

For every accepted finite Packet/budget no-lower certificate, Lean indexes a checked finite BCEL-ready problem by the same candidate and model, retains its computed ready nucleus, and uses a bijective anchor map with explicit injectivity and surjectivity proofs plus a Boolean-reflected exact list equality to identify that nucleus with the exact grouped Packet carrier. The inherited nontrivial-size bound, positive-Packet exclusion, and constant-activation exclusion therefore hold on one coherently bound family consumed by the report-facing ZeroSlack boundary.

The terminal problem, initial positive full-slack premise, grouped Packet family, bijective anchor map, Packet payloads, budget, typed realizer table, dependency table, and rank maps remain supplied proof-bearing inputs. The carrier identity does not identify Packet-family activation weights with proper-cut projection excess or derive constant activation from positive residual slack. It does not construct BN3--BN6 data from terminal data, complete the no-lower ledger, prove unconditional ZeroSlack or PCCMin, establish polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (5)

PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.family_carrier_eq
PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.carrier_at_least_two
PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.no_positive_packet
PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.not_constant_activation
PNP.terminal_finite_bcel_packet_carrier_coherent_checked_complete

Finite BCEL/Packet activation-coherence obstruction

For every arbitrary finite M184 carrier-coherence certificate, Lean computes the exact selected M183 nucleus defect and exhaustively checks the M180 Packet cut value plus every canonical nonempty proper Packet-cut activation weight. Acceptance reconstructs full finite activation coherence and identifies each mapped terminal cut's activation with its projection excess. The same-family Packet exclusion forces rejection, and a deterministic classifier returns either the declared cut-value mismatch or a proof-bearing proper-cut activation mismatch; the report-facing ZeroSlack record derives the same obstruction without duplicate family data or a caller flag.

The checker proves that the numerical bridge fails on the current accepted finite family; it does not prove activation coherence. The terminal problem, initial positive full-slack premise, grouped Packet family, bijective anchor map, activation cells and masses, payloads, budget, typed realizer table, dependency table, and rank maps remain supplied proof-bearing inputs. Exhaustive proper-cut enumeration may be exponential. This milestone does not derive the family or activation weights from positive residual slack, construct BN3--BN6 data from every valid input, complete the global route or no-lower systems, prove unconditional SaturatePositive, BCELReady, ZeroSlack or PCCMin, establish polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (6)

PNP.checkTerminalFiniteBCELPacketActivationCoherence_eq_true_iff
PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.activation_coherent_mapped_cut_equation
PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.not_activation_coherent
PNP.TerminalFiniteBCELPacketCarrierCoherenceCertificate.activation_coherence_check_eq_false
PNP.terminal_finite_bcel_packet_activation_obstruction_checked_complete
PNP.zeroslack_bcel_packet_activation_obstruction_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-185: formal artefact coverage becomes 161 of 163; risk-weighted estimate remains 30%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Residual terminal RankWF

For the fixed manuscript residual rank of exactly ten natural coordinates in the stated witness-type, span-type, mode, frontier-defect, projection-defect, saturation-defect, anchor-count, charge-size, profile-size, canonical-code priority order, Lean provides the exact lexicographic proposition, an equivalent executable comparison, all ten priority witnesses, proof-bearing descent, accessibility, induction, and kernel-checked well-foundedness.

This establishes the fixed residual rank domain and RankWF only. It does not map the current finite terminal routes into the manuscript's complete global outcome system, prove that any existing route strictly decreases the rank, establish route completeness or Package E, remove the explicit positive premise from the finite composition, establish full manuscript-wide SaturatePositive or BCELReady, prove ZeroSlack, PCCMin, polynomial runtime, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (18)

PNP.DirectWire.TerminalResidualRank.coordinates_mk
PNP.DirectWire.TerminalResidualRank.coordinates_length
PNP.DirectWire.terminalResidualRankLTBool_eq_true_iff
PNP.DirectWire.terminalResidualRankLTBool_eq_false_iff
PNP.DirectWire.terminalResidualRankLexLT_wellFounded
PNP.DirectWire.terminalResidualRank_accessible
PNP.DirectWire.terminalResidualRank_induction
PNP.DirectWire.terminalResidualRank_witnessType_lt
PNP.DirectWire.terminalResidualRank_spanType_lt
PNP.DirectWire.terminalResidualRank_mode_lt
PNP.DirectWire.terminalResidualRank_frontierDefect_lt
PNP.DirectWire.terminalResidualRank_projectionDefect_lt
PNP.DirectWire.terminalResidualRank_saturationDefect_lt
PNP.DirectWire.terminalResidualRank_anchorCount_lt
PNP.DirectWire.terminalResidualRank_chargeSize_lt
PNP.DirectWire.terminalResidualRank_profileSize_lt
PNP.DirectWire.terminalResidualRank_canonicalCode_lt
PNP.DirectWire.TerminalResidualRankDescent.sound

Candidate-derived finite BN3 request envelope

From every successful computed finite BCEL anchor nucleus, Lean uses one canonical duplicate-free primitive-record identity list across every proper cut; gives exact executable monotone request membership stable under extensional transport and exact singleton minimal consumers; accounts active incidences without duplicates; selects one canonical full or quotient side-tight coherent basis for every proper cut; and preserves all upstream proof-bearing classifier failures in a total outcome.

This establishes one exact candidate-derived finite BN3 envelope only after the existing computed BCEL anchor-nucleus classifier succeeds. Proper cuts are enumerated through all subsets, so the construction is exponential reference computation rather than a polynomial algorithm. It does not derive the terminal dependency system, map local routes into the manuscript's complete global outcome system, construct BN4-BN6, prove selector or realizer completeness, establish global ZeroSlack or PCCMin, prove SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.terminalListSubsets_sublist
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.requestAtoms_nodup
PNP.DirectWire.terminalBN3RequestPredicateBool_eq_true_iff
PNP.DirectWire.terminalBN3RequestPredicate_monotone
PNP.DirectWire.terminalBN3RequestPredicate_stable
PNP.DirectWire.terminalBN3MinimalConsumer_exact
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.mem_activeRequestAtoms_iff_properCut
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.activeRequestAtoms_nodup
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.canonicalRequestBasis_jointlySideTight
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.computedBN3RequestEnvelope
PNP.DirectWire.classifyTerminalBN3RequestEnvelope_exhaustive

Finite BN4 activation-exact cancellation kernel

After a successful computed finite BN3 envelope, Lean gives every request atom a canonical singleton activation code; proves activation-code equality exactly equivalent to equality of activation functions without enumerating cuts; checks equality of a complete typed key containing the atom, explicit semantic signature, and explicit transport type; totals positive and negative natural mass only at that same complete key; classifies a canonical balanced, positive, or negative residual; proves exact integer mass conservation, complete-key preservation, positive residual mass, and absence of opposite-sign residual pairs; computes duplicate-free ledger keys; and preserves all upstream failure branches while rejecting foreign request atoms.

This is a finite cancellation kernel over an explicit typed cell ledger. It does not derive cells, semantic signatures, or transport types from four-corner bases and is not the full historical BN4 theorem. It supplies no polynomial construction or size bound; does not construct PkgC or BN6; does not complete global routes, selectors, or realizers; does not establish ZeroSlack or PCCMin; does not put SAT in P; does not remove a project assumption; and does not prove P = NP.

Reviewed theorem interfaces (13)

PNP.DirectWire.terminalBN4ActivationCode_active_iff
PNP.DirectWire.terminalBN4ActivationCode_eq_iff_activation
PNP.DirectWire.terminalBN4ActivationKey_eq_iff
PNP.DirectWire.terminalBN4IntegerMassLedger_exact
PNP.DirectWire.TerminalBN4KeyCancellation.residual_key_eq
PNP.DirectWire.TerminalBN4KeyCancellation.residual_mass_positive
PNP.DirectWire.TerminalBN4KeyCancellation.no_opposite_sign_residual
PNP.DirectWire.TerminalBN4KeyCancellation.residual_signedContribution_exact
PNP.DirectWire.terminalBN4CancelAtKey_signedContribution_exact
PNP.DirectWire.terminalBN4CanonicalKeys_nodup
PNP.DirectWire.terminalBN4CellsUseCanonicalAtoms_iff
PNP.DirectWire.TerminalComputedBCELAnchorNucleus.computedBN4ActivationCancellation
PNP.DirectWire.classifyTerminalBN4ActivationCancellation_exhaustive

Finite BN5 full-shadow localization kernel

For every explicit finite negative-unit refinement and quotient-shadow ledger, Lean preserves the complete exact-coordinate data, validates the negative mass refinement, computes whether the cut is silent, and otherwise returns either complete multiplicity coverage or a strict Hall deficit with a literal smaller shadow-neighbor fibre, complete-coordinate preservation, and a proof-bearing local X1 route that prevents active unmatched units from disappearing silently.

This kernel starts from explicit finite inputs: one complete BN4 key, a negative cancellation result, a payload list, a cut, and a quotient-shadow coordinate list. It does not derive payloads or shadows from four-corner bases, connect complete matching back to a BN4 contradiction, or prove the full CritC/Q/E/L/X2/X3/X4 diagnosis, so it is not the full historical BN5 theorem. It does not construct PkgC or BN6; complete global routes, selectors, or realizers; establish polynomial generation or runtime, ZeroSlack, or PCCMin; put SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (12)

PNP.DirectWire.terminalBN5ShadowCoordinate_eq_iff
PNP.DirectWire.terminalBN5FullUnits_length
PNP.DirectWire.terminalBN5FullUnits_key_eq
PNP.DirectWire.TerminalBN5HallDeficit.neighbor_card_lt_full_card
PNP.DirectWire.TerminalBN5HallDeficit.fullSubset_coordinate_eq
PNP.DirectWire.TerminalBN5HallDeficit.neighbor_coordinate_eq
PNP.DirectWire.classifyTerminalBN5ShadowMatching_exhaustive
PNP.DirectWire.TerminalBN4KeyCancellation.negativeResidualMass?_positive
PNP.DirectWire.TerminalBN5HallDeficit.namedLocalRoute_eq_x1Hall
PNP.DirectWire.classifyTerminalBN5FullShadowLocalization_active
PNP.DirectWire.TerminalBN5HallDeficit.unmatchedShadowNotSilent
PNP.DirectWire.classifyTerminalBN5FullShadowLocalization_exhaustive

Finite PkgC separating-consumer restoration dichotomy

For an arbitrary finite explicit minimal-consumer antichain, Lean canonically scans for the first disjoint pair that is not singleton-singleton. Absence proves exactly V54's singletonization premise. A found pair's atoms are canonically indexed into exact-coordinate quotient units and an explicit full-restoration universe is classified into complete multiplicity coverage or a strict Hall deficit with a deterministic local Q route.

The restoration coordinate universe remains explicit. This theorem does not derive consumers or restorations from a terminal candidate, connect complete coverage back to a BN4 or BN5 contradiction, embed the Hall route into the complete global outcome system, prove global route silence, or establish the full historical PkgC theorem. It does not prove full BN6 or Packet selector-realizer completeness, polynomial generation or runtime, ZeroSlack or PCCMin, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (9)

PNP.DirectWire.terminalPkgCPairNeedsRestoration_eq_true_iff
PNP.DirectWire.firstTerminalPkgCSeparatingPair?_sound
PNP.DirectWire.firstTerminalPkgCSeparatingPair?_eq_none_iff
PNP.DirectWire.TerminalPkgCSeparatingPair.quotientUnits_length
PNP.DirectWire.TerminalPkgCSeparatingPair.quotientUnits_nonempty
PNP.DirectWire.terminalPkgC_restorationEdge_preservesCoordinate
PNP.DirectWire.TerminalBN5HallDeficit.pkgCRestorationNotSilent
PNP.DirectWire.terminalPkgC_separatingConsumers_restorationDichotomy
PNP.DirectWire.classifyTerminalPkgCSeparatingConsumers_exhaustive

Finite PkgC typed restoration realization

For an arbitrary finite explicit minimal-consumer antichain and a typed coordinate-preserving restoration operation, Lean materializes typed full-restoration candidates for every atom of the canonical first disjoint nonsingleton pair, proves exact candidate count and positional coordinate preservation, derives complete equality-fibre multiplicity coverage, excludes a strict Hall deficit for that graph, and otherwise proves V54 singletonization.

The typed restoration operation remains explicit caller data. This milestone does not construct it from a terminal candidate or prove its full semantic adequacy. It does not connect complete restoration to a BN4 or BN5 contradiction, embed local routes into the complete global outcome system, prove global PkgC route silence or the full historical PkgC theorem, establish full BN6 or Packet selector-realizer completeness, polynomial generation or runtime, ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (9)

PNP.DirectWire.TerminalPkgCSeparatingPair.fullRestorationCandidates_length
PNP.DirectWire.TerminalPkgCSeparatingPair.fullRestorationCandidates_coordinates
PNP.DirectWire.TerminalPkgCTypedRestorer.coordinateUniverse_coordinates
PNP.DirectWire.terminalBN5FullMultiplicity_indexed_eq
PNP.DirectWire.terminalBN5ShadowMultiplicity_indexed_eq
PNP.DirectWire.TerminalPkgCSeparatingPair.typedRestoration_exactCoverage
PNP.DirectWire.terminalBN5CompleteMultiplicityMatching_not_hallDeficit
PNP.DirectWire.terminalPkgC_typedRestoration_realization
PNP.DirectWire.classifyTerminalPkgCTypedRestoration_exhaustive

Finite PkgC typed restoration same-key cancellation

For an arbitrary finite explicit minimal-consumer antichain and typed exact-BN5-coordinate restoration operation, Lean mechanically pairs every quotient atom with its restored full candidate as opposite-sign unit cells, proves the complete BN5 coordinate gives the same nested BN4 key, proves exact cell count and positive/negative multiplicity equality at every BN4 key, computes an empty canonical residual and zero signed mass at every key, and derives V54 singletonization from exact absence of every such proof-bearing cancellation outcome.

The typed restoration operation and its complete coordinate maps remain explicit inputs, and the generated opposite-sign cells are not yet proved to be the cells of the terminal candidate's ambient BN4 ledger. This milestone does not construct semantic restorations from a terminal candidate, embed cancellation or Hall outcomes into the complete global route system, prove global route silence or the full historical PkgC theorem, establish full BN6 or Packet selector-realizer completeness, polynomial generation or runtime, ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.terminalPkgCRestorationCancellationCellsForAtom_key_eq
PNP.DirectWire.terminalPkgCRestorationCancellationCellsForAtom_balanced
PNP.DirectWire.terminalPkgCRestorationCancellationCellsForAtoms_length
PNP.DirectWire.terminalPkgCRestorationCancellationCellsForAtoms_balanced
PNP.DirectWire.TerminalPkgCSeparatingPair.restorationCancellationCells_length
PNP.DirectWire.TerminalPkgCSeparatingPair.restorationCancellation_balanced
PNP.DirectWire.TerminalPkgCSeparatingPair.restorationCancellation_residualCells_empty
PNP.DirectWire.TerminalPkgCSeparatingPair.restorationCancellation_signedMass_zero
PNP.DirectWire.terminalPkgC_typedRestoration_sameKeyCancellation
PNP.DirectWire.terminalPkgC_sameKeyCancellation_silence_singletonizes
PNP.DirectWire.classifyTerminalPkgCSameKeyCancellation_exhaustive

Finite PkgC ambient BN4 ledger embedding

For arbitrary finite explicit BN4 cell ledgers, Lean proves that a proof-bearing exact multiset embedding identifies the generated PkgC opposite-sign cancellation ledger with an ambient subledger and preserves every duplicate. Positive and negative mass decompose at every complete key; removing the balanced generated subledger leaves the ambient signed mass and executable residual signed contribution exactly equal to an explicit remainder. A successful candidate-derived BN4 kernel additionally proves every embedded generated cell uses its canonical request-atom space, and complete bindings plus exact absence of every computed bridge imply V54 singletonization.

The ambient ledger, typed restoration operation, exact permutation certificate or canonical serialization, and successful candidate-derived BN4 kernel remain explicit proof-bearing inputs. This milestone does not derive the ambient ledger or restorer from a terminal candidate, prove the restorer's semantic adequacy, embed local cancellation or Hall outcomes into the complete global route system, prove global PkgC route silence or the full historical PkgC theorem, establish full BN6 or Packet selector-realizer completeness, polynomial generation or runtime, ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (12)

PNP.DirectWire.terminalBN4PositiveMass_perm
PNP.DirectWire.terminalBN4NegativeMass_perm
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.generatedCell_mem_ambient
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.cellMultiplicity
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.length_eq
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.positiveMass_decomposition
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.negativeMass_decomposition
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.signedMass_eq_remainder
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.residualSignedContribution_eq_remainder
PNP.DirectWire.classifyTerminalPkgCAmbientBN4LedgerBinding_exhaustive
PNP.DirectWire.TerminalPkgCComputedAmbientBN4Cancellation.generatedCell_usesCanonicalAtom
PNP.DirectWire.terminalPkgC_computedAmbientBN4_silence_singletonizes

Finite PkgC ambient BN4 residual reduction

For arbitrary finite explicit ambient BN4 ledgers, Lean proves that removing an exactly embedded balanced PkgC generated subledger preserves the executable residual cell at every complete key and the complete canonical executable residual ledger over the ambient key universe. Every remainder key occurs in that universe; a fail-closed canonical classifier constructs the exact reduction without caller-provided proof bits; and an empty remainder yields an empty ambient residual ledger, including for the existing candidate-derived computed bridge.

The ambient ledger, typed restoration operation, exact embedding, and explicit remainder remain proof-bearing inputs. This milestone does not derive those inputs from an arbitrary terminal candidate, prove that the remainder is empty or route-producing, establish restoration semantic adequacy or complete global route silence, reconstruct the full historical PkgC/BN6/Packet path, prove polynomial generation or runtime, establish ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (8)

PNP.DirectWire.terminalBN4ResidualCells_add_common
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.residualCells_eq_remainder
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.residualLedgerOver_eq_remainder
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.remainderKey_mem_ambientCanonicalKeys
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.canonicalResidualLedger_eq_remainder
PNP.DirectWire.TerminalPkgCAmbientBN4LedgerEmbedding.canonicalResidualLedger_empty_of_remainder_empty
PNP.DirectWire.classifyTerminalPkgCAmbientBN4ResidualReduction_exhaustive
PNP.DirectWire.TerminalPkgCComputedAmbientBN4Cancellation.residualLedger_empty_of_remainder_empty

Finite V54 consumer-antichain normal form

For an arbitrary finite carrier and its explicit minimal-consumer antichain, Lean proves monotonicity and empty-request inactivity, proves that nonzero two-sided cut activation is equivalent to the existence of a disjoint consumer pair, and under the exact singletonized-disjoint-pair premise proves literal equality with the corresponding footprint cut indicator.

This finite kernel starts from an explicit minimal-consumer antichain and an explicit proof that every disjoint consumer pair is singletonized. It does not construct PkgC, derive that singletonization premise, or connect the footprint back to the full BN6 proof. It does not construct complete global routes, selectors, or realizers; establish polynomial generation or runtime, ZeroSlack, or PCCMin; put SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalV54ConsumerSystem.requestActive_monotone
PNP.DirectWire.TerminalV54ConsumerSystem.requestActive_empty_false
PNP.DirectWire.TerminalV54ConsumerSystem.consumer_is_minimal
PNP.DirectWire.TerminalV54ConsumerSystem.cutActive_has_disjoint_consumers
PNP.DirectWire.terminalV54_cutActivation_nonzero_iff_disjoint_consumers
PNP.DirectWire.terminalV54_consumerAntichain_normal_form_iff
PNP.DirectWire.terminalV54_consumerAntichain_normal_form

Finite V53 constant-cut hypergraph rigidity

For an arbitrary finite duplicate-free carrier and sparse nonnegative weighted hypergraph with positive listed cells, exact equality of every nonempty proper cut proves the complete V53 q=2, q=3, and q>=4 classification: full-span weight D; one common pair weight p with w_A + 2p = D; or zero weight on every proper footprint with full-span weight D.

This theorem consumes an explicit sparse positive hypergraph and an explicit proof that every nonempty proper cut has the same positive value. It does not construct PkgC, derive the hypergraph from a terminal candidate or the V54 consumer system, build BN6 cells or payloads, complete global routes, selectors, or realizers, establish polynomial generation or runtime, prove ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.TerminalV53Hypergraph.cell_partition
PNP.DirectWire.TerminalV53Hypergraph.cut_partition
PNP.DirectWire.TerminalV53Hypergraph.pair_complement_identity
PNP.DirectWire.TerminalV53Hypergraph.pairWeights_equal_of_shared
PNP.DirectWire.TerminalV53Hypergraph.pairWeight_eq_zero_of_four
PNP.DirectWire.TerminalV53Hypergraph.properFootprintWeight_eq_zero_of_four
PNP.DirectWire.TerminalV53Hypergraph.twoAnchor_fullWeight
PNP.DirectWire.TerminalV53Hypergraph.threeAnchor_rigidity
PNP.DirectWire.TerminalV53Hypergraph.fourAnchor_rigidity
PNP.DirectWire.terminalV53_constantCut_hypergraph_rigidity

Finite BN6 grouped hypergraph packet bridge

For an arbitrary finite duplicate-free anchor carrier and explicit already-grouped family of positive payload-bearing survivor cells, V54 activation is transported exactly into the constructed V53 hypergraph cut sum. A positive BCEL constant-cut premise then yields the complete pair, mixed three-anchor balanced-triple/full-span, or four-or-more-anchor full-span classification with original payload witnesses.

This finite bridge consumes explicit exact footprint grouping, PkgC singletonization proofs, positive atom ledgers, payload data, and the BCEL constant-cut equation. It does not construct PkgC, derive or group survivors from a terminal candidate, establish full historical BN6 or Packet selector/realizer completeness, complete global routes, prove polynomial generation or runtime, ZeroSlack or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (8)

PNP.DirectWire.TerminalBN6GroupedCell.massPositive
PNP.DirectWire.TerminalBN6GroupedCell.crosses_iff_footprintCrosses
PNP.DirectWire.TerminalBN6GroupedCell.crossesBool_eq_cutActivationBool
PNP.DirectWire.TerminalBN6GroupedFamily.cutWeight_eq_activationWeight
PNP.DirectWire.TerminalBN6GroupedFamily.constantProperCuts
PNP.DirectWire.TerminalBN6GroupedFamily.footprintWeight_eq_groupedMass
PNP.DirectWire.TerminalBN6GroupedFamily.hasPayloadAt_of_footprintWeight_positive
PNP.DirectWire.terminalBN6_hypergraph_packet

Finite Packet selector-seed extraction

For an arbitrary finite exact BN6 packet conclusion, Lean extracts a carrier-contained payload-backed raw selector seed at the positive pair footprint, at every positive pair footprint of a balanced triple, or at the positive full-span footprint. The mixed three-anchor positive alternative is handled without asserting that both masses are positive, and the construction fixes no carrier cardinality.

This milestone consumes an exact finite BN6 packet conclusion and preserves only carrier containment, selector-relevant footprint size, and original grouped cell-and-atom payload evidence. It does not prove selector-universe membership, selector faithfulness or compatibility, construct a realizer or route, establish enumeration or polynomial generation/runtime, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (3)

PNP.DirectWire.TerminalBN6GroupedFamily.hasPacketSelectorSeedAt_of_hasPayloadAt
PNP.DirectWire.TerminalBN6PacketConclusion.selectorSeeds
PNP.DirectWire.terminalBN6_packet_selector_seeds

Finite Packet payload-selector universe membership

For every arbitrary finite explicit grouped BN6 family, Lean enumerates the exact duplicate-free list of grouped footprints, proves membership equivalent to an original grouped cell at that footprint, and upgrades every payload-backed pair, balanced-triple pair, or full-span seed to membership in that same finite universe.

This finite universe is exactly the grouped-footprint list already present in an explicit BN6 family. It is not the manuscript's encoded or polynomial selector universe, and payload retention is not manuscript-level selector faithfulness. It does not prove selector compatibility, construct a realizer or route, derive the grouped family from a terminal candidate, establish polynomial enumeration or size bounds, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (6)

PNP.DirectWire.TerminalBN6GroupedFamily.packetPayloadSelectorUniverse_nodup
PNP.DirectWire.TerminalBN6GroupedFamily.mem_packetPayloadSelectorUniverse_iff
PNP.DirectWire.TerminalBN6GroupedFamily.hasPacketPayloadSelectorAt_of_seed
PNP.DirectWire.TerminalPacketSelectorSeedConclusion.payloadSelectors
PNP.DirectWire.TerminalBN6PacketConclusion.payloadSelectors
PNP.DirectWire.terminalBN6_packet_payload_selectors

Canonical finite Packet selector handles

For every arbitrary finite explicit grouped BN6 family, Lean defines canonical indexed grouped-footprint handles, proves exact decoding is injective and every payload selector has a unique handle, retains original payload evidence, and proves every decoded footprint remains carrier-contained and has length at least two across the pair, balanced-triple, and full-span Packet branches.

These handles are input-relative list positions, not the manuscript's bit encoding or a polynomially enumerable selector universe. The milestone does not prove manuscript-level selector faithfulness or compatibility, construct a selector realizer or route, derive or group BN6 survivors from a terminal candidate, establish polynomial encoding length or runtime, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_mem_universe
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_injective
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_sublist_carrier
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_large
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_hasPayloadAt
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_hasPacketPayloadSelectorAt
PNP.DirectWire.TerminalBN6GroupedFamily.hasFinitePacketSelectorHandleAt_iff_payloadSelector
PNP.DirectWire.TerminalBN6GroupedFamily.existsUnique_packetSelectorHandle_iff_payloadSelector
PNP.DirectWire.TerminalPacketPayloadSelectorConclusion.selectorHandles
PNP.DirectWire.TerminalBN6PacketConclusion.selectorHandles
PNP.DirectWire.terminalBN6_packet_selector_handles

Canonical fail-closed Packet selector-handle codec

For every arbitrary finite explicit grouped BN6 family, Lean gives each canonical input-relative selector handle a unary bitstring with fail-closed total decoding of missing delimiters, trailing data, and out-of-range indices, proves exact round trip, injectivity, canonical successful decoding, exact and explicit-universe-bounded length, retains payload, carrier, size, cell, and atom evidence, and gives every payload selector one unique accepted code across the pair, balanced-triple, and full-span Packet branches.

The code-length bound is relative to the explicit grouped-family list and does not bound that list by encoded circuit size. This milestone does not prove polynomial enumeration or runtime, encode atom or payload data, prove manuscript-level selector faithfulness or compatibility, construct a selector realizer or route, derive or group BN6 survivors from a terminal candidate, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_encode
PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_injective
PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_length
PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_length_le_universe
PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_canonical
PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_payloadEvidence
PNP.DirectWire.TerminalBN6GroupedFamily.hasEncodedPacketSelectorAt_iff_payloadSelector
PNP.DirectWire.TerminalBN6GroupedFamily.existsUnique_encodedPacketSelector_iff_payloadSelector
PNP.DirectWire.TerminalPacketPayloadSelectorConclusion.selectorCodes
PNP.DirectWire.TerminalBN6PacketConclusion.selectorCodes
PNP.DirectWire.terminalBN6_packet_selector_codes

Total fail-closed Packet source-payload realization

For every arbitrary finite explicit grouped BN6 family, Lean defines a total fail-closed function that maps each accepted canonical selector code to its exact decoded handle, original source cell, decoded footprint, and a canonical original positive payload atom. Successful results re-encode to the exact input, remain in the supplied family, retain strict atom positivity, are equivalent to the finite payload-selector predicate, and preserve the pair, balanced-triple, and full-span Packet branches.

This is source-payload materialization relative to a supplied explicit grouped family, not the manuscript's gain-or-blocker selector realizer. The unary code still encodes only a list position and does not serialize atom or payload data. This milestone does not construct a replacement circuit, prove selector faithfulness or compatibility, return a gain or typed blocker route, derive or group BN6 survivors from a terminal candidate, bound the selector family by encoded circuit size, prove polynomial generation or runtime, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorCell_footprint
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadAtom_mem
PNP.DirectWire.TerminalBN6GroupedFamily.realizePacketSelectorPayload_eq_none_iff
PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_eq_some_of_realize
PNP.DirectWire.TerminalBN6GroupedFamily.exists_realizePacketSelectorPayload_encode
PNP.DirectWire.TerminalBN6GroupedFamily.realizePacketSelectorPayload_sound
PNP.DirectWire.TerminalBN6GroupedFamily.isRealizedPacketSelectorAt_iff_encoded
PNP.DirectWire.TerminalBN6GroupedFamily.hasRealizedPacketSelectorAt_iff_payloadSelector
PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.selectorPayloadRealizations
PNP.DirectWire.TerminalBN6PacketConclusion.selectorPayloadRealizations
PNP.DirectWire.terminalBN6_packet_selector_payload_realizations

Checked Packet selector candidate-gain scan

For every arbitrary finite explicit grouped BN6 family whose payloads are direct-wire implementations, Lean decodes each accepted canonical Packet selector, scans every original candidate payload in the exact selected source cell with the executable strict-equivalent-gain checker, and returns only a genuine source-atom StrictEquivalentGain or proof that the selected cell has no such candidate. Every gain strictly decreases residual slack, decoder rejection is exact, and the pair, balanced-triple, and full-span Packet alternatives are preserved.

The candidate implementations and grouped BN6 family remain explicit input data. A local no-gain result excludes only payload candidates in one selected source cell; it is not a manuscript BotHN, BotBUD, or lower-rank BotSeed and does not imply global minimality or ZeroSlack. This milestone does not construct replacement candidates, prove selector faithfulness or compatibility, connect payload mass to charge surplus, derive or group survivors from a terminal candidate, bound the selector family by encoded circuit size, prove polynomial generation or runtime, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (12)

PNP.DirectWire.TerminalBN6GroupedFamily.mem_packetSelectorCandidateImplementations_iff
PNP.DirectWire.TerminalPacketCandidateGainOutcome.sound
PNP.DirectWire.TerminalPacketCandidateGainOutcome.gain_strictResidualDescent
PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorGains_eq_none_iff
PNP.DirectWire.TerminalBN6GroupedFamily.exists_scanPacketSelectorGains_iff
PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_eq_some_of_gainScan
PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorGains_sound
PNP.DirectWire.TerminalBN6GroupedFamily.exists_scanPacketSelectorGains_encode
PNP.DirectWire.TerminalBN6GroupedFamily.hasPacketSelectorGainScanAt_iff_encoded
PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.gainScans
PNP.DirectWire.TerminalBN6PacketConclusion.gainScans
PNP.DirectWire.terminalBN6_packet_selector_gain_scans

Exhaustive Packet selector-universe gain scan

For every arbitrary finite explicit grouped BN6 family whose payloads are direct-wire implementations, Lean enumerates every canonical input-relative selector handle, scans every original candidate payload in each exact source cell with the executable strict-equivalent-gain checker, and returns only a canonical source-atom StrictEquivalentGain or proof that the complete supplied selector universe has no such candidate. Every gain retains a canonical accepted code and strictly decreases residual slack, while the pair, balanced-triple, and full-span Packet alternatives are preserved literally.

The grouped BN6 family and candidate implementations remain explicit inputs. Family-wide no-gain is silence only for that supplied input-relative selector universe; it is not a manuscript BotHN, BotBUD, or lower-rank BotSeed, does not establish selector faithfulness or compatibility, and does not imply global minimality or ZeroSlack. This milestone does not construct replacement candidates, connect payload mass to charge surplus, derive or group survivors from terminal data, bound the family by encoded circuit size, prove polynomial enumeration or runtime, complete PkgC, ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.TerminalBN6GroupedFamily.mem_packetSelectorHandles
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorHandles_length
PNP.DirectWire.TerminalPacketSelectorHandleListGainOutcome.sound
PNP.DirectWire.TerminalPacketSelectorUniverseGainOutcome.sound
PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorUniverseGains_sound
PNP.DirectWire.TerminalPacketSelectorUniverseGainOutcome.gain_strictResidualDescent
PNP.DirectWire.TerminalBN6GroupedFamily.universeGain_source_and_code
PNP.DirectWire.TerminalBN6GroupedFamily.universeNoGain_of_gainScan
PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.universeGainScan_packet
PNP.DirectWire.terminalBN6_packet_selector_universe_gain_scan_sound

Conditional Packet selector gain-or-ZeroSlack coverage

For every arbitrary finite explicit grouped BN6 family whose payloads are direct-wire implementations, an explicit proof-bearing coverage certificate requires every strict equivalent gain from the current implementation to occur as an original payload atom in an exact canonical selector source cell. Under precisely that premise, the exhaustive scan returns either a source-atom gain with strict residual descent or a proof-bearing semantic minimum and zero residual slack, while preserving the pair, balanced-triple, and full-span Packet alternatives literally.

The explicit gain-coverage certificate, grouped BN6 family, and candidate implementations remain inputs. This milestone does not construct the coverage certificate from terminal data, prove selector faithfulness or compatibility, construct or polynomially enumerate replacement candidates, establish encoded-size or runtime bounds, produce typed blockers or HB/rank closure, or complete global PkgC, ZeroSlack, or PCCMin. It is conditional and not unconditional ZeroSlack; it does not put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalPacketSelectorGainCoverage.noStrictEquivalentGain
PNP.DirectWire.TerminalPacketSelectorGainCoverage.residualSlack_eq_zero_of_noGain
PNP.DirectWire.TerminalPacketSelectorCoveredGainOutcome.sound
PNP.DirectWire.TerminalPacketSelectorCoveredGainOutcome.residualSlack_spec
PNP.DirectWire.TerminalBN6GroupedFamily.scanCoveredPacketSelectorGains_sound
PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.coveredGainScan_packet
PNP.DirectWire.terminalBN6_packet_selector_covered_gain_scan_sound

Finite Packet charge-surplus realizer kernel

For arbitrary finite support and replacement charge ledgers, exact multiplicity-preserving occurrence pairing and pairwise weight preservation leave an unmatched positive support charge and derive strict occurrence count and strict total replacement weight. When the totals exactly account for current and replacement NAND gates and semantic equivalence is proved independently, Lean constructs a genuine StrictEquivalentGain and strict reference-residual descent without assuming either strict inequality.

The finite ledgers, exact occurrence pairing, gate accounting, and semantic equivalence remain explicit inputs. This milestone does not construct a replacement or its charge ledger from a Packet blueprint or terminal data, prove selector faithfulness or compatibility, produce BotHN, BotBUD, or a lower-rank BotSeed, close HB/rank routing, establish encoded-size or polynomial-runtime bounds, or complete global PkgC, ZeroSlack, or PCCMin. It is not unconditional ZeroSlack; it does not put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (8)

PNP.DirectWire.TerminalPacketChargeSurplus.matchedWeight_eq
PNP.DirectWire.TerminalPacketChargeSurplus.supportWeight_eq_matched_add_unmatched
PNP.DirectWire.TerminalPacketChargeSurplus.replacementWeight_eq_matched
PNP.DirectWire.TerminalPacketChargeSurplus.unmatchedWeight_pos
PNP.DirectWire.TerminalPacketChargeSurplus.replacementLength_lt_supportLength
PNP.DirectWire.TerminalPacketChargeSurplus.replacementWeight_lt_supportWeight
PNP.DirectWire.TerminalPacketChargeSurplusRealization.strictEquivalentGain
PNP.DirectWire.TerminalPacketChargeSurplusRealization.strictResidualDescent

Checked Packet unit-charge blueprint realizer

For arbitrary direct-wire input and output arities and every finite explicit grouped BN6 family of replacement blueprints, Lean validates canonical unit-charge gate-occurrence ledgers with a constructive exact permutation checker, a nonempty unmatched current-gate remainder, and semantic equivalence. Acceptance mechanically constructs the generic charge-surplus realization, a genuine StrictEquivalentGain, and strict residual descent without accepting a gate inequality. Every original blueprint atom behind every canonical handle is scanned, and the complete pair, balanced-triple, and full-span Packet conclusion is retained literally.

The grouped BN6 family, candidate implementations, replacement blueprints, occurrence pairings, and unmatched lists remain explicit inputs. Supplied-family validator silence is not BotHN, BotBUD, a lower-rank BotSeed, global absence of strict gains, semantic minimality, or ZeroSlack. This milestone does not derive blueprints from terminal data, establish manuscript selector faithfulness or compatibility, close HB/rank routing, establish encoded-size or polynomial-runtime bounds, or complete global PkgC, ZeroSlack, or PCCMin. It does not put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (13)

PNP.DirectWire.eraseFirstNat_sound
PNP.DirectWire.natOccurrencePermBool_sound
PNP.DirectWire.natOccurrencePermBool_complete
PNP.DirectWire.natOccurrencePermBool_eq_true_iff
PNP.DirectWire.TerminalPacketUnitChargeBlueprint.check_eq_true_iff
PNP.DirectWire.unitChargeRange_sum
PNP.DirectWire.TerminalPacketUnitChargeBlueprint.strictEquivalentGain_of_check
PNP.DirectWire.TerminalPacketUnitChargeBlueprint.strictResidualDescent_of_check
PNP.DirectWire.TerminalPacketUnitChargeBlueprintAtomOutcome.sound
PNP.DirectWire.TerminalPacketUnitChargeBlueprintRealizerOutcome.sound
PNP.DirectWire.TerminalPacketUnitChargeBlueprintRealizerOutcome.gain_descent
PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.unitChargeBlueprintRealizer_packet
PNP.DirectWire.terminalBN6_packet_unit_charge_blueprint_realizer_sound

Checked Packet typed-realizer contract

For arbitrary selector types, finite selector lists, positive finite rank carriers, executable faithfulness and blocker-activity tables, and data-only realizer claims, Lean accepts a faithful selector row exactly as a checked unit-charge gain, an active same-or-lower-rank HN bot, an active same-or-lower-rank budget bot, or a faithful strictly lower-rank seed bot. The list validator covers every faithful member, and its grouped-BN6 specialization covers every canonical input-relative Packet handle.

The selector family, finite rank assignment, faithfulness predicate, realizer claims, hereditary activity table, and budget activity table remain explicit inputs. Finite indices are not the manuscript's tuple-valued packet ranks, and an invalid faithful row is rejected rather than reinterpreted as a bot. This milestone does not construct blueprints or blockers from terminal data, prove selector faithfulness or compatibility, establish blocker semantics or HB acyclicity, derive global selector silence, or establish encoded-size or polynomial-runtime bounds. It does not complete PkgC, unconditional ZeroSlack, or PCCMin, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (5)

PNP.DirectWire.TerminalPacketTypedRealizerBot.check_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerClaim.check_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerEvidence.sound
PNP.DirectWire.checkTerminalPacketFaithfulRealizerClaims_sound
PNP.DirectWire.terminalBN6_packet_typed_realizer_contract

Checked exact-rank HB blocker-graph acyclicity

For arbitrary finite HN/BUD data-edge graphs, Lean exhaustively checks that the supplied finite rank indices embed strictly into the exact ten-coordinate residual rank and that every supplied dependency edge strictly descends that rank. Acceptance derives accessibility and well-foundedness of the exact supplied dependency relation, proves that it has no nonempty directed cycle, upgrades valid lower-seed bots to exact-rank descent, and composes these facts with every faithful canonical handle in an accepted Packet typed-realizer table.

The graph, edges, finite-to-exact rank mapping, selector family, faithfulness predicate, blocker activity tables, and realizer claims remain explicit inputs. This milestone does not prove dependency completeness, blocker semantics, that every active HN or budget row records all dependencies, or construction of the graph or rank mapping from terminal data. It does not establish selector compatibility, rank-complete selector silence, the full HB.NegativeClosure theorem, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalPacketHBDependencyGraph.checkRankEmbedding_eq_true_iff
PNP.DirectWire.TerminalPacketHBDependencyGraph.check_eq_true_iff
PNP.DirectWire.TerminalPacketHBDependencyGraph.depends_rank_lt
PNP.DirectWire.TerminalPacketHBDependencyGraph.depends_wellFounded
PNP.DirectWire.TerminalPacketHBDependencyGraph.noCycle
PNP.DirectWire.TerminalPacketHBDependencyGraph.lowerSeed_rankTuple_lt_of_valid
PNP.DirectWire.terminalBN6_packet_typed_realizer_hb_acyclicity_contract

Checked total-table HB dependency closure

For every arbitrary finite rank carrier, Lean enumerates all HN and budget nodes, assigns each node one total data-only dependency row, and materializes the graph mechanically from all rows without accepting a second edge list. The checker exhaustively validates the finite-to-exact ten-coordinate rank embedding and strict exact-rank descent for every row dependency. Acceptance proves exact row-to-edge coverage, accessibility, well-founded rank induction for arbitrary predicates with an explicit local premise, absence of every nonempty dependency cycle, covered HN/BUD bot rows, and exact-rank descent for lower seeds.

The dependency table, finite-to-exact rank mapping, selector family, faithfulness predicate, blocker activity tables, and realizer claims remain explicit inputs. Total table coverage means only that every finite HN/BUD node has a row and every dependency listed in that row becomes a graph edge. It does not prove blocker semantics, semantic dependency completeness relative to terminal data, or the local invariant premise needed by generic rank induction. It does not establish selector compatibility, rank-complete selector silence, the full HB.NegativeClosure theorem, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.mem_allTerminalPacketHBNodes
PNP.DirectWire.TerminalPacketHBDependencyTable.edge_mem_toGraph_iff
PNP.DirectWire.TerminalPacketHBDependencyTable.toGraph_depends_iff
PNP.DirectWire.TerminalPacketHBDependencyTable.rowCovered
PNP.DirectWire.TerminalPacketHBDependencyTable.check_eq_true_iff
PNP.DirectWire.TerminalPacketHBDependencyTable.depends_rank_lt
PNP.DirectWire.TerminalPacketHBDependencyTable.depends_wellFounded
PNP.DirectWire.TerminalPacketHBDependencyTable.depends_induction
PNP.DirectWire.TerminalPacketHBDependencyTable.noCycle
PNP.DirectWire.TerminalPacketTypedRealizerEvidence.hbTableSound
PNP.DirectWire.terminalBN6_packet_typed_realizer_hb_dependency_table_closure_contract

Checked HB active-dependency closure

For every arbitrary finite rank carrier and supplied typed-realizer environment, Lean exhaustively checks that every active HN or budget node has an active dependency in its own total row and independently checks strict exact-rank descent for every row dependency. Well-founded induction then proves every supplied HN and budget activity bit is false. Composition with every faithful canonical grouped-BN6 handle eliminates HN/BUD typed bots while preserving a genuine checked strict gain or a faithful strictly lower-rank seed.

The activity bits, dependency rows, finite-to-exact rank mapping, selector family, faithfulness predicate, and realizer claims remain explicit inputs. The local check does not derive blocker activity, blocker semantics, or semantic dependency completeness from terminal data. It eliminates HN/BUD bots only after the supplied tables pass; a checked gain or faithful lower-rank seed remains. This milestone does not establish selector compatibility, gain exclusion, lower-seed closure, rank-complete selector silence, the full HB.NegativeClosure theorem, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalPacketHBDependencyTable.checkActiveDependencyClosed_eq_true_iff
PNP.DirectWire.TerminalPacketHBDependencyTable.checkNoOutcomeActiveClosure_eq_true_iff
PNP.DirectWire.TerminalPacketHBDependencyTable.noActive_of_noOutcomeActiveClosure
PNP.DirectWire.TerminalPacketHBDependencyTable.hnActive_eq_false
PNP.DirectWire.TerminalPacketHBDependencyTable.budgetActive_eq_false
PNP.DirectWire.TerminalPacketTypedRealizerEvidence.hbActiveClosureSound
PNP.DirectWire.terminalBN6_packet_typed_realizer_hb_active_dependency_closure_contract

Conditional HB selector-silence rank closure

For every arbitrary finite accepted typed-realizer table, checked HN/BUD active-dependency closure and semantic exclusion of every strict equivalent gain leave a faithful selector only if there is a faithful selector at strictly lower finite rank. Strong induction proves every canonical selector in the supplied grouped-BN6 family nonfaithful. A second theorem obtains the global gain-exclusion premise from the existing explicit gain-coverage certificate and exact source-cell no-gain evidence.

The global semantic gain exclusion is an explicit proof-bearing premise. The coverage specialization still requires a supplied certificate covering every strict equivalent gain plus exact source-cell no-gain evidence. The grouped family, finite rank and faithfulness tables, realizer claims, blocker activity, dependency rows, and rank map remain explicit inputs. This does not establish selector faithfulness or compatibility, construct those inputs from terminal data, derive blocker semantics or semantic dependency completeness, prove the unconditional HB.NegativeClosure theorem, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (4)

PNP.DirectWire.TerminalPacketTypedRealizerTable.noFaithful_of_noStrictEquivalentGain
PNP.DirectWire.TerminalPacketTypedRealizerTable.noFaithful_of_gainCoverageNoGain
PNP.DirectWire.terminalBN6_packet_typed_realizer_hb_selector_silence_closure_contract
PNP.DirectWire.terminalBN6_packet_typed_realizer_hb_selector_silence_gain_coverage_contract

Executable HB selector-silence induction

For every arbitrary finite accepted typed-realizer table, one exhaustive executable check proves that every canonical realizer claim is a typed bottom and retains faithful-row validity. Checked HB active-dependency closure eliminates HN and budget bottoms, while strong induction on the supplied finite rank eliminates faithful strictly lower-rank seeds. Every canonical selector is therefore nonfaithful without global semantic no-gain as a theorem premise.

The grouped family, finite rank and faithfulness functions, realizer claim function, blocker activity functions, dependency rows, and finite-to-exact rank map remain explicit data inputs. The checker validates these data but does not construct them from terminal candidates or prove selector faithfulness, selector compatibility, blocker semantics, or semantic dependency completeness. This milestone does not establish the full unconditional HB.NegativeClosure theorem, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalPacketTypedRealizerClaim.isBotBool_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerTable.checkSelectorSilent_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerTable.checkFaithful_of_selectorSilent
PNP.DirectWire.TerminalPacketTypedRealizerTable.claim_eq_bot_of_selectorSilent
PNP.DirectWire.TerminalPacketTypedRealizerTable.noFaithful_of_selectorSilent
PNP.DirectWire.TerminalPacketTypedRealizerTable.noFaithfulAtOrBelow_of_selectorSilent
PNP.DirectWire.terminalBN6_packet_typed_realizer_hb_selector_silence_induction_contract

Packet selector-faithfulness routing and HB contradiction

For every arbitrary finite explicit grouped BN6 family, exhaustive route-clear canonical payload checks plus exact binding to the supplied HB faithfulness table turn every positive Packet conclusion into a faithful canonical handle. Accepted executable HB selector silence and active-dependency closure prove that same handle nonfaithful, yielding a contradiction with selector silence. A fixed first-failure classifier exposes colour, frontier, charge, obligation, activation, direction, budget, rank, exact-route, or descent failure.

The grouped family, payload field Booleans, finite rank tags, route-clear payload checks, exact HB binding, realizer claims, blocker activity, dependency rows, and finite-to-exact rank map remain explicit terminal-relative inputs. The checkers do not derive those inputs from a terminal candidate or prove their external manuscript semantics. This milestone does not derive positive slack, SaturatePositive, BCELReady, the grouped family, or the no-lower ledger; establish unconditional HB.NegativeClosure or complete route silence; prove unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (11)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.check_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.firstRoute_eq_none_of_check
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.check_eq_false_of_firstRoute
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFaithful_eq_true_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRoute_eq_none
PNP.DirectWire.TerminalBN6GroupedFamily.checkPacketSelectorRoutesClear_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerTable.checkPacketSelectorFaithfulnessBinding_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorHandleConclusion.existsHandle
PNP.DirectWire.TerminalBN6PacketConclusion.existsPacketSelectorHandle
PNP.DirectWire.TerminalBN6PacketConclusion.existsFaithfulHandle_of_routesClear
PNP.DirectWire.terminalBN6_packet_selector_faithfulness_hb_contradiction

Canonical Packet faithfulness-table construction

For every arbitrary finite explicit grouped BN6 family and finite rank carrier, Lean canonicalizes a typed-realizer table by replacing its free faithfulness function with the canonical positive source-payload computation while preserving rank, HN activity, budget activity, and every realizer claim exactly. Exhaustive faithfulness binding accepts by construction, and a route-clear positive Packet contradicts accepted executable HB selector silence without an independent binding premise.

The grouped family, ten payload field Booleans, finite rank tags and rank assignment, route-clear acceptance, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. The constructor does not derive those inputs from a terminal candidate or prove their external manuscript semantics. This milestone does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (8)

PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorFaithfulness_rankOf
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorFaithfulness_hnActive
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorFaithfulness_budgetActive
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorFaithfulness_claim
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorFaithfulness_faithful
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorFaithfulness_binding
PNP.DirectWire.TerminalBN6PacketConclusion.existsFaithfulHandle_of_computedTable
PNP.DirectWire.terminalBN6_packet_computed_faithfulness_hb_contradiction

Total Packet selector first-route outcome

For every arbitrary finite explicit grouped BN6 family and finite rank carrier, Lean proves the canonical payload first-route classifier total: no route exactly on acceptance and one earliest typed route exactly on rejection. Every positive Packet under the canonicalized HB table, accepted executable selector silence, and accepted active-dependency closure yields a first typed route without route-clear or binding premises.

The grouped family, ten payload field Booleans, finite rank tags and rank assignment, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. The result does not prove any route's external semantics and does not map reported routes into a decreasing complete global outcome system. It does not construct those inputs from a terminal candidate, establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.firstRoute_eq_none_iff_check_eq_true
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.exists_firstRoute_iff_check_eq_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRoute_eq_none_iff
PNP.DirectWire.TerminalBN6GroupedFamily.exists_packetSelectorPayloadFirstRoute_iff
PNP.DirectWire.TerminalBN6PacketConclusion.existsFaithfulOrFirstRoute
PNP.DirectWire.TerminalBN6PacketConclusion.existsFirstRoute_of_computedTableSelectorSilence
PNP.DirectWire.terminalBN6_packet_computed_faithfulness_hb_first_route

Exact Packet first-route failure semantics

For every arbitrary finite payload rank and all ten route constructors, Lean proves the executable first route is equivalent to the exact earliest failed supplied field, with every preceding condition accepted. The failure is unique, rejection is equivalent to exact failure existence, and the canonical positive Packet/HB outcome carries the route and exact field-failure proof without route-clear or binding premises.

The grouped family, ten payload field Booleans, finite rank tags and rank assignment, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. The result does not derive the payload fields or family from terminal data, does not prove their external manuscript semantics, and does not map a reported failure into a decreasing complete global outcome system. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (6)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.firstRoute_eq_some_iff_failureAt
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.failureAt_unique
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.check_eq_false_iff_exists_failureAt
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRoute_eq_some_iff_failureAt
PNP.DirectWire.TerminalBN6PacketConclusion.existsFirstRouteFailure_of_computedTableSelectorSilence
PNP.DirectWire.terminalBN6_packet_computed_faithfulness_hb_first_route_failure

Rank-reflected Packet descent route

For every arbitrary finite grouped BN6 family and selector-rank carrier, the final strict-descent payload condition is computed from the exact ten-coordinate RankWF comparison while the preceding fields are preserved. Accepted computed payloads carry actual rank descent, a final descent failure carries actual nondecrease, and the positive Packet/HB endpoint returns either an earlier exact field route or proof that the supplied transition is nondecreasing, without route-clear or descent-binding premises.

The first nine payload fields, before/after residual ranks and their handle assignment, grouped family, finite selector-rank map, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. The result does not construct the grouped family or ranks from terminal data, prove external manuscript semantics for the earlier fields, map those other nine routes into the complete global outcome system, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (9)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedDescent_valid_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedDescent_failureAt_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedDescent_firstRoute_eq_some_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.rankDescent_of_withComputedDescent_check
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedDescent_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computed_firstRoute_descent
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorDescentFaithfulness_preserves
PNP.DirectWire.TerminalBN6PacketConclusion.existsRankReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_rank_reflected_hb_first_route_failure

Canonical Packet rank-tag route reflection

For every arbitrary finite grouped BN6 family and selector-rank carrier, the payload rank tag is copied from the authoritative handle rank while final residual descent remains computed from the exact ten-coordinate RankWF comparison. The canonical first-route classifier cannot return rank; a final descent route proves the supplied transition is nondecreasing, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The finite rank map, before/after residual ranks and their handle assignment, seven earlier Boolean payload fields, exactRouteClear, grouped family, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. The result does not construct the grouped family or rank map from terminal data, prove external manuscript semantics for the eight remaining routes, map those routes into the complete global outcome system, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (12)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedRankDescent_valid_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedRankDescent_failureAt_rank_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedRankDescent_failureAt_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedRankDescent_firstRoute_eq_some_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.rankDescent_of_withComputedRankDescent_check
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedRankDescent_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedRankDescent_firstRoute_descent
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorRankDescentFaithfulness_preserves
PNP.DirectWire.TerminalBN6PacketConclusion.existsRankTagReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_rank_tag_reflected_hb_first_route_failure

Canonical Packet exact-route reflection

For every arbitrary finite grouped BN6 family and selector-rank carrier, each canonical handle selects an original positive payload atom from its exact grouped cell and footprint. That canonical handle-to-cell-to-payload source route is marked clear by construction while the authoritative handle rank is copied and residual descent is computed from the exact ten-coordinate RankWF comparison. The first-route classifier cannot return exactRoute or rank; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The seven semantic Boolean payload fields, finite rank map, before/after residual ranks, grouped family, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. This internal route is not an external exact minimum or a proof of manuscript exact-minimum semantics. The seven remaining routes still lack complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, derive the seven fields from a terminal candidate, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (16)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_valid_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_failureAt_rank_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_failureAt_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedExactRouteRankDescent_firstRoute_eq_some_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.rankDescent_of_withComputedExactRouteRankDescent_check
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorCanonicalSourceRoute
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedExactRouteRankDescent_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedExactRouteRankDescent_firstRoute_descent
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorExactRouteRankDescentFaithfulness_preserves
PNP.DirectWire.TerminalBN6PacketConclusion.existsExactRouteReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_exact_route_reflected_hb_first_route_failure

Canonical Packet charge-route reflection

For every arbitrary finite grouped BN6 family and selector-rank carrier, each canonical handle selects a strictly positive source payload atom. That positive-source-charge fact is reflected by construction while the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison remain canonical. The first-route classifier cannot return charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The six remaining semantic Boolean payload fields, finite rank map, before/after residual ranks, grouped family, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. Strictly positive source mass is not the full external charge-surplus, budget, replacement, or selector-compatibility semantics. The six remaining routes still lack complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, derive those six fields from a terminal candidate, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (19)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_valid_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_failureAt_charge_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_failureAt_rank_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_firstRoute_ne_some_charge
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_failureAt_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedChargeExactRouteRankDescent_firstRoute_eq_some_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.rankDescent_of_withComputedChargeExactRouteRankDescent_check
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorCanonicalPositiveCharge
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedChargeExactRouteRankDescent_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedChargeExactRouteRankDescent_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedChargeExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedChargeExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedChargeExactRouteRankDescent_firstRoute_descent
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorChargeExactRouteRankDescentFaithfulness_preserves
PNP.DirectWire.TerminalBN6PacketConclusion.existsChargeReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_charge_reflected_hb_first_route_failure

Canonical Packet colour-route reflection

For every arbitrary finite grouped BN6 family and selector-rank carrier, each canonical handle has a grouped footprint proved to lie in the family carrier and to have selector-relevant size. That internal grouped-footprint colour check is computed by construction while positive charge, the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison remain canonical. The first-route classifier cannot return colour, charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The internal colour check proves only canonical grouped-footprint eligibility: selector-relevant size with carrier-sublist membership retained as a separate theorem. It is not the full external manuscript colour equivalence. The five remaining semantic Boolean payload fields, finite rank map, before/after residual ranks, grouped family, realizer claims, HN/BUD activity, dependency rows, and finite-to-exact rank map remain explicit inputs. The five remaining routes still lack complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, derive those five fields from a terminal candidate, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (22)

PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_valid_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_failureAt_colour_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_failureAt_charge_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_failureAt_rank_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_firstRoute_ne_some_colour
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_firstRoute_ne_some_charge
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_failureAt_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.withComputedColourChargeExactRouteRankDescent_firstRoute_eq_some_descent_iff
PNP.DirectWire.TerminalPacketSelectorFaithfulnessPayload.rankDescent_of_withComputedColourChargeExactRouteRankDescent_check
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorCanonicalColourEligibility
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedColourChargeExactRouteRankDescent_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedColourChargeExactRouteRankDescent_firstRoute_ne_some_colour
PNP.DirectWire.TerminalBN6GroupedFamily.computedColourChargeExactRouteRankDescent_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedColourChargeExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedColourChargeExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedColourChargeExactRouteRankDescent_firstRoute_descent
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorColourChargeExactRouteRankDescentFaithfulness_preserves
PNP.DirectWire.TerminalBN6PacketConclusion.existsColourReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_colour_reflected_hb_first_route_failure

Canonical Packet typed-frontier route reflection

For every arbitrary finite grouped BN6 family, selector-rank carrier, and typed frontier-signature domain with decidable equality, the canonical payload computes frontier acceptance from exact equality of the supplied source and selector signatures while retaining grouped colour, positive charge, the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison. A frontier first route is exactly typed signature inequality; equal signatures exclude it. The first-route classifier also cannot return colour, charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The source and selector frontier signatures remain explicit inputs: this milestone does not construct the supplied signatures from terminal data, bind them to a BN5 coordinate, or prove the manuscript's full frontier-faithful comparison. Obligation, activation, direction, and budget remain supplied Boolean fields. Those four remaining routes still lack complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (23)

PNP.DirectWire.TerminalPacketSelectorTypedFrontierPayload.frontierCheck_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorTypedFrontierPayload.frontierCheck_eq_false_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_fields
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_valid_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_failureAt_colour_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_failureAt_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_failureAt_charge_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_failureAt_rank_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedTypedFrontierColourChargeExactRouteRankDescent_failureAt_descent_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedTypedFrontierColourChargeExactRouteRankDescent_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedTypedFrontierColourChargeExactRouteRankDescent_eq_some_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedTypedFrontierColourChargeExactRouteRankDescent_ne_some_frontier_of_eq
PNP.DirectWire.TerminalBN6GroupedFamily.computedTypedFrontierColourChargeExactRouteRankDescent_firstRoute_ne_some_colour
PNP.DirectWire.TerminalBN6GroupedFamily.computedTypedFrontierColourChargeExactRouteRankDescent_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedTypedFrontierColourChargeExactRouteRankDescent_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedTypedFrontierColourChargeExactRouteRankDescent_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedTypedFrontierColourChargeExactRouteRankDescent_firstRoute_descent
PNP.DirectWire.TerminalBN6GroupedFamily.rankDescent_of_packetSelectorPayloadFaithfulWithComputedTypedFrontierColourChargeExactRouteRankDescent
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorTypedFrontierColourChargeExactRouteRankDescentFaithfulness_preserves
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorTypedFrontierColourChargeExactRouteRankDescentFaithfulness_faithful
PNP.DirectWire.TerminalBN6PacketConclusion.existsTypedFrontierReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_typed_frontier_reflected_hb_first_route_failure

BN5-bound Packet frontier and obligation route reflection

For every arbitrary finite grouped BN6 family, selector-rank carrier, and typed terminal BN5 coordinate, the canonical payload computes frontier and obligation acceptance from exact equality of the corresponding source and selector BN5 fields while retaining grouped colour, positive charge, the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison. A frontier first route is exactly frontier inequality; an obligation first route is prior frontier equality together with exact obligation inequality. The first-route classifier also cannot return colour, charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The source and selector terminal BN5 coordinates remain explicit inputs: this milestone does not construct those coordinates from terminal data or prove the manuscript's complete BN5 or Packet adequacy bridge. Activation, direction, and budget remain supplied Boolean fields. Those three remaining routes still lack complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (26)

PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.frontierCheck_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.frontierCheck_eq_false_iff
PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.obligationCheck_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.obligationCheck_eq_false_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_fields
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_valid_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_colour_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_charge_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_rank_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationRoutes_failureAt_descent_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationRoutes_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationRoutes_eq_some_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationRoutes_eq_some_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationRoutes_firstRoute_ne_some_colour
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationRoutes_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationRoutes_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationRoutes_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedBN5FrontierObligationRoutes_firstRoute_descent
PNP.DirectWire.TerminalBN6GroupedFamily.rankDescent_of_packetSelectorPayloadFaithfulWithComputedBN5FrontierObligationRoutes
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationFaithfulness_preserves
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationFaithfulness_faithful
PNP.DirectWire.TerminalBN6PacketConclusion.existsBN5FrontierObligationReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_bn5_frontier_obligation_reflected_hb_first_route_failure

BN4 activation-exact Packet route reflection

For every arbitrary finite grouped BN6 family, selector-rank carrier, and typed terminal BN5 coordinate with decidable equality of activation atoms, the canonical payload computes frontier and obligation acceptance from the corresponding BN5 fields and activation acceptance from equality of the nested BN4 activation atoms while retaining grouped colour, positive charge, the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison. Activation-atom equality is equivalent to equality of the canonical BN4 activation predicates on every cut. An activation first route is prior frontier and obligation equality together with exact activation-atom inequality. The first-route classifier also cannot return colour, charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The source and selector terminal BN5 coordinates remain explicit inputs: this milestone does not construct those coordinates from terminal data or prove the manuscript's complete BN4, BN5, or Packet adequacy bridge. Direction and budget remain supplied Boolean fields. Those two remaining routes still lack complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (28)

PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.activationCheck_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.activationCheck_eq_false_iff
PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.activationCheck_eq_true_iff_activation
PNP.DirectWire.TerminalPacketSelectorBN5ObligationPayload.activationCheck_eq_false_iff_not_activation
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_fields
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_valid_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_colour_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_charge_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_activation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_rank_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationRoutes_failureAt_descent_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationRoutes_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationRoutes_eq_some_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationRoutes_eq_some_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationRoutes_eq_some_activation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationRoutes_firstRoute_ne_some_colour
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationRoutes_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationRoutes_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationRoutes_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedBN5FrontierObligationActivationRoutes_firstRoute_descent
PNP.DirectWire.TerminalBN6GroupedFamily.rankDescent_of_packetSelectorPayloadFaithfulWithComputedBN5FrontierObligationActivationRoutes
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationFaithfulness_preserves
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationFaithfulness_faithful
PNP.DirectWire.TerminalBN6PacketConclusion.existsBN4ActivationReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_bn4_activation_reflected_hb_first_route_failure

Typed Packet direction-route reflection

For every arbitrary finite grouped BN6 family, selector-rank carrier, and domain of typed direction values with decidable equality, the canonical payload computes direction acceptance from exact source and selector direction equality while retaining computed BN5 frontier, obligation, and BN4 activation acceptance, grouped colour, positive charge, the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison. A direction first route is prior frontier, obligation, and activation equality together with exact typed-direction inequality. The first-route classifier also cannot return colour, charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The source and selector direction values remain explicit inputs: this milestone does not construct those direction values from terminal data or prove the manuscript's complete Dir(u) or Packet adequacy bridge. Budget is the sole remaining supplied Boolean field. That sole remaining route still lacks complete external semantics and global integration. The result does not construct the grouped family or rank map from terminal data, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (28)

PNP.DirectWire.TerminalPacketSelectorBN5DirectionPayload.directionCheck_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorBN5DirectionPayload.directionCheck_eq_false_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_fields
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_valid_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_colour_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_charge_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_activation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_direction_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_rank_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionRoutes_failureAt_descent_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionRoutes_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionRoutes_eq_some_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionRoutes_eq_some_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionRoutes_eq_some_activation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionRoutes_eq_some_direction_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionRoutes_firstRoute_ne_some_colour
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionRoutes_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionRoutes_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionRoutes_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedBN5FrontierObligationActivationDirectionRoutes_firstRoute_descent
PNP.DirectWire.TerminalBN6GroupedFamily.rankDescent_of_packetSelectorPayloadFaithfulWithComputedBN5FrontierObligationActivationDirectionRoutes
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationDirectionFaithfulness_preserves
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationDirectionFaithfulness_faithful
PNP.DirectWire.TerminalBN6PacketConclusion.existsDirectionReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_direction_reflected_hb_first_route_failure

Typed Packet budget-route reflection

For every arbitrary finite grouped BN6 family, selector-rank carrier, and domain of typed budget values with decidable equality, the canonical payload computes budget acceptance from exact source and selector budget equality while retaining computed BN5 frontier, obligation, BN4 activation, and typed direction acceptance, grouped colour, positive charge, the internal source route, authoritative handle rank, and exact ten-coordinate descent comparison. A budget first route is prior frontier, obligation, activation, and direction equality together with exact typed-budget inequality. The first-route classifier cannot return colour, charge, rank, or exactRoute; a final descent route proves nondecrease, and the positive Packet/HB endpoint carries exact failure evidence without route-clear or binding premises.

The source and selector budget values remain explicit inputs: this milestone does not construct those budget values from terminal data, prove the manuscript's complete Bud(u) budget-envelope or Packet adequacy bridge, or identify local Packet budget coherence with BudgetResolve or HB budget activity. Computing every local Packet classifier field does not establish that terminal data supplies adequate values or that all routes are globally excluded. The result does not construct the grouped family or rank map from terminal data, prove that a decreasing transition exists, or construct the no-lower ledger. It does not establish full external selector compatibility, complete route silence, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (30)

PNP.DirectWire.TerminalPacketSelectorBN5BudgetPayload.budgetCheck_eq_true_iff
PNP.DirectWire.TerminalPacketSelectorBN5BudgetPayload.budgetCheck_eq_false_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_fields
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_valid_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_colour_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_charge_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_activation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_direction_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_budget_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_rank_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_exactRoute_iff_false
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_failureAt_descent_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_eq_some_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_eq_some_frontier_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_eq_some_obligation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_eq_some_activation_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_eq_some_direction_iff
PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadFirstRouteWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes_eq_some_budget_iff
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionBudgetRoutes_firstRoute_ne_some_colour
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionBudgetRoutes_firstRoute_ne_some_charge
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionBudgetRoutes_firstRoute_ne_some_rank
PNP.DirectWire.TerminalBN6GroupedFamily.computedBN5FrontierObligationActivationDirectionBudgetRoutes_firstRoute_ne_some_exactRoute
PNP.DirectWire.TerminalBN6GroupedFamily.not_rankDescent_of_computedBN5FrontierObligationActivationDirectionBudgetRoutes_firstRoute_descent
PNP.DirectWire.TerminalBN6GroupedFamily.rankDescent_of_packetSelectorPayloadFaithfulWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationDirectionBudgetFaithfulness_preserves
PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationDirectionBudgetFaithfulness_faithful
PNP.DirectWire.TerminalBN6PacketConclusion.existsBudgetReflectedFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_budget_reflected_hb_first_route_failure

Checked Packet budget/HB activity binding

For every arbitrary finite grouped BN6 family, the executable binding checker exhaustively requires each typed source/selector budget mismatch to imply activity of the HB budget node at the table-owned handle rank. When that check and the existing checked well-founded HB no-outcome closure both pass, every canonical handle has equal typed budgets, the Packet first-route classifier excludes the budget route, and the positive Packet endpoint is confined to frontier, obligation, activation, direction, or exact residual nondecrease.

The Packet-to-HB budget binding is still an explicit checked input over a supplied grouped family, rank map, activity environment, and dependency table; this milestone does not construct that binding, the typed budget values, or a manuscript Bud(u) envelope from terminal data. It does not implement BudgetResolve, prove blocker semantic completeness, derive the HB table or its local closure premise from terminal data, or exclude the remaining frontier, obligation, activation, direction, and descent routes. It does not establish full Packet adequacy, unconditional HB.NegativeClosure, positive slack, SaturatePositive, BCELReady, unconditional ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (5)

PNP.DirectWire.TerminalPacketTypedRealizerTable.checkPacketBudgetHBActivityBinding_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerTable.packetBudget_eq_of_checkedHBActivityBinding
PNP.DirectWire.TerminalPacketTypedRealizerTable.packetSelectorBudgetFirstRoute_ne_of_checkedHBActivityBinding
PNP.DirectWire.TerminalBN6PacketConclusion.existsBudgetHBBoundFirstRouteFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_budget_hb_activity_bound_first_route_failure

Checked Packet semantic/HN activity binding

For every arbitrary finite grouped BN6 family, the executable binding checker exhaustively requires any failure of simultaneous frontier, obligation, activation, and direction agreement to imply activity of the HN node at the table-owned handle rank. When that check and the existing checked well-founded HB no-outcome closure both pass, all four typed semantic fields agree. Combined with the separately checked budget/HB binding and executable selector silence, every semantic first route is excluded and the positive Packet endpoint has the sole exact residual-nondecrease route.

The Packet-to-HN semantic binding is still an explicit checked input over a supplied grouped family, typed BN5 coordinates, activation atoms, direction values, rank map, activity environment, and dependency table; this milestone does not construct that binding or those values from terminal data. It does not establish HN blocker semantics, semantic dependency completeness, a decreasing transition, a no-lower contradiction, complete external Packet adequacy, or unconditional HB negative closure. It does not prove ZeroSlack, PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (5)

PNP.DirectWire.TerminalPacketTypedRealizerTable.checkPacketSemanticHNActivityBinding_eq_true_iff
PNP.DirectWire.TerminalPacketTypedRealizerTable.packetSemanticFieldsAgree_of_checkedHNActivityBinding
PNP.DirectWire.TerminalPacketTypedRealizerTable.packetSelectorSemanticFirstRoutes_ne_of_checkedHNActivityBinding
PNP.DirectWire.TerminalBN6PacketConclusion.existsSemanticHNBudgetBoundDescentFailure_of_selectorSilence
PNP.DirectWire.terminalBN6_packet_semantic_hn_activity_bound_descent_failure

Checked Packet descent no-lower binding

For every arbitrary finite grouped BN6 family and selector-rank carrier, the executable local Packet descent no-lower checker scans every canonical handle and accepts exactly when no fully computed first route is residual nondecrease. Under a supplied positive Packet conclusion, checked semantic/HN and budget/HB bindings, executable selector silence, and checked well-founded HB no-outcome closure, the checker is forced to reject; assuming that same local row accepted yields a contradiction.

This is one checked local Packet no-lower row over a supplied finite grouped family, rank map, residual ranks, typed fields, realizer table, dependency table, and accepted binding, silence, and closure checks. It does not construct those inputs from terminal data or complete the manuscript's no-lower ledger. It does not cover HResolve, BudgetResolve, normalization, named descent routes, saturation, or replay; derive unconditional HB closure; establish complete Packet adequacy or unconditional ZeroSlack; prove PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (4)

PNP.DirectWire.TerminalBN6GroupedFamily.checkPacketDescentNoLower_eq_true_iff
PNP.DirectWire.TerminalBN6PacketConclusion.checkPacketDescentNoLower_eq_false_of_selectorSilence
PNP.DirectWire.TerminalBN6PacketConclusion.false_of_checkedPacketDescentNoLower_and_selectorSilence
PNP.DirectWire.terminalBN6_packet_descent_no_lower_rejected

Checked Packet no-lower ledger

For every supplied arbitrary finite grouped BN6 family, typed realizer table, HB dependency table, finite rank map, and before/after residual ranks, one Boolean recomputes the five executable checks for semantic/HN binding, budget/HB binding, selector silence, HB no-outcome closure, and Packet descent/no-lower. Its reflection theorem characterizes exact acceptance, a positive Packet forces rejection, and an accepted ledger excludes a positive Packet conclusion for those same inputs.

This closes the Packet branch only, not the complete no-lower ledger. The grouped family, BN5 coordinates, activation atoms, direction and budget values, rank map, residual ranks, realizer claims, activity environment, dependency rows, and all terminal data remain supplied. It does not implement HResolve, BudgetResolve, normalization, other named obstructions, saturation, or replay; derive unconditional HB closure; establish unconditional ZeroSlack; prove PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (4)

PNP.DirectWire.TerminalPacketTypedRealizerTable.checkPacketNoLowerLedger_eq_true_iff
PNP.DirectWire.TerminalBN6PacketConclusion.checkPacketNoLowerLedger_eq_false
PNP.DirectWire.TerminalPacketTypedRealizerTable.not_packetConclusion_of_checkedPacketNoLowerLedger
PNP.DirectWire.terminalBN6_packet_no_lower_ledger_excludes_positive_packet

Checked finite HResolve coverage ledger

For every arbitrary finite supplied HResolve candidate family with decidable equality and arbitrary decidable exact, gain, and blocker predicates, Lean computes a fixed-priority exact, gain, blocked, or unresolved route for every candidate, generates a sound and complete route ledger, and checks both duplicate-free enumeration and all-candidate blocked coverage. The checker accepts exactly a NoHereditary sidecar for that supplied family, and acceptance excludes exact and gain routes for every enumerated candidate.

The finite HResolve candidate family and its decidable exact, gain, and blocker predicates remain supplied. This milestone does not construct the governed hereditary universe from terminal data or prove that those predicates implement the manuscript's HN grammar, BWL exactness, H-disjointness, exact-minimum semantics, strict-gain semantics, or blocker dependency semantics. It does not discharge the full historical HResolve theorem, implement BudgetResolve, normalization, the complete no-lower ledger, saturation, or replay; establish unconditional HB closure or ZeroSlack; prove PCCMin, encoded-size or polynomial-runtime bounds, SAT in P; remove a project assumption; or prove P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.terminalHResolveClassify_eq_exact_iff
PNP.DirectWire.terminalHResolveClassify_eq_gain_iff
PNP.DirectWire.terminalHResolveClassify_eq_blocked_iff
PNP.DirectWire.terminalHResolveClassify_eq_unresolved_iff
PNP.DirectWire.TerminalHResolveFamily.routeLedger_sound
PNP.DirectWire.TerminalHResolveFamily.routeLedger_complete
PNP.DirectWire.TerminalHResolveFamily.checkNoHereditarySidecar_eq_true_iff
PNP.DirectWire.TerminalHResolveFamily.not_exact_of_checkedNoHereditarySidecar
PNP.DirectWire.TerminalHResolveFamily.not_gain_of_checkedNoHereditarySidecar
PNP.DirectWire.terminal_hresolve_checked_sidecar_excludes_constructive_routes

Terminal-derived HResolve support resolver

For every finite direct-wire candidate and profile-width model, Lean constructs the complete duplicate-free family of canonical terminal support seeds, saturates each seed in the candidate-derived terminal system, and computes either an exact route with semantic-minimum evidence or a gain route with a strict-equivalent-gain witness.

The reference search is exhaustive over the complete finite terminal support universe and may be exponential in the number of primitive records. This milestone does not implement the manuscript's HN grammar, BWL exactness, H-disjointness, blocker or NoHereditary semantics, polynomial HResolve, BudgetResolve, the complete no-lower ledger, unconditional ZeroSlack, PCCMin, polynomial runtime, SAT in P, or P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.terminalListSubsets_nodup
PNP.DirectWire.terminalHResolveSupportFamily_nodup
PNP.DirectWire.canonicalTerminalSupportSeed_mem_terminalHResolveSupportFamily
PNP.DirectWire.terminalHResolveSupportExact_iff_semanticallyMinimum
PNP.DirectWire.terminalHResolveSupportGain_iff_exists_strictEquivalentGain
PNP.DirectWire.terminalHResolveSupport_exact_or_gain
PNP.DirectWire.terminalHResolveSupportClassify_eq_exact_iff
PNP.DirectWire.terminalHResolveSupportClassify_eq_gain_iff
PNP.DirectWire.terminalHResolveSupportClassify_constructive
PNP.DirectWire.terminal_hresolve_support_resolver_constructive_complete

Terminal budget-envelope resolver

For every finite direct-wire candidate, candidate-derived saturation model, and supplied natural resource caps, Lean scans the canonical terminal support universe, recomputes nonempty gate and interface feasibility plus gate and saturated-record caps, and returns a feasible semantic minimum, a feasible strict equivalent gain, or complete NoBudget exclusion for every canonical seed.

The budget caps remain supplied, and the complete terminal subset scan, candidate-derived saturation, and reference minimization are exhaustive and may be exponential. This milestone does not implement the manuscript's HN/BUD grammar, BWL or budget-envelope dynamic program, blocker dependency semantics, polynomial BudgetResolve, the complete no-lower ledger, unconditional ZeroSlack, PCCMin, polynomial runtime, SAT in P, or P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalSupportBudget.check_eq_true_iff
PNP.DirectWire.findTerminalBudgetFeasibleSupport_sound
PNP.DirectWire.findTerminalBudgetFeasibleSupport_exists_of_seed
PNP.DirectWire.findTerminalBudgetFeasibleSupport_eq_none_iff
PNP.DirectWire.findTerminalBudgetFeasibleSupport_unique
PNP.DirectWire.TerminalBudgetEnvelopeOutcome.sound
PNP.DirectWire.terminal_budget_envelope_resolver_constructive_complete

Terminal budget no-lower ledger

For every finite direct-wire candidate, candidate-derived saturation model, and supplied natural resource caps, Lean classifies every canonical terminal support as exact, strict gain, or NoBudget, materializes the complete route ledger, and proves that accepted exhaustive coverage makes every budget-feasible governed support a semantic minimum while excluding every feasible strict equivalent gain.

The budget caps remain supplied, and complete terminal subset enumeration, candidate-derived saturation, and reference minimization are exhaustive and may be exponential. This closes only the finite terminal-derived budget branch. It does not implement the manuscript's HN/BUD grammar, BWL or budget-envelope dynamic program, blocker dependency semantics, polynomial BudgetResolve, Packet or complete no-lower composition, unconditional ZeroSlack, PCCMin, polynomial runtime, SAT in P, or P = NP.

Reviewed theorem interfaces (8)

PNP.DirectWire.terminalBudgetNoLowerClassify_eq_exact_iff
PNP.DirectWire.terminalBudgetNoLowerClassify_eq_gain_iff
PNP.DirectWire.terminalBudgetNoLowerClassify_eq_noBudget_iff
PNP.DirectWire.terminalBudgetNoLowerRouteLedger_complete
PNP.DirectWire.terminalBudgetNoLowerRouteLedger_sound
PNP.DirectWire.checkTerminalBudgetNoLowerLedger_eq_true_iff
PNP.DirectWire.TerminalBudgetNoLowerLedgerAccepted.iff_all_feasible_minimum
PNP.DirectWire.terminal_budget_no_lower_ledger_excludes_feasible_gain

Terminal Packet-budget no-lower composition

For every finite direct-wire candidate, candidate-derived saturation model, supplied caps, and supplied Packet family and tables over that same direct-wire candidate, one Boolean recomputes both finite ledgers. Acceptance makes every governed budget-feasible canonical support a semantic minimum, excludes every feasible strict equivalent gain, and excludes a positive Packet conclusion.

The caps, Packet family, typed payloads, ranks, realizer claims, activity environment, and dependency tables remain supplied. This is a finite two-branch composition, not the complete no-lower ledger. It does not construct Packet data from terminal data, implement HN/BUD grammar, polynomial HResolve or BudgetResolve, cover normalization, remaining named routes, saturation, or replay, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (4)

PNP.DirectWire.checkTerminalPacketBudgetNoLowerComposition_eq_true_iff
PNP.DirectWire.terminal_packet_budget_no_lower_composition_excludes_gain_and_packet
PNP.DirectWire.checkTerminalPacketBudgetNoLowerComposition_eq_false_of_feasible_gain
PNP.DirectWire.TerminalBN6PacketConclusion.checkTerminalPacketBudgetNoLowerComposition_eq_false

Terminal HResolve maximal H-disjoint family

For every arbitrary finite duplicate-free family of supplied hereditary footprints over eight decidable coordinate domains, Lean deterministically constructs a governed duplicate-free maximal pairwise H-disjoint family. Every rejected governed candidate has a selected blocker carrying the exact first support, frontier, origin, kernel, obligation, prefix-tail, charge, or interface interference route.

The hereditary footprints remain supplied inputs. This milestone does not derive them from a terminal candidate, formalize the HN pair/tripod/spine/non-flat grammar, prove BWL exactness or ParseOrExit, establish leaf tightness or solve a leaf, construct the full H0-H4 NoHereditary sidecar, connect blockers to HB ranks, implement full HResolve, complete the no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (10)

PNP.DirectWire.checkTerminalHCoordinateDisjoint_eq_true_iff
PNP.DirectWire.terminalHCoordinateDisjoint_symm
PNP.DirectWire.TerminalHereditaryFootprint.checkHDisjoint_eq_true_iff
PNP.DirectWire.TerminalHereditaryFootprint.hDisjoint_symm
PNP.DirectWire.TerminalHereditaryFootprint.firstInterference?_eq_none_iff_hDisjoint
PNP.DirectWire.terminalHResolveGreedyHDisjointFamily_subset
PNP.DirectWire.terminalHResolveGreedyHDisjointFamily_nodup
PNP.DirectWire.terminalHResolveGreedyHDisjointFamily_pairwise
PNP.DirectWire.terminalHResolveGreedyHDisjointFamily_maximal
PNP.DirectWire.terminal_hresolve_maximal_hdisjoint_family_complete

Terminal HN BWL certified-path minimum

For every nonempty finite supplied family of certified hereditary paths, Lean computes the exact four-coordinate lexicographic minimum by realized cost, residual rank, frontier deviation, and direct-wire code. The selected member preserves semantic fidelity, frontier fidelity, nonempty block coverage, and one of four HN shapes; an explicit completeness premise extends its lower bound to every path in the supplied governed predicate.

The certified path family, governed predicate, and family completeness remain supplied inputs. This milestone does not derive accepted paths from terminal data, prove shape-grammar soundness or completeness, LN confluence, ParseOrExit, independent leaf tightness, or the full BWL theorem, solve a leaf, construct the H0-H4 NoHereditary sidecar, implement full HResolve, complete the no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial generation and runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (15)

PNP.DirectWire.checkTerminalNatVectorLexLE_eq_true_iff
PNP.DirectWire.terminalNatVectorLexLE_total_of_length_eq
PNP.DirectWire.terminalNatVectorLexLE_refl
PNP.DirectWire.terminalNatVectorLexLE_trans
PNP.DirectWire.TerminalHNBWLObjective.checkLexLE_eq_true_iff
PNP.DirectWire.TerminalHNBWLObjective.lexLE_refl
PNP.DirectWire.TerminalHNBWLObjective.lexLE_total
PNP.DirectWire.TerminalHNBWLObjective.lexLE_trans
PNP.DirectWire.terminalHNBWLChoose_eq_left_or_right
PNP.DirectWire.terminalHNBWLChoose_lexLE_left
PNP.DirectWire.terminalHNBWLChoose_lexLE_right
PNP.DirectWire.terminalHNBWLMinimum?_eq_none_iff
PNP.DirectWire.terminalHNBWLMinimum?_sound
PNP.DirectWire.terminalHNBWLMinimum?_exists_of_ne_nil
PNP.DirectWire.terminal_hn_bwl_certified_path_minimum_complete

Terminal HResolve certified-path family

For every duplicate-free finite supplied family of proof-bearing hereditary candidates, Lean constructs a duplicate-free maximal pairwise H-disjoint selected family. Every selected candidate has an exact four-coordinate certified-path minimum preserving semantic, frontier, block, shape, and footprint-coherence evidence; every rejected candidate has a selected blocker carrying the exact first interference route.

The candidates, certified paths, hereditary footprints, governed predicates, family-completeness proofs, and path-to-footprint coherence proofs remain supplied inputs. This milestone does not derive them from terminal data, prove HN grammar soundness or completeness, LN confluence, ParseOrExit, independent leaf tightness, or the H0-H4 NoHereditary sidecar, connect blockers to HB rank semantics, implement full or polynomial HResolve, complete the no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.DirectWire.TerminalHResolveCertifiedPathCandidate.checkHDisjoint_eq_true_iff
PNP.DirectWire.TerminalHResolveCertifiedPathCandidate.minimum?_complete
PNP.DirectWire.terminalHResolveGreedyCertifiedPathFamily_subset
PNP.DirectWire.terminalHResolveGreedyCertifiedPathFamily_nodup
PNP.DirectWire.terminalHResolveGreedyCertifiedPathFamily_pairwise
PNP.DirectWire.terminalHResolveGreedyCertifiedPathFamily_maximal
PNP.DirectWire.terminal_hresolve_certified_path_family_complete

Proof-bearing HResolve ZeroSlack sidecar

For every arbitrary finite supplied governed HResolve family, the report-facing ZeroSlack boundary now consumes a checked proof-bearing NoHereditary sidecar: duplicate-free total blocked coverage is recomputed, exact and gain routes are excluded for every listed candidate, and those route predicates are separately bound to semantic minimum and strict equivalent gain propositions.

The governed candidate family, implementation map, exact, gain, and blocked predicates, their decidability, and blocker semantics remain supplied inputs. This milestone does not derive hereditary candidates from terminal data, prove HN grammar soundness or completeness, BWL, ParseOrExit, leaf tightness, H0-H4 blocker semantics, full or polynomial HResolve, complete the no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.HResolveSidecarCertificate.accepted
PNP.HResolveSidecarCertificate.not_exact
PNP.HResolveSidecarCertificate.not_gain
PNP.HResolveSidecarCertificate.blocked_of_mem
PNP.HResolveSidecarCertificate.exact_route_sound
PNP.HResolveSidecarCertificate.gain_route_sound
PNP.hresolve_zeroslack_sidecar_checked_complete

Proof-bearing Budget ZeroSlack sidecar

For arbitrary finite direct-wire candidates and supplied natural caps, the report-facing ZeroSlack boundary now consumes a checked proof-bearing NoBudget sidecar. A failed exhaustive search over the complete canonical terminal support universe excludes every budget-feasible support, while separately checked exact and gain routes entail semantic minimum and strict equivalent gain propositions.

The natural terminal support caps are supplied inputs, and exhaustive enumeration, saturation, and reference minimization may be exponential. This milestone does not formalize the B0-B4 Budget grammar or blocker semantics, implement full or polynomial BudgetResolve, prove a complete no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (5)

PNP.BudgetSidecarCertificate.excluded
PNP.BudgetSidecarCertificate.no_feasible_support
PNP.BudgetSidecarCertificate.exact_route_sound
PNP.BudgetSidecarCertificate.gain_route_sound
PNP.budget_zeroslack_sidecar_checked_complete

Proof-bearing Selector/HB ZeroSlack sidecar

For arbitrary finite supplied grouped BN6, typed-realizer, and exact-rank HB dependency tables, the report-facing ZeroSlack boundary now consumes one checked proof-bearing Selector/HB sidecar. The exact executable checks yield all-canonical-selector nonfaithfulness, exact typed-bottom rows, complete no-outcome closure, all-node HN/BUD inactivity, and a well-founded dependency relation.

The grouped BN6 family, typed-realizer and dependency tables, environment, realizer claims, activity bits, dependency rows, and finite rank map remain supplied inputs. This milestone does not derive them from terminal data, prove selector faithfulness or compatibility, establish HN/BUD blocker semantics or semantic dependency completeness, connect selector silence to the BCEL contradiction, complete the no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.SelectorHBZeroSlackSidecarCertificate.accepted
PNP.SelectorHBZeroSlackSidecarCertificate.no_faithful
PNP.SelectorHBZeroSlackSidecarCertificate.claim_eq_bot
PNP.SelectorHBZeroSlackSidecarCertificate.hb_closure_valid
PNP.SelectorHBZeroSlackSidecarCertificate.no_hb_active
PNP.SelectorHBZeroSlackSidecarCertificate.depends_wellFounded
PNP.selector_hb_zeroslack_sidecar_checked_complete

Proof-bearing Packet/budget no-lower ZeroSlack sidecar

For arbitrary finite supplied same-candidate Packet and terminal-budget data, the report-facing ZeroSlack boundary now consumes one checked proof-bearing Packet/budget no-lower sidecar. Its exact executable composition equation proves every governed budget-feasible support semantically minimum, excludes every such strict equivalent gain, and excludes a positive Packet conclusion for the supplied family.

The caps, candidate-derived model, grouped BN6 family, typed payloads, finite ranks, realizer claims, activity environment, dependency rows, and rank maps remain supplied inputs. This finite two-branch sidecar does not complete no-lower ledger coverage for the manuscript, derive its inputs from terminal data, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (5)

PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.accepted
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.all_feasible_support_minimum
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.no_feasible_gain
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.no_positive_packet
PNP.packet_budget_no_lower_zeroslack_sidecar_checked_complete

Proof-bearing BCEL/Packet no-lower ZeroSlack sidecar

For every arbitrary finite supplied M180 Packet/budget no-lower certificate whose grouped carrier passes the exact at-least-two-anchor check, the report-facing ZeroSlack boundary now consumes one checked proof-bearing BCEL/Packet contradiction sidecar. BCEL constant activation would construct a positive BN6 Packet, contradicting the accepted same-family no-lower exclusion.

The grouped BN6 family and all terminal, budget, Packet, realizer, dependency, and rank inputs inherited from M180 remain supplied. This milestone does not derive the family or BCEL constant activation from positive residual slack, construct BCELReady from a terminal candidate, complete the manuscript no-lower ledger, establish unconditional ZeroSlack, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (4)

PNP.BCELContradictionCertificate.carrier_at_least_two
PNP.BCELContradictionCertificate.no_positive_packet
PNP.BCELContradictionCertificate.not_constant_activation
PNP.bcel_packet_no_lower_zeroslack_sidecar_checked_complete

Same-family Selector/HB, Packet, and BCEL ZeroSlack coherence

For every arbitrary finite accepted M180 certificate and its dependent M181 boundary, the report-facing ZeroSlack layer now derives same-family Selector/HB, Packet, and BCEL evidence from the exact grouped family, computed realizer table, and dependency table. Definitional identities prevent a detached Selector/HB certificate from being paired with the checked Packet and BCEL exclusions.

The grouped family and all terminal, budget, Packet, realizer, dependency, rank, and BCEL data remain supplied inputs. This milestone does not derive those inputs or BCEL constant activation from positive residual slack, establish unconditional ZeroSlack, complete the manuscript no-lower ledger, prove PCCMin or polynomial runtime, put SAT in P, remove a project assumption, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.selector_silence_accepted
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.hb_closure_accepted
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.selectorHB_family
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.selectorHB_realizerTable
PNP.PacketBudgetNoLowerZeroSlackSidecarCertificate.selectorHB_dependencyTable
PNP.packet_selector_hb_bcel_coherent_checked_complete
PNP.zeroslack_packet_selector_hb_bcel_coherent_checked_complete

Global locked-NAND construction and threshold

A uniform encoded polynomial-time SAT instance builder and the report-level locked-NAND threshold theorem linked to that builder.

This closes the uniform all-bitstring CNFSAT-to-concrete-locked-threshold builder in the finite charged-pipeline model. The downstream M186 compatibility milestone now activates that exact reduction in the report-facing bridge. Neither milestone puts the concrete locked threshold language in P, discharges residual-band minimization, ZeroSlack or PCCMin, proves concrete CNFSAT NP-hardness, or proves P = NP.

Reviewed theorem interfaces (1)

PNP.Main.locked_nand_threshold

Concrete report-facing locked-NAND compatibility

The report-facing language, decider, verifier, reduction, P/NP class, and P-equals-NP interfaces are exact compatibility names for the concrete finite-pipeline model. SAT and LockedNANDThreshold are definitionally the concrete CNFSAT and EncodedLockedNANDThreshold languages, and the active bridge reuses the checked all-bitstring reduction without a caller-supplied trust field.

This removes the duplicate locked-NAND project axiom and caller-supplied reduction edge, but it does not put the concrete locked target in P, construct the residual-band reduction, prove PCCMin or ZeroSlack soundness, prove concrete CNFSAT NP-hardness, create the eligible root theorem, open any global gate, or prove P = NP.

Reviewed theorem interfaces (6)

PNP.concrete_legacy_locked_nand_compatibility_checked_complete
PNP.report_locked_nand_eq_concrete_threshold
PNP.report_sat_eq_concrete_cnfsat
PNP.sat_in_np_witness_model
PNP.sat_in_p_from_locked_nand_in_p
PNP.sat_reduces_to_locked_nand_checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-186: formal artefact coverage becomes 162 of 164; risk-weighted estimate is 32%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Concrete report-facing residual-band compatibility

The report-facing residual-band endpoint is the concrete fail-closed direct-wire candidate/threshold language. Every intrinsically typed finite candidate has exact reference-minimum semantics after encoding, and the active locked-to-residual compatibility edge is the compiled identity polynomial reduction rather than caller-supplied trust.

This removes the residual-band language axiom and caller-supplied locked-to-residual reduction edge by identifying both endpoints with one concrete encoded exact-minimum threshold predicate. It does not construct an executable PCCMin algorithm, prove that exhaustive reference minimization is polynomial, establish residual-band promise bounds, prove unconditional ZeroSlack, put SAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (7)

PNP.Concrete.LockedNAND.encodedDirectWireMinimumThreshold_ofCandidate_iff
PNP.residual_band_encoded_candidate_iff_reference_minimum
PNP.locked_nand_reduces_to_residual_band_checked
PNP.locked_nand_in_p_from_residual_band_in_p
PNP.report_residual_band_eq_concrete_minimum_threshold
PNP.report_locked_nand_eq_residual_band
PNP.concrete_residual_band_compatibility_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-24-187: formal artefact coverage becomes 163 of 165; risk-weighted estimate is 33%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Typed PCCPack generation and structural reflection

For every explicit proof-bearing PCCMin loop certificate, transparent Lean generation preserves that exact certificate, the canonical generated identifier is accepted by structural computation, every mismatched identifier is rejected, and the active bridge projects the supplied certificate directly rather than relying on package or checker axioms.

This removes the two opaque package/checker declarations and the caller-supplied reflection field from the active Lean bridge. It does not construct a PCCMinLoopCertificate, verify historical JavaScript package bytes, prove the semantic string fields, implement PCCMin, establish unconditional ZeroSlack or polynomial bounds, prove concrete SAT hardness, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.typed_pccpack_reflection_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-24-188: formal artefact coverage becomes 164 of 166; risk-weighted estimate is 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Proof-bearing PCCMin total-oracle loop

For every finite direct-wire implementation and every explicit proof-bearing total oracle, transparent well-founded recursion follows strict equivalent gains until exact-minimum or ZeroSlack evidence is returned, preserves semantics, returns a global minimum with zero residual slack, and bounds strict-gain iterations by the starting residual slack.

The total oracle remains an explicit proof-bearing argument, and the regression fixture uses exhaustive reference minimization. This milestone does not construct an executable PCCMin oracle, derive terminal families or routes, establish unconditional ZeroSlack, encode the loop as a raw machine, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_total_oracle_loop_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-24-189: formal artefact coverage becomes 165 of 167; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Proof-bearing PCCMin normalization/oracle composition

For every finite direct-wire implementation, explicit proof-bearing total normalizer, and explicit proof-bearing total oracle, non-increasing semantic normalization lifts later oracle gains to strict gains from the original implementation, transports exact-minimum and ZeroSlack endpoints, and reuses the checked well-founded loop with its exact result and gain-iteration bound.

The total normalizer and total oracle remain explicit proof-bearing arguments, and the regression fixtures use exhaustive reference minimization. This milestone does not construct either executable stage, derive terminal families or routes, establish unconditional ZeroSlack, encode the stages as raw machines, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_normalize_oracle_loop_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-190: formal artefact coverage becomes 166 of 168; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Rank-ordered proof-bearing PCCOracle orchestration

For every finite direct-wire implementation, explicit proof-bearing normalizer, and explicit rank-ordered oracle builder, HResolve precedes BudgetResolve, every selector in every canonical finite rank row is scanned, gains return immediately, complete typed silence is required before ZeroSlack, and the resulting total oracle reuses the checked well-founded exact loop and gain-iteration bound.

The normalizer, HResolve and BudgetResolve algorithms, rank rows, selector universe, realizer, typed blocker semantics, and final ZeroSlack closure remain explicit proof-bearing inputs. The exhaustive reference fixture is not polynomial. This milestone does not construct executable PCCMin, derive terminal objects, establish unconditional ZeroSlack, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_normalize_rank_ordered_oracle_loop_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-191: formal artefact coverage becomes 167 of 169; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Checked Packet-backed rank-selector construction

For every finite direct-wire implementation and supplied checked Packet table, every canonical handle claim is validated as a data-only unit-charge gain or typed HN, budget, or lower-seed blocker; exact rank rows are derived by filtering the exhaustive canonical handle list with the table-owned rank map; and the resulting plan reuses the M191 rank-ordered oracle and checked well-founded loop.

The grouped terminal family, rank assignment, data-only claim table, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and complete-silence-to-ZeroSlack implication remain explicit supplied inputs. The exhaustive reference fixture is not polynomial. This milestone does not derive terminal objects or claims from an arbitrary implementation, construct executable PCCMin, establish unconditional ZeroSlack, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_normalize_checked_packet_rank_ordered_oracle_loop_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-192: formal artefact coverage becomes 168 of 170; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Checked Packet/HB conditional ZeroSlack bridge

For every finite direct-wire implementation and supplied checked Packet/HB data, complete checked rank-row silence and checked HB no-outcome closure derive that every canonical handle is nonfaithful; one explicit positive-slack-to-faithful-selector bridge then yields conditional ZeroSlack, and the resulting adapter reuses the M192 selector construction and checked well-founded loop.

The positive-residual-slack-to-faithful-selector implication, grouped terminal family, rank assignment, data-only claim table, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and encoded-size bounds remain explicit supplied inputs. The exhaustive reference fixture is not polynomial. This milestone does not derive terminal objects or the positive-slack bridge from an arbitrary implementation, construct executable polynomial PCCMin, establish unconditional ZeroSlack, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_normalize_checked_packet_hb_zeroslack_loop_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-193: formal artefact coverage becomes 169 of 171; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

BN6 computed-faithfulness checked Packet/HB ZeroSlack bridge

For every finite direct-wire implementation and supplied checked Packet/BN6/HB data, positive residual slack reaches a general BN6 Packet through the explicit constant-activation boundary; route-clear payload checks construct a faithful selector in the canonicalized table; checked rank-row silence and checked HB closure then derive conditional ZeroSlack; and the resulting adapter reuses the M193 contradiction and checked well-founded loop.

The positive-residual-slack-to-constant-activation implication, grouped terminal family, carrier lower bound, rank assignment, route-clear payload checks, data-only claim table, HB dependency table, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and encoded-size bounds remain explicit supplied inputs. The exhaustive reference fixture is not polynomial. This milestone does not derive terminal objects or constant activation from an arbitrary implementation, prove manuscript-wide SaturatePositive or BCELReady, construct executable polynomial PCCMin, establish unconditional ZeroSlack, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_normalize_checked_packet_bn6_hb_zeroslack_loop_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-194: formal artefact coverage becomes 170 of 172; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Same-candidate BCEL activation-route classifier and conditional ZeroSlack bridge

For every finite same-candidate checked BCEL nucleus and supplied grouped BN6 Packet family, a total classifier compares the exact carrier, cut value, and every canonical nonempty proper-cut activation weight. It returns one proof-bearing carrier, cut-value, or activation mismatch route, or derives coherent constant activation, identifies it with the BCEL projection excess, and reuses M194 to derive conditional ZeroSlack under checked selector silence.

The terminal problem, positive premise, checked finite BCEL-ready certificate, grouped Packet family, payloads, claim table, rank map, route-clear equation, dependency table, checked HB closure, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and encoded-size bounds remain explicit supplied inputs. The proper-cut classifier enumerates a finite powerset and is not proved polynomial. Its mismatch results are typed diagnostic routes, not constructed gains or globally decreasing transitions. This milestone does not derive the family or supporting data from every source input, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_bn6_bcel_activation_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-26-195: formal artefact coverage becomes 171 of 173; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

BCEL-derived BN6 family skeleton and conditional ZeroSlack bridge

For every finite same-candidate checked BCEL nucleus and supplied grouped-cell ledger, the BN6 family carrier, duplicate-freedom, cut value, and cut-value positivity are constructed from the computed nucleus. M195's carrier and cut-value mismatch routes are impossible by construction; checked selector silence yields either an exact proper-cut activation mismatch or conditional ZeroSlack.

The terminal problem, positive premise, checked finite BCEL-ready certificate, grouped cells and payloads, exact grouping proofs, claim table, rank map, route-clear equation, dependency table, checked HB closure, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and encoded-size bounds remain explicit supplied inputs. The inherited proper-cut classifier enumerates a finite powerset and is not proved polynomial. Its remaining activation mismatch is a typed diagnostic route, not a constructed gain or globally decreasing transition. This milestone does not derive the grouped cells or supporting data from every source input, complete PkgC/BN3--BN6 integration, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_bn6_bcel_derived_family_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-26-196: formal artefact coverage becomes 172 of 174; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Canonical BN6 positive-cell grouping and conditional ZeroSlack bridge

For every finite same-candidate checked BCEL nucleus and supplied raw positive support/payload ledger, supports are normalized inside the computed carrier, singleton consumer systems are constructed, duplicate footprints are coalesced, and every positive payload atom is preserved. The resulting canonical grouped family reuses M196, so checked selector silence yields either an exact proper-cut activation mismatch or conditional ZeroSlack.

The terminal problem, positive premise, checked finite BCEL-ready certificate, raw positive supports and payload atoms, claim table, rank map, route-clear equation, dependency table, checked HB closure, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and encoded-size bounds remain explicit supplied inputs. The inherited proper-cut classifier enumerates a finite powerset and is not proved polynomial. Its remaining activation mismatch is a typed diagnostic route, not a constructed gain or globally decreasing transition. This milestone does not derive the raw cells from BN3, BN4, BN5, PkgC, or every terminal input, complete PkgC/BN3--BN6 integration, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_grouping_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-26-197: formal artefact coverage becomes 173 of 175; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Canonical BN6 raw cut-ledger conservation and conditional ZeroSlack bridge

For every finite same-candidate checked BCEL nucleus, supplied raw positive-cell ledger, and cut, canonical coalescing preserves the exact direct crossing-mass sum. The M197 grouped-family activation mismatch is therefore exposed directly against the raw ledger, so checked selector silence yields either an exact proper-cut raw activation mismatch or conditional ZeroSlack.

The terminal problem, positive premise, checked finite BCEL-ready certificate, raw positive cells and payloads, claim table, rank map, route-clear equation, dependency table, checked HB closure, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and encoded-size bounds remain explicit supplied inputs. The inherited proper-cut classifier enumerates a finite powerset and is not proved polynomial. The direct raw-ledger mismatch is a typed diagnostic route, not a constructed gain or globally decreasing transition, and the constant-activation equation is not derived. This milestone does not derive the raw cells from BN3, BN4, BN5, PkgC, or every terminal input, complete PkgC/BN3--BN6 integration, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_cut_ledger_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-198: formal artefact coverage becomes 174 of 176; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Canonical sparse V53 constant-cut basis and checked conditional ZeroSlack bridge

For every finite sparse V53 hypergraph with at least two anchors, a shape-specific basis is equivalent to the complete constant equation on every nonempty proper cut. A total classifier checks the two-anchor full weight, three singleton cuts, or four-plus full-span support and weight without enumerating carrier subsets. At the same-candidate checked BN6/BCEL/HB boundary, accepted evidence derives constant activation and conditional ZeroSlack under checked selector silence, while rejection preserves one typed structural route and every inspected cut retains M198's exact raw-ledger reflection.

The terminal problem, positive premise, checked finite BCEL-ready certificate, raw positive cells and payloads, claim table, rank map, route-clear equation, dependency table, checked HB closure, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and complete encoded-size bounds remain explicit supplied inputs. A rejected basis is a typed structural diagnostic route, not a constructed gain or globally decreasing transition. Removing this endpoint's proper-cut powerset scan does not prove that upstream terminal or BCEL construction avoids subset enumeration or that the complete construction is polynomial. This milestone does not derive the raw cells from BN3, BN4, BN5, PkgC, or every terminal input, force basis acceptance or route every rejection to a gain, complete PkgC/BN3--BN6 integration, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_cut_basis_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-199: formal artefact coverage becomes 175 of 177; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Sparse V53 proper-cut activation route and checked conditional ZeroSlack bridge

For every finite sparse positive V53 hypergraph with at least two anchors, the duplicate-free singleton and order-preserving pair proper cuts form a quadratic-size test family equivalent to the complete constant equation on every nonempty proper cut. A total first-mismatch classifier either derives that equation or retains one exact small proper-cut mismatch. At the same-candidate checked BN6/BCEL/HB boundary, a mismatch is reflected through the direct raw positive-cell activation ledger, while coherence yields conditional ZeroSlack under checked selector silence.

The terminal problem, positive premise, checked finite BCEL-ready certificate, raw positive cells and payloads, claim table, rank map, route-clear equation, dependency table, checked HB closure, HResolve and BudgetResolve algorithms, normalizer, blocker semantics, and complete encoded-input bounds remain explicit supplied inputs. The singleton/pair family has a direct quadratic list-length bound, but this is not a complete polynomial construction or runtime theorem. A returned raw activation mismatch is an exact diagnostic route, not a verified gain or globally decreasing transition. This milestone does not derive the raw cells from BN3, BN4, BN5, PkgC, or every terminal input, map the mismatch into a decreasing route, complete PkgC/BN3--BN6 integration, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_bn6_bcel_sparse_activation_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-200: formal artefact coverage becomes 176 of 178; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

PkgC same-key cancellation or derived BN6 positive cellization

For every finite list of supplied active V54 consumer systems over one common carrier and supplied typed restorer, a total classifier returns the first exact same-key PkgC cancellation realization or proves all systems singletonized. The latter branch derives each raw BN6 positive-cell support and support-size fact from its active consumer data, preserves payload order, and conserves the exact V54 activation weight on every cut.

The terminal problem, source V54 consumer systems, active cuts, positive payload atoms, typed restorer, and all upstream BN3--BN5 construction remain explicit supplied inputs. A returned same-key cancellation is exact proof-bearing PkgC evidence, not a verified global gain or rank-decreasing transition. This milestone does not construct those sources from every valid terminal input, integrate them with the checked BCEL/Packet family, complete PkgC/BN3--BN6, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.terminalPkgC_bn6_positive_cellization_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-201: formal artefact coverage becomes 177 of 179; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-derived PkgC/BN6 sparse BCEL route and checked conditional ZeroSlack

For every arbitrary finite supplied active PkgC source ledger over the exact checked BCEL nucleus, M201's total classifier either retains an exact source-member same-key cancellation or constructs the only raw BN6 positive-cell ledger admitted downstream. That derived ledger enters M200's canonical checked Packet/HB classifier, whose small-cut mismatch is reflected back through all-cut activation conservation to the original PkgC source ledger; the coherent branch yields genuine conditional ZeroSlack under supplied checked selector silence.

The terminal problem, checked finite BCEL-ready certificate, active V54 source systems and cuts, positive payload atoms, typed restorer, realizer table, accepted claims, rank assignment, dependency table, checked HB closure, route-clear result, and selector silence remain explicit supplied inputs. A returned PkgC cancellation or source-ledger activation mismatch is exact proof-bearing evidence, not a verified gain or globally rank-decreasing transition. This milestone does not construct the sources or downstream tables from every valid terminal input, construct upstream BN3--BN5 data, prove complete PkgC/BN3--BN6 route integration, derive blocker semantics or semantic dependency completeness, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_pkgc_bn6_bcel_source_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-202: formal artefact coverage becomes 178 of 180; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed PkgC ambient-BN4 extraction and checked source-route composition

For every arbitrary finite supplied active PkgC source ledger and arbitrary finite ambient BN4 ledger tied to the same checked BCEL nucleus, constructive remove-first recursion preserves multiplicity and ambient order independence while computing the exact remainder, multiset embedding, and complete residual-ledger reduction, or proving that no exact remainder embedding exists. The four-way composition preserves M202's conditional ZeroSlack and source activation mismatch branches.

The terminal problem, checked finite BCEL-ready certificate, active V54 source systems and cuts, positive payload atoms, typed restorer, ambient BN4 ledger, realizer table, accepted claims, rank assignment, dependency table, checked HB closure, route-clear result, and selector silence remain explicit supplied inputs. The computed ambient residual reduction does not prove that its remainder is empty or contradict a surviving residual, and an exact no-embedding result is a compatibility failure rather than a verified gain or globally rank-decreasing transition. This milestone does not construct the ambient ledger, sources, payloads, restorer, or downstream tables from every valid terminal input, construct upstream BN3--BN5 data, prove complete PkgC/BN3--BN6 route integration, derive blocker semantics or semantic dependency completeness, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove encoded-size polynomial construction, runtime, output-size, or certificate-size bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_pkgc_ambient_bn4_extraction_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-203: formal artefact coverage becomes 179 of 181; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

PkgC restoration coverage, exact Hall route, and computed ambient BN4 reduction

For every arbitrary finite supplied consumer system, restoration-coordinate universe and ambient BN4 ledger, the finite exact-coordinate classifier returns singletonization, the first proof-bearing Hall deficit with its qRestorationHall route, or complete coordinate coverage. Coverage constructs one balanced opposite-sign BN4 unit pair for every canonical quotient unit and exact arbitrary-order extraction computes the ambient remainder with complete residual-ledger equality or proves that no exact embedding exists.

The consumer system, finite restoration-coordinate universe, quotient coordinate map, full-restoration coordinate lists, and ambient BN4 ledger remain explicit supplied inputs. Complete coordinate coverage is equality-fibre multiplicity evidence and does not materialize semantic full candidates or prove restoration adequacy. A Hall deficit is an exact local qRestorationHall route, not a verified gain or globally rank-decreasing transition. The computed residual reduction does not prove that the remainder is empty, and no-embedding is a compatibility failure rather than a complete global route. This milestone does not derive the restoration universe or ambient ledger from every valid terminal input, complete PkgC/BN3--BN6 integration, derive blocker semantics or semantic dependency completeness, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove complete encoded-size polynomial bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.terminalPkgC_restorationCoverage_ambientBN4_route_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-204: formal artefact coverage becomes 180 of 182; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Family-level PkgC restoration coverage and exact BN6 ledger cellization

For every arbitrary finite supplied active PkgC source ledger with per-source restoration and ambient BN4 data, the list-order classifier either proves all source systems singletonized and constructs the complete BN6 positive-cell ledger with exact length, payload order and all-cut activation conservation, or retains the first exact source-member Hall deficit, computed ambient reduction, or no-embedding witness.

The active PkgC source cells and cuts, positive payload atoms, per-source restoration-coordinate universes and maps, full-restoration coordinate lists, and ambient BN4 ledgers remain explicit supplied inputs. Complete coordinate coverage does not materialize semantic full candidates or derive restoration adequacy. A Hall deficit is not a verified gain or globally rank-decreasing transition, the computed remainder is not proved empty, and no-embedding is not a complete global route. This milestone does not derive the source ledger or restoration and ambient data from every valid terminal input, complete PkgC/BN3--BN6 integration, derive blocker semantics or semantic dependency completeness, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove complete encoded-size polynomial bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.terminalPkgC_restorationCoverage_bn6_cellization_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-205: formal artefact coverage becomes 181 of 183; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Candidate-bound PkgC restoration coverage and checked BN6/BCEL route

For every arbitrary finite M205 restoration-coverage source ledger tied to one computed BCEL nucleus, the total classifier preserves the first exact Hall deficit, ambient residual reduction, or no-embedding witness. Only the all-singletonized branch constructs the source-derived BN6 ledger and enters the checked sparse BN6/BCEL Packet/HB classifier, yielding conditional ZeroSlack or one exact small-cut mismatch reflected to the original enriched source activation ledger.

The terminal problem, checked BCEL-ready certificate, active PkgC source cells and cuts, restoration-coordinate universes and maps, ambient BN4 ledgers, ranks, claims, dependency table, checked HB closure, route-clear result, and selector silence remain explicit supplied inputs. The candidate binding does not materialize semantically adequate full candidates or derive these objects from every valid terminal input. A Hall deficit is not a verified global gain or rank-decreasing transition, the computed ambient remainder is not proved empty, and ambient incompatibility or source activation mismatch is not a complete global route. This milestone does not finish PkgC/BN3--BN6 integration, derive blocker semantics or semantic dependency completeness, prove manuscript-wide SaturatePositive or BCELReady, establish unconditional ZeroSlack, construct executable polynomial PCCMin, prove complete encoded-size polynomial bounds, put CNFSAT in P, open a global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_pkgc_restoration_coverage_bn6_bcel_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-206: formal artefact coverage becomes 182 of 184; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

PkgC restoration coverage and exact ambient charge-coordinate descent

For every arbitrary finite exact ambient embedding returned by M206, unsigned BN4 charge is computed as the sum of cell masses. Exact permutation decomposes ambient charge into a strictly positive coverage-derived cancellation charge plus remainder charge. The remainder therefore strictly decreases the eighth chargeSize coordinate of the exact ten-coordinate TerminalResidualRank for every fixed surrounding context while preserving the complete canonical residual ledger. All other M206 outcomes remain explicit.

The terminal problem, checked BCEL-ready certificate, active PkgC source cells and cuts, restoration-coordinate universes and maps, ambient BN4 ledgers, semantic full candidates, Packet ranks and claims, dependency table, checked HB closure, route-clear result, and selector silence remain explicit supplied inputs. M207 proves exact charge-coordinate descent only for M206's successful ambient embedding. It does not prove the computed remainder is empty or turn Hall deficits, ambient incompatibility, or activation mismatches into complete global routes. This milestone does not finish terminal-input derivation, complete PkgC/BN3--BN6 integration, HN/BUD/HB semantic completeness, manuscript-wide SaturatePositive or BCELReady, unconditional ZeroSlack, executable polynomial PCCMin, complete encoded-size polynomial bounds, CNFSAT in P, a global gate, the eligible root theorem, or P = NP.

Reviewed theorem interfaces (1)

PNP.DirectWire.pccmin_checked_packet_pkgc_restoration_coverage_charge_route_or_zeroslack_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-207: formal artefact coverage becomes 183 of 185; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Global ZeroSlack, PCCMin, and polynomial runtime

Complete residual routing, global ZeroSlack contradiction, exact minimization, and polynomial bounds.

The finite candidate-derived BN3 envelope supplies stable request identities and one jointly side-tight canonical basis family; the finite BN4 kernel supplies activation-exact same-key integer cancellation over an explicit typed cell ledger; the finite BN5 kernel localizes explicit full/shadow multiplicity failure to a strict Hall deficit and local X1 route; the exhaustive Packet scan verifies strict gains or exact no-gain over every canonical selector in one supplied explicit grouped family; an explicit global gain-coverage certificate conditionally upgrades that silence to a proof-bearing ZeroSlack result; the generic finite R-ChargeSurplus kernel derives strict gain from exact ledgers, an unmatched positive support charge, exact gate accounting, and separately proved semantics; the checked unit-charge blueprint realizer derives canonical ledgers and gains for every valid blueprint in one supplied family; the checked typed-realizer contract rejects every faithful-table row except a genuine blueprint gain or an explicitly active bounded-rank HN, budget, or strictly lower faithful seed bot; the checked exact-rank HB graph contract validates every edge in a supplied finite HN/BUD dependency graph; the checked total-table HB contract gives every finite HN/BUD node one row, materializes every listed dependency as an edge, and derives well-founded induction and cycle exclusion for that supplied table; the checked HB active-dependency closure combines an exhaustive active-to-active row condition with strict rank descent to prove every supplied HN/BUD activity bit false and remove HN/budget typed-bot branches; and the executable selector-silence induction exhaustively checks that every canonical realizer claim is a typed bottom, then combines supplied-table HB inactivity with strong finite-rank induction to prove every canonical handle in the accepted table nonfaithful without a global semantic no-gain premise. The Packet selector-faithfulness routing milestone checks ten canonical source-payload fields and derives a contradiction for every positive Packet under explicit route-clear inputs; the canonical table constructor now computes the HB faithfulness function from those payloads and removes the separate binding premise; and total first-route classification turns every canonical payload rejection into one earliest typed route, which canonical HB selector silence forces for a positive Packet without route-clear or binding premises. The exact first-route semantics milestone additionally identifies every returned route with its unique earliest failed supplied payload field. The descent-reflection milestone computes the final descent field from the exact ten-coordinate RankWF relation and proves a forced final route is genuinely nondecreasing. The rank-tag-reflection milestone then copies the table-owned handle rank into the payload and excludes the duplicate rank route. The exact-route-reflection milestone marks the already proved internal handle-to-cell-to-positive-payload source route clear by construction and excludes the duplicate exact-route result as well; this internal route is not an external exact minimum. The charge-route-reflection milestone then derives the internal charge check from the canonical source atom with strictly positive mass and excludes the charge result; that positive mass is not the full external charge-surplus or replacement semantics. The colour-route-reflection milestone then derives internal grouped-footprint eligibility from each canonical handle and excludes colour; this is not external manuscript colour equivalence. The typed-frontier-route-reflection milestone replaces the caller frontier bit with executable equality of explicit typed source and selector signatures, so a frontier route carries exact inequality. The BN5-bound frontier-and-obligation milestone then binds both checks to exact fields of explicit typed terminal BN5 coordinates: frontier and obligation routes carry their corresponding inequalities, with frontier equality preceding an obligation failure. The BN4 activation-exact milestone computes activation from the coordinates' nested activation atoms. The typed-direction milestone computes direction from equality of explicit source and selector direction values. The typed-budget milestone computes the last caller-supplied Packet Boolean from equality of explicit source and selector budget values. Those coordinates, direction values, and budget values are not constructed from terminal data, and local budget equality is not BudgetResolve or HB budget semantics. The checked Packet budget/HB activity-binding milestone now exhaustively maps each typed budget mismatch to budget-node activity at the table-owned rank and, with the supplied checked well-founded HB closure, proves typed budget equality and excludes the local budget route. The binding, rank map, activity environment, dependency table, and closure premise remain explicit; this is not BudgetResolve, a terminal-data construction, or semantic completeness. The checked Packet semantic/HN activity-binding milestone now maps any failure of simultaneous frontier, obligation, activation, and direction agreement to the HN node at the table-owned rank. With the same supplied checked HB closure and the separately checked budget/HB binding, it excludes every semantic first route and leaves exact residual nondecrease. That binding and all typed semantic and HB data remain explicit; it does not construct HN blocker semantics, semantic dependency completeness, a decreasing transition, or a no-lower contradiction. The checked Packet descent no-lower milestone now exhaustively connects that forced route to one local no-lower row and proves its checker rejects; it does not construct the complete ledger or terminal inputs. The finite rank map remains explicit. M197 derives the structural BN6 grouping over the checked BCEL carrier by normalizing supplied raw supports, constructing singleton consumer systems, coalescing duplicate footprints, and preserving every positive payload atom. M198 additionally proves that this coalescing preserves the exact raw positive-cell crossing-mass sum on every cut and exposes the remaining BCEL mismatch directly against that raw ledger. The construction still does not derive the raw BN4/BN5/PkgC supports or payloads, replacement blueprints, occurrence pairing, rank assignment, payload values, exhaustive realizer claims, or blocker tables from terminal data; connect matching back to a contradiction; derive blocker semantics, semantic dependency completeness, or the checked local active-dependency premise from terminal data; prove the reported routes' external semantics or map all residual routes into a decreasing complete global outcome system; or provide full external selector compatibility, an independently constructed realizer, unconditional global silence, and polynomial-runtime completeness. Global unconditional ZeroSlack and polynomial PCCMin therefore remain unformalized.

Concrete standard P-versus-NP target and root theorem

Raw-machine-linked complexity classes, concrete SAT completeness and a SAT decider, plus the publication root theorem.

The concrete target definition remains inactive: CNF-SAT has a raw-machine verifier, NP-membership proof, an all-input finite-machine polynomial reduction through NAND to the concrete locked target, and an exact report-facing compatibility link, but a deterministic polynomial-time CNF-SAT decider, SAT NP-hardness and CNFSAT NP-completeness transport, and PNP.Main.p_eq_np remain absent.

All-route staged-request physical dispatch

For every concrete verifier problem and every coordinate in its complete post-header schedule, M227 runs M226's fixed terminal-joined classifier over a protected canonical optional-token request, proves common body-or-Finish terminal geometry, crosses the blank-free classifier prefix with M225's fixed 14-rule request relay, and executes M217's reflected fixed 64-rule dispatcher to the exact next canonical emitted prefix. The resulting collision-free 816-rule composition has exact work, six-for-one compiled, one-step-short and source-input-size polynomial evidence. All 65 public declarations are axiom-audited: 23 have empty closure, four use only propext, and 38 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone keeps the canonical optional-token request explicitly staged on the protected initial tape. It does not synthesize the request from raw classifier state, connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatch.cook_levin_builder_physical_classifier_all_route_staged_request_mirrored_dispatch_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-04-227: formal artefact coverage becomes 203 of 205; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-route derived-Finish physical request split

For every concrete verifier problem and every coordinate in its complete post-header schedule, M228 runs M226's terminal-joined classifier without a staged request cell. A fixed 20-rule relay reads the physical body-or-Finish terminal, crosses the exact blank-free classifier prefix, writes a collision-free body-pending marker for every body route, and writes the canonical Finish request only for the unique Finish route. A fixed 65-rule conditional reflected dispatcher rejects the body-pending marker and sends Finish to the exact next canonical emitted prefix. The collision-free 823-rule composition has exact work, six-for-one compiled, one-step-short and source-input-size polynomial evidence. All 91 public declarations are axiom-audited: 50 have empty closure, 18 use only propext, and 23 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone derives only the unique Finish request. Every body route halts at an explicit non-request pending marker; body-token and padding request synthesis remain open. It does not connect successive schedule configurations, implement one repeated raw-machine builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteDerivedFinishSplit.cook_levin_builder_physical_classifier_all_route_derived_finish_split_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-05-228: formal artefact coverage becomes 204 of 206; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

All-route physical body-remainder split

For every concrete verifier problem and every coordinate in its complete post-header schedule, M229 runs M228 without a staged request, route, remainder or success certificate. It preserves the completed Finish endpoint and sends every body route through one fixed 36-rule physical scanner. The scanner crosses the retained clause-count and exterior boundaries, skips consumed-dividend marks, and distinguishes zero from positive remainder by the actual separator or unit symbol. The physical remainder equals the canonical body token coordinate. The collision-free 895-rule graph has exact work, six-for-one compiled execution, one-step-short nonhalting, and a verifier-input-size polynomial bound. All 71 public declarations are axiom-audited: 39 have empty closure, nine use only propext, and 23 use only propext and Quot.sound, with no project axiom or Classical.choice.

This milestone reads the physical body remainder but leaves clause occupancy and body-token and padding request synthesis open. Both body outcomes remain incomplete terminal configurations, distinguished by tape content. It does not connect successive schedule configurations, implement the repeated builder loop, prove builder FunctionProgram.RawRefinement, or package the Cook-Levin PolynomialReduction. It does not establish CNFSAT NP-hardness or NP-completeness transport or CNFSAT in P, close a fixed checkpoint or global gate, create the eligible root theorem, or prove P = NP.

Reviewed theorem interfaces (1)

PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteBodyRemainderSplit.cook_levin_builder_physical_classifier_all_route_body_remainder_split_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-05-229: formal artefact coverage becomes 205 of 207; risk-weighted estimate remains 35%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Complete all-input Cook-Levin formula builder and reduction

For every concrete polynomial verifier and every ordinary raw bitstring, including empty and odd-length inputs, M230 runs the complete source-derived formula loop and physical output finalizer in one finite raw machine. Its exact ordinary output is the original canonical encoded Cook-Levin CNF formula, with total halting, runtime and output-size bounds polynomial in the original input length. The concrete PolynomialTimeFunction is a machine leaf; recursive FunctionProgram.RawRefinement preserves its output. The packaged PolynomialReduction to CNFSAT uses the already checked original formula semantics. No accepting certificate, execution trace, route, finite family, rank map or correctness certificate is supplied by the caller.

This completes the fixed all-input builder checkpoint, not a deterministic SAT algorithm. The separate named concrete NP-hardness or NP-completeness transport remains to be published. Unconditional residual minimization and ZeroSlack, complete polynomial PCCMin construction and certificate bounds, deterministic CNFSAT in P, and the eligible root theorem remain open. No global gate closes and P = NP is not proved. Execution theorem closures use only propext and Quot.sound; reduction-facing semantic closures additionally use the already allowed Lean standard axiom Classical.choice, never a project-specific axiom.

Reviewed theorem interfaces (6)

PNP.Concrete.CookLevin.formulaBuilderMachine_accept
PNP.Concrete.CookLevin.formulaBuilderMachine_output
PNP.Concrete.CookLevin.formulaBuilder_output
PNP.Concrete.CookLevin.formulaBuilder_rawRefinement_output
PNP.Concrete.CookLevin.polynomialReduction_output
PNP.Concrete.CookLevin.cook_levin_formula_builder_checked_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-10-230: formal artefact coverage becomes 206 of 208; risk-weighted estimate is 38%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Concrete CNF-SAT NP-hardness and NP-completeness

For every language in the concrete bounded-certificate NP class, M231 extracts its polynomial-time verifier from NP membership and applies the complete source-derived all-input Cook-Levin PolynomialReduction to CNFSAT. Together with the existing concrete CNFSAT verifier, the closed theorem proves NPComplete CNFSAT in the selected finite-machine model. No reduction, execution trace, finite-instance restriction or correctness certificate is supplied. Both complete theorem interfaces are root-built and axiom-audited; their closures contain only the Lean standard axioms Classical.choice, Quot.sound and propext.

NP-completeness is hardness plus NP membership, not a deterministic polynomial-time SAT algorithm. This closes only the fixed concrete NP-hardness checkpoint. It does not close the separate final complexity transport to P = NP, unconditional residual minimization or ZeroSlack, complete polynomial PCCMin construction and certificate bounds, deterministic CNFSAT in P, or the eligible root theorem. All five global proof gates and the publication gate remain open; P = NP is not proved.

Reviewed theorem interfaces (2)

PNP.Concrete.CookLevin.cnfSAT_np_hard
PNP.Concrete.CookLevin.cnfSAT_np_complete

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-231: formal artefact coverage becomes 207 of 209; risk-weighted estimate is 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Candidate-derived terminal profile dependency reflection and noninterference

For every finite direct-wire candidate size, executable terminal model, profile coordinate and gate, M232 proves that the computed profile-influence bit is true exactly when insertion changes the actual ambient observation in a canonical subset context. It identifies each computed profile-to-gate dependency with the coordinate's exact rule role and that influence bit. For every seed, a gate absent from the actual computed saturation cannot change a retained profile coordinate in any canonical context. The observation definition and all three general theorem interfaces are root-built and axiom-audited using only propext and Quot.sound. No dependency relation, coverage certificate or soundness proof is supplied in place of the existing computation.

The executable observer and profile model remain supplied data, and influence construction enumerates all subsets. This is a local semantic reflection and noninterference theorem, not an input-derived terminal family, arbitrary-record normalization, unconditional SaturatePositive or BCELReady, global route coverage or ZeroSlack, exact PCCMin construction, or an encoded-size polynomial runtime result. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root theorem remain absent; P = NP is not proved.

Reviewed theorem interfaces (3)

PNP.DirectWire.terminalGateInfluencesProfile_eq_true_iff
PNP.DirectWire.terminalCandidateProfileRequires_eq_influence
PNP.DirectWire.terminalCandidateSaturate_profile_noninterference

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-232: formal artefact coverage becomes 208 of 210; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Retained ambient-profile locality and whole-support preservation

For every finite direct-wire candidate size, executable terminal model, seed and retained profile coordinate, M233 proves that arbitrary primitive-record supports with the same computed-saturation gate membership have equal actual ambient observations. Structural extraction and ambient-implementation equalities account for record order, duplicates and non-gate metadata without an observer-congruence premise. General omitted-gate elimination extends M232 from canonical contexts to arbitrary supports. The actual saturated support therefore preserves each retained observation of the complete gate universe. All five theorem interfaces are root-built and axiom-audited using only propext and Quot.sound. No dependency relation, normalization certificate or correctness proof is supplied in place of the existing computation.

The executable observer and profile model remain supplied data, and influence construction enumerates all subsets. The theorem does not derive profile semantics or terminal families from every valid input, identify the ambient observer with the differently typed profileSystem.observe, prove transparent cost or complete route coverage, establish unconditional SaturatePositive, BCELReady or ZeroSlack, or supply an exact polynomial PCCMin construction and certificate bound. The retained-profile premise is necessary. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root theorem remain absent; P = NP is not proved.

Reviewed theorem interfaces (5)

PNP.DirectWire.extractTerminalSupport_eq_of_gateSelected_eq
PNP.DirectWire.terminalAmbientSupportImplementation_eq_of_gateSelected_eq
PNP.DirectWire.terminalCandidateProfileObservation_eq_of_gateMembership_iff
PNP.DirectWire.terminalCandidateSaturate_profile_locality
PNP.DirectWire.terminalCandidateSaturate_profile_preserved

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-233: formal artefact coverage becomes 209 of 211; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed saturation trace fidelity and metadata cost balance

For arbitrary finite terminal systems and seeds, M234 proves that the actual cost-accounting replay contains exactly the canonical computed saturated records and that every emitted event adds its required record with a valid selected dependency rule. For every finite direct-wire candidate and executable terminal model, the replay and canonical endpoints have equal ambient implementations and equal cost snapshot coordinates, with the stored record list kept explicit. Every generated non-gate metadata event is structurally cost-transparent. All five theorem interfaces are root-built and axiom-audited using only propext and Quot.sound. No trace-validity, replay-correctness, observer-congruence or balance certificate is supplied in place of the existing computation.

The executable observer and profile model remain supplied data. Influence and semantic minima use exhaustive finite reference constructions; no polynomial runtime is proved. Metadata cost balance does not establish physical-gate transparency, obligation discharge or complete closure safety. The theorem does not derive terminal families from every valid input, prove global route coverage, unconditional SaturatePositive, BCELReady or ZeroSlack, or construct the exact polynomial PCCMin algorithm and certificate bounds. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root theorem remain absent; P = NP is not proved.

Reviewed theorem interfaces (5)

PNP.DirectWire.terminalSaturateTrace_replayRecords_iff
PNP.DirectWire.terminalSaturateTrace_event_valid
PNP.DirectWire.terminalCandidateSaturateTrace_ambient_eq
PNP.DirectWire.terminalCandidateSaturateTrace_costSnapshot_eq
PNP.DirectWire.terminalCandidateSaturateTrace_metadata_transparent

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-234: formal artefact coverage becomes 210 of 212; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Actual physical saturation accounting and first-obstruction fidelity

For arbitrary finite terminal systems, seeds and actual generated events, M235 derives that the dependent is already active and the required record is genuinely new. For every finite direct-wire candidate and executable terminal model, the unchanged extractor charges exactly one physical gate for a generated gate event and zero for metadata, and the selected rule/dependent pair belongs to the computed active-owner list. Every generated nontransparent event is a physical insertion with a genuine nonunique-owner, full-minimum-growth or quotient-cost obstruction. The existing total classifier either preserves full slack and nondecreasing projection defect at canonical computed saturation or returns its exact first such obstruction with a transparent prefix. All five general interfaces are root-built and audited using only propext and Quot.sound. No freshness, charge-balance, active-owner, all-transparent-history or preselected-route certificate replaces the actual computation.

The executable observer and profile model remain supplied data. Influence and semantic minima use exhaustive finite reference constructions; no polynomial runtime is proved. An active dependency owner need not be unique. Exact physical support growth does not establish full-minimum growth, a quotient bound, obligation discharge, complete closure safety or a global named route. The first physical obstruction is not thereby a verified gain, an exact route or strict descent. This theorem does not derive terminal families from every valid input, prove global route coverage, unconditional SaturatePositive, BCELReady or ZeroSlack, or construct the exact polynomial PCCMin algorithm and certificate bounds. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root theorem remain absent; P = NP is not proved.

Reviewed theorem interfaces (5)

PNP.DirectWire.terminalSaturateTrace_event_context
PNP.DirectWire.terminalCandidateSaturateTrace_supportCostBalanced
PNP.DirectWire.terminalCandidateSaturateTrace_event_owner
PNP.DirectWire.terminalCandidateSaturateTrace_physicalObstruction
PNP.DirectWire.terminalCandidateSaturateTrace_balance_or_physicalObstruction

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-235: formal artefact coverage becomes 211 of 213; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed physical-charge partition and introduction provenance

For arbitrary finite terminal systems and seeds, M236 constructs a physical-NAND charge ledger directly from the normalized initial records and actual computed saturation trace. Its physical gate identifiers are duplicate-free and occur exactly when the corresponding gate records occur in the computed saturated support. Each entry has inherited seed provenance or an actual generating event with its exact rule and dependent, active context and fresh required gate. The deterministic lookup returns exactly the provenance of the corresponding ledger entry. For every finite direct-wire candidate and executable terminal model, the complete computed ledger length equals the unchanged extractor's support size at canonical saturation. All five general interfaces are root-built and audited using only propext and Quot.sound. No supplied charge list, coverage certificate, freshness premise or ownership certificate replaces the actual computation.

This is a physical-NAND charge partition with seed- and traversal-dependent introduction provenance, not the complete manuscript charge universe or its fixed global ownership function. Active requesting pairs are not assigned manuscript owners, and multiple physical charges may have the same requesting dependency. Materializer grouping and cross-support ownership transport remain open. The executable observer and profile model remain supplied data, while influence and semantic minima use exhaustive finite reference constructions. No full-minimum growth, quotient bound, global named route, input-derived terminal family, unconditional SaturatePositive, BCELReady or ZeroSlack, or complete polynomial PCCMin runtime and certificate bounds is established. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root theorem remain absent; P = NP is not proved.

Reviewed theorem interfaces (5)

PNP.DirectWire.terminalSaturatePhysicalCharges_nodup
PNP.DirectWire.terminalSaturatePhysicalCharges_complete
PNP.DirectWire.terminalSaturatePhysicalCharges_provenance
PNP.DirectWire.terminalSaturatePhysicalChargeProvenance?_iff
PNP.DirectWire.terminalCandidateSaturatePhysicalCharges_size

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-236: formal artefact coverage becomes 212 of 214; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed saturated-support replacement context and physical slack

For every finite direct-wire candidate, executable terminal model and seed list, M237 computes a concrete replacement frame from production saturation and the actual physical gate complement. Gate-source closure proves that the selected support boundary contains only primary inputs. The unchanged extractor constructs both gate halves, and every complement boundary gate is bound to an actual selected-support interface port. The frame preserves the original ordered Boolean outputs when the extracted support is plugged back in. Every equivalent replacement on the exact extracted boundary and interface preserves the whole circuit, with an exact gate-count equation that counts every original physical NAND gate once and permits arbitrary replacement size. Transport through the existing constructive frame theorem bounds the computed support's physical Boolean residual slack by whole-circuit slack. All five general interfaces are root-built and audited using only propext and Quot.sound. No caller-supplied frame, fan-in-closure certificate, gate partition or whole-circuit correctness proof replaces the computation.

These are physical Boolean replacement and slack laws for actual production saturated supports, not arbitrary raw supports or full-profile compatibility. The complete manuscript profile/materializer charge universe, fixed global ownership map and full-profile replacement transport remain open. The executable observer and profile model remain supplied data, while influence and semantic minima use exhaustive finite reference constructions; no polynomial runtime is proved. No full-minimum growth, quotient bound, global named route, input-derived complete terminal family, unconditional SaturatePositive, BCELReady or ZeroSlack, or complete polynomial PCCMin runtime and certificate bounds is established. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root theorem remain absent; P = NP is not proved.

Reviewed theorem interfaces (5)

PNP.DirectWire.terminalCandidateSaturate_boundary_isInput
PNP.DirectWire.terminalCandidateSaturatePhysicalContext_size
PNP.DirectWire.terminalCandidateSaturatePhysicalContext_equivalent
PNP.DirectWire.terminalCandidateSaturatePhysicalContext_replace_equivalent
PNP.DirectWire.terminalCandidateSaturatePhysicalSupport_slack_le

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-237: formal artefact coverage becomes 213 of 215; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed proper-support physical gain and exact slack descent

For every finite direct-wire candidate, executable terminal profile model and seed list, M238 computes the whole physical replacement using the existing reference-minimum witness and the actual production saturated-support context. The complete ordered Boolean output word is preserved. The replacement gate count plus the computed local gain equals the original gate count, and replacement residual slack plus that gain equals the original physical residual slack. These equations require no properness, positivity, supplied frame or supplied charge partition. The total optional gain step maps this construction over the existing candidate-derived proper-positive support search. Every returned result carries an actually selected canonical proper positive seed and strictly decreases whole physical gate count and residual slack. Failure is exactly absence of every canonical proper positive seed for that computed system, not global minimality. All five universal interfaces are root-built and audited using only propext and Quot.sound. The caller supplies no search result, replacement, seed, context or correctness certificate to the gain-step algorithm.

These are physical Boolean reference gain-realization and search-failure laws, not full-profile replacement compatibility or a complete named global route. The observer and profile model remain supplied data, while influence, canonical seed search and semantic minima use exhaustive finite reference constructions; no polynomial encoded-size or runtime bound is proved. Failure of the proper-support search does not imply global minimality or ZeroSlack. Complete profile/materializer charge coverage, fixed global ownership, obligation transport, full-minimum growth, quotient bounds, input-derived complete terminal families and global rank-decreasing route coverage remain open. No unconditional SaturatePositive, BCELReady or ZeroSlack, complete polynomial PCCMin, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (5)

PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_equivalent
PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_size_gain
PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_slack_gain
PNP.DirectWire.findTerminalCandidatePhysicalGain_sound
PNP.DirectWire.findTerminalCandidatePhysicalGain_eq_none_iff

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-238: formal artefact coverage becomes 214 of 216; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed full-profile gain acceptance and exact slack descent

For every finite direct-wire candidate and supplied executable terminal profile model, M239 classifies the exact result of the existing production physical-gain search. No result is exactly the existing proper-support search failure. A result is scanned at every full-profile coordinate in canonical order. Rejection identifies the actual first mismatching coordinate and complete agreeing prefix; acceptance constructs the existing full-carrier realization without a caller-supplied result, seed, profile-equality proof or correctness certificate. Complete full-carrier realizations preserve the exhaustive full-profile minimum, and every accepted computed gain decreases full-profile slack by exactly the local physical gain of its actually selected proper-positive support. Existing obligation discharge transports through the full realization; an open obligation is not thereby discharged. The seven universal interfaces are explicit-root built with their reviewed standard axiom closures. The classifier reuses M238's proved Boolean equivalence rather than repeating an exhaustive equivalence check.

These are computed finite full-profile acceptance and accepted-result transport laws for the supplied executable profile system, not a derivation of manuscript carrier data or a theorem that every physical gain is full-profile compatible. A first profile mismatch is not a completed named global route. The observer and profile model remain supplied data; influence, canonical seed search and semantic minima remain exhaustive finite reference constructions, with no polynomial encoded-size or runtime theorem. The classifier does not search alternative physical gains after a mismatch or identify ambient observations with the differently typed global profile system. Complete materializer charges, fixed global ownership, full-minimum growth during saturation, quotient bounds, terminal-family derivation and global rank-decreasing route coverage remain open. No unconditional SaturatePositive, BCELReady or ZeroSlack, complete polynomial PCCMin, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (7)

PNP.DirectWire.firstTerminalGainProfileMismatch_eq_none_iff
PNP.DirectWire.firstTerminalGainProfileMismatch_spec
PNP.DirectWire.terminalFullProfileMinimum_eq_of_fullRealization
PNP.DirectWire.classifyTerminalCandidateGainProfile_accepted_iff
PNP.DirectWire.classifyTerminalCandidateGainProfile_noGain_iff
PNP.DirectWire.classifyTerminalCandidateGainProfile_mismatch_iff
PNP.DirectWire.TerminalCandidateFullProfileGain.fullSlack_gain

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-239: formal artefact coverage becomes 215 of 217; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Independent NAND materializer exact minimum-cost additivity

For every finite direct-wire circuit and every finite bank size, M240 physically appends one NAND for each disjoint pair of fresh Boolean inputs while retaining all original ordered outputs. The seven universal interfaces prove exact size and both output semantics, preservation of complete Boolean equivalence, a lower bound against every equivalent competing topology, exact reference-minimum additivity and unchanged physical residual slack. The original circuit need not be minimum, and its outputs may be constant, repeated or direct primary-input wires. The lower bound derives distinct actual bank-output gates from semantic output conditions, restricts fresh inputs to false and computes an erasure/rebinding that removes exactly those gates, including through retained consumers. The resulting implementation realizes the original function. Appending the bank to its attained minimum witness gives the matching upper bound. No correctness certificate or supplied minimum is an algorithm input. All seven interfaces are explicit-root built with their exact reviewed standard axiom closures.

This is an independent physical Boolean materializer forced-cost subcase, not transparency of every manuscript profile materializer or every actual saturation step. Fresh primary inputs and distinct appended NAND outputs are essential; repeating an existing output or reusing the original input pair does not justify additive cost. The result does not change or derive the full profile observer, global materializer ownership, quotient costs, obligation discharge, terminal families or complete rank-decreasing route coverage. Reference minima remain exhaustive finite constructions, not a polynomial-time algorithm. No unconditional SaturatePositive, BCELReady or ZeroSlack, complete polynomial PCCMin, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (7)

PNP.DirectWire.appendIndependentNandMaterializers_size
PNP.DirectWire.appendIndependentNandMaterializers_original
PNP.DirectWire.appendIndependentNandMaterializers_materializer
PNP.DirectWire.appendIndependentNandMaterializers_lower_bound
PNP.DirectWire.appendIndependentNandMaterializers_equivalent
PNP.DirectWire.appendIndependentNandMaterializers_referenceMinimum
PNP.DirectWire.appendIndependentNandMaterializers_residualSlack

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-240: formal artefact coverage becomes 216 of 218; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Support-independent physical ownership and exact materializer charges

For every finite candidate, arbitrary finite raw request family and terminal record list, M241 computes a first-requesting ambient owner before support selection, retaining unrequested physical gates in a fixed remainder bucket. Ten universal interfaces characterize the first requester and unrequested case, exact partition membership, disjointness and restriction stability, actual extracted gate counts, the complete integer charge identity, open semantics, induced-boundary reconnection and the whole-circuit charge total. Overlapping and duplicate requests require no supplied disjointness or coverage certificate. Each owned piece is an existing physical support extraction with its actual NAND size, not an arbitrary numerical weight. All ten interfaces are explicit-root built with their exact reviewed standard axiom closures.

This is a support-independent physical ownership and charge partition kernel, not the complete manuscript computational-record universe or proof of admissible materializer ownership. The raw finite request family is supplied data; a canonical assignment does not discharge unique active ownership, carrier, frontier or obligation conditions. The existing production nonunique-owner rejection is unchanged. Metadata records do not become free computational materializers or receive invented physical cost. The result does not establish HN assembly, forced full-profile minimum growth, quotient bounds, terminal-family derivation or complete rank-decreasing routes. Reference minima remain exhaustive finite constructions, not a polynomial-time algorithm. No unconditional SaturatePositive, BCELReady or ZeroSlack, complete polynomial PCCMin, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (10)

PNP.DirectWire.terminalPhysicalOwner_none_iff
PNP.DirectWire.terminalPhysicalOwner_first
PNP.DirectWire.terminalOwnedPhysicalGates_partition
PNP.DirectWire.terminalOwnedPhysicalGates_disjoint
PNP.DirectWire.terminalOwnedPhysicalGates_restrict
PNP.DirectWire.terminalOwnedPhysicalMaterializer_gateCount
PNP.DirectWire.terminalOwnedPhysicalMaterializer_chargeIdentity
PNP.DirectWire.terminalOwnedPhysicalMaterializer_semantics
PNP.DirectWire.terminalOwnedPhysicalMaterializer_induced
PNP.DirectWire.terminalOwnedPhysicalMaterializer_wholeCharge

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-241: formal artefact coverage becomes 217 of 219; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Constructive whole-program NAND sharing and checked normalization

For every finite direct-wire NAND program and complete ordered output word, M242 computes a full structural-sharing traversal, translating every source through earlier computed aliases and searching the actual retained program for equal or commuted NAND input pairs. Each successful lookup reuses one existing gate; each unsuccessful lookup appends one translated gate. Nine universal interfaces prove every alias value, exact retained-plus-fold gate accounting, complete multi-output equivalence, non-increasing physical size, invariant reference minimum, exact residual-slack savings, strict gain exactly when a fold occurs, strict residual descent and the computed normalizer outcome. The caller supplies only the implementation, not an optimizer or correctness certificate. The pass performs structural lookup, not semantic enumeration. All nine interfaces are explicit-root built with only propext and Quot.sound.

This is a computed physical R1/R4 structural-sharing stage, not complete manuscript N1-N10 normalization or a proof that every latent-sharing opportunity is found. A no-fold branch does not imply semantic minimality, absence of other gains or ZeroSlack; a checked regression gives a smaller equivalent circuit after the pass has no structural fold. The result does not construct a proper-support Package E ledger, arbitrary replacement pullback, full-profile carrier or obligation transport, terminal-derived families, global rank-decreasing route coverage or the complete PCCMin oracle. Reference minimum occurs in specification theorems, not in execution of this pass. No uniformly encoded-size polynomial execution theorem for the complete PCCMin construction is proved. No unconditional SaturatePositive, BCELReady or ZeroSlack, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (9)

PNP.DirectWire.compileNANDSharing_alias_semantics
PNP.DirectWire.compileNANDSharing_exact_accounting
PNP.DirectWire.sharingImplementation_equivalent
PNP.DirectWire.sharingImplementation_gateCount_le
PNP.DirectWire.sharingImplementation_referenceMinimum
PNP.DirectWire.sharingImplementation_residualSlack
PNP.DirectWire.sharingImplementation_strictGain_iff
PNP.DirectWire.sharingImplementation_strictResidualDescent
PNP.DirectWire.nandSharingNormalizer_checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-242: formal artefact coverage becomes 218 of 220; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Checked concrete SAT hardness in the active conditional final-report bridge

M243 connects the already checked all-input Cook-Levin NP-hardness and NP-completeness theorem to the exact report-facing SAT predicate. The existing accepted-generated-package consequence and final_report_bridge no longer take a CheckerTrustModel or supplied SAT-hardness argument. They consume the checked theorem while retaining the explicit PCCMinLoopCertificate, its concrete residual-band polynomial decider and the loop-existence antecedent. This strengthens the active conditional interface rather than adding an unused parallel route. Four reviewed interfaces have exact kernel types and the same standard axioms as the consumed M231 theorem: Classical.choice, Quot.sound and propext.

This is a conditional final-report bridge, not the eligible unconditional root theorem. No complete PCCMin loop certificate is constructed: the concrete residual-band decider remains an explicit certificate field. Canonical package acceptance does not supply missing algorithmic correctness, encoded-size bounds or loop existence. This does not establish unconditional SaturatePositive, BCELReady or ZeroSlack, a complete exact polynomial PCCMin construction, polynomial output and certificate bounds, deterministic CNFSAT in P or P = NP. M231 hardness was already credited; connecting it here earns no duplicate checkpoint points. No fixed weighted checkpoint or global gate closes.

Reviewed theorem interfaces (4)

PNP.sat_np_hard_checked
PNP.sat_np_complete_checked
PNP.accepted_generated_package_implies_p_eq_np
PNP.final_report_bridge

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-243: formal artefact coverage becomes 219 of 221; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Derived physical output cones and checked unused-gate pruning

For every finite direct-wire NAND candidate and complete ordered output word, M244 computes the least physical gate-predecessor closure of actual gate-valued outputs using the existing finite work-list saturation. It proves output inclusion, predecessor closure, leastness and absence of gate-valued external boundary wires. The existing checked support extractor is reused, its boundary is renamed to original primary inputs, and every ordered output position is reconnected, including constants and repeated wires. Eleven universal interfaces establish complete input/output equivalence, non-increasing physical gate count, exact retained-plus-deleted accounting, invariant semantic reference minimum, exact residual-slack savings, strict gain exactly when a gate is deleted and the concrete PCCMin normalizer outcome. The caller supplies only the implementation. All eleven interfaces are explicit-root built with only propext and Quot.sound.

This is a computed physical unused-gate pruning stage, not complete manuscript N1-N10 normalization or full-profile/metadata support derivation. The empty profile index describes only this physical closure; arbitrary full-profile observers may distinguish the pruned implementation. A no-deletion branch does not imply semantic minimality or ZeroSlack. The pass reuses executable closure and checked extraction; reference minimum occurs in specification theorems, not in execution. No proper-support Package E rewrite ledger, full-profile carrier/obligation transport, global terminal family, complete rank-decreasing route coverage or total PCCMin oracle is constructed. No uniformly encoded-size polynomial execution theorem for the complete construction is proved. No unconditional SaturatePositive, BCELReady or ZeroSlack, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (11)

PNP.DirectWire.outputConeRecords_output
PNP.DirectWire.outputConeRecords_closed
PNP.DirectWire.outputConeRecords_least
PNP.DirectWire.outputConeRecords_noExternalGate
PNP.DirectWire.outputConeImplementation_equivalent
PNP.DirectWire.outputConeImplementation_gateCount_le
PNP.DirectWire.outputConeImplementation_exact_accounting
PNP.DirectWire.outputConeImplementation_referenceMinimum
PNP.DirectWire.outputConeImplementation_residualSlack
PNP.DirectWire.outputConeImplementation_strictGain_iff
PNP.DirectWire.outputConeNormalizer_checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-244: formal artefact coverage becomes 220 of 222; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed dead-support frames and proper physical deletion

For every finite direct-wire NAND implementation, M245 computes the physical complement of its output cone and proves that the actual extracted dead support has no outgoing interface. Its incoming wires are connected to original inputs or the computed live frontier; the live program also carries every original ordered output as bypass. The support is the actual extracted candidate, reindexed only by its proved empty interface. A concrete FramedContext inserts that support with the original physical gate count and plugs a zero-gate replacement with complete original output semantics. Twenty general interfaces establish exact boundary values, extraction identity, local and framed equivalence, retained-plus-dead gate accounting, exact residual-slack savings and a computed physical gain witness precisely when both dead support and live cone are nonempty. All twenty interfaces are explicit-root built with only propext and Quot.sound. No support, frame or correctness certificate is supplied by the caller.

This is a computed proper physical deletion component, not complete manuscript Package E admissibility or a complete N1-N10 rewrite ledger. Properness concerns the actual gate subset and concrete frame, not full-profile carrier and obligation compatibility. An all-unused circuit is not accepted as a proper-subset witness. Rejecting this route does not imply semantic minimality or ZeroSlack. The construction does not search reference minima; the reference minimum occurs only in specification theorems. No arbitrary full-profile preservation, complete Package E verifier, terminal-derived global family, complete rank-decreasing route coverage or total PCCMin oracle is constructed. No uniformly encoded-size polynomial execution theorem for the complete construction is proved. No unconditional SaturatePositive, BCELReady or ZeroSlack, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (20)

PNP.DirectWire.outputConeFrontierCandidate_semantics
PNP.DirectWire.deadSupport_interface_empty
PNP.DirectWire.deadSupportGateCount_partition
PNP.DirectWire.deadSupportGateCount_eq_deleted
PNP.DirectWire.deadSupportEnvironment_boundary
PNP.DirectWire.deadSupportEnvironment_bypass
PNP.DirectWire.deadSupportCandidate_extracted
PNP.DirectWire.deadSupportCandidate_program
PNP.DirectWire.deadSupportEmptyReplacement_equivalent
PNP.DirectWire.deadSupportContext_plug_equivalent
PNP.DirectWire.deadSupportContext_original_size
PNP.DirectWire.deadSupportReplacement_gateCount
PNP.DirectWire.deadSupportReplacement_equivalent
PNP.DirectWire.deadSupportReplacement_accounting
PNP.DirectWire.deadSupportReplacement_residualSlack
PNP.DirectWire.deadSupportReplacement_strictGain_iff
PNP.DirectWire.deadSupportProperGain_isSome_iff
PNP.DirectWire.deadSupportProperGain_sound
PNP.DirectWire.deadSupportProperGain_none_of_all_dead
PNP.DirectWire.deadSupportProperGain_none_of_no_dead

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-245: formal artefact coverage becomes 221 of 223; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Full finite-profile and obligation acceptance for computed dead-support gains

For every finite direct-wire implementation and input finite profile observation system, M246 classifies the actual M245 proper dead-support replacement without an exhaustive physical support or reference-minimum search. It reuses the complete profile mismatch scan and adds a canonical obligation-role scan. No proper support, first full-profile mismatch, first open obligation and accepted full-mode result are distinct proof-bearing outcomes. Eight general interfaces prove exact obligation-scan completeness, first-failure prefixes, acceptance precisely when computed properness, complete profile equality and observed obligation discharge all hold, exact no-proper-support rejection, full-profile minimum invariance as a specification theorem, and branch soundness with physical equivalence, properness, exact size/slack savings and strict descent. Accepted results inhabit the existing full-carrier interface. All eight interfaces are explicit-root built with only propext and Quot.sound. No result, profile-invariance premise or correctness certificate is supplied by the caller.

This is computed acceptance against an input finite profile observation system, not derivation of the manuscript carrier or its semantic dependency graph. Checking observed obligation bits is not a constructed R5 creation or R6-R8 discharge ledger, and does not by itself establish complete Package E admissibility. Full-profile equality is not replaced by quotient equality; matching profiles with an open obligation are rejected. No-proper-support rejection excludes only this computed dead-support route, not every physical gain or a smaller semantic implementation. A mismatch or open obligation is explicit rejecting data, not a completed global routing theorem. The full-profile reference minimum appears only in a specification theorem; it is not computed by the classifier. No bound on the supplied observer computation or uniformly encoded-size polynomial runtime is established. No terminal-derived global family, complete N1-N10 normalization, full Package E verifier, total PCCMin oracle, unconditional SaturatePositive, BCELReady or ZeroSlack, deterministic CNFSAT in P or eligible root theorem is established. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (8)

PNP.DirectWire.firstTerminalOpenObligation_eq_none_iff
PNP.DirectWire.firstTerminalOpenObligation_spec
PNP.DirectWire.DeadSupportFullModeGain.currentObligationsDischarged
PNP.DirectWire.classifyDeadSupportFullMode_accepted_iff
PNP.DirectWire.classifyDeadSupportFullMode_noProperSupport_iff
PNP.DirectWire.DeadSupportFullModeGain.fullProfileMinimum
PNP.DirectWire.DeadSupportFullModeGain.checked
PNP.DirectWire.classifyDeadSupportFullMode_checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-246: formal artefact coverage becomes 222 of 224; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed constant propagation through arbitrary NAND programs

For every finite direct-wire NAND program, M247 computes retained-source aliases for all original gates, substitutes them before inspecting each NAND operation, eliminates a gate exactly when literal constant NAND identities determine its value, and rewrites the complete ordered output tuple. Ten general interfaces prove primitive constant recognition sound for every valuation, alias semantics, exact retained-plus-eliminated gate accounting, complete multi-output equivalence, non-increasing size, invariant reference minimum, exact residual-slack savings, strict gain exactly when an elimination occurs, strict residual descent and the computed outcome of the existing total normalizer interface. Earlier constant eliminations propagate through arbitrarily later gates. The primitive recognition theorem is axiom-free; the other nine interfaces use only propext and Quot.sound. No optimizer, result, semantic equivalence certificate or caller correctness assertion is supplied.

This is the physical literal-constant structural-congruence component, not complete manuscript R1-R9 verification or N1-N10 normalization. No-elimination does not imply semantic minimality or ZeroSlack: the regression retains NAND(x, NAND(x,x)) even though a zero-gate constant-true word is equivalent. No full-profile preservation, derived manuscript carrier, arbitrary-support pullback/expansion, obligation lifecycle ledger, complete Package E or total PCCMin oracle is established. The reference minimum is used only in specification theorems, not executed by the pass. No uniformly encoded-size polynomial runtime, output-size or certificate-size theorem is established. Unconditional SaturatePositive, BCELReady and ZeroSlack, deterministic CNFSAT in P and the eligible root theorem remain open. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (10)

PNP.DirectWire.constantGateValue_sound
PNP.DirectWire.compileNANDConstantPropagation_alias_semantics
PNP.DirectWire.compileNANDConstantPropagation_exact_accounting
PNP.DirectWire.constantPropagationImplementation_equivalent
PNP.DirectWire.constantPropagationImplementation_gateCount_le
PNP.DirectWire.constantPropagationImplementation_referenceMinimum
PNP.DirectWire.constantPropagationImplementation_residualSlack
PNP.DirectWire.constantPropagationImplementation_strictGain_iff
PNP.DirectWire.constantPropagationImplementation_strictResidualDescent
PNP.DirectWire.nandConstantPropagationNormalizer_checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-247: formal artefact coverage becomes 223 of 225; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed closure of constant propagation, NAND sharing and output-cone pruning

For every finite direct-wire implementation, M248 computes a priority-respecting loop over the actual constant-propagation, NAND-sharing and output-cone-pruning constructions. It selects the first positive saving, recurses on strictly smaller physical gate count, and stops only when all three computed savings vanish on the same final implementation. Twelve general interfaces prove complete ordered-output equivalence, exact per-pass and telescoping trace savings, strict selected gains, priority, common quiescence, unchanged quiescent inputs, idempotent re-execution, invariant semantic reference minimum, exact residual-slack savings and a gain-iteration bound by the original slack. The existing normalizer interface exposes every positive total saving as a strict gain. All proof fields are derived by the construction, with no supplied normalizer, oracle, result or stopping certificate. The twelve interfaces use only propext and Quot.sound.

This is operational quiescence for exactly three physical passes, not semantic minimality, all structural congruences, complete manuscript N1-N10 normalization or ZeroSlack. The regression remains quiescent on NAND(x, NAND(x,x)) while a zero-gate constant-true word is strictly smaller and equivalent. The trace is not the arbitrary-support Pull/Expand materializer transport required by the complete Traceable normalization theorem. Full-profile preservation, the manuscript carrier and R5/R6-R8 obligation lifecycle ledger, complete Package E and the total PCCMin oracle remain open. Semantic reference minima occur only in specifications and are not executed by this loop. An iteration bound is not a runtime bound: no uniformly encoded-size polynomial construction, runtime, output-size or certificate-size theorem is established. Unconditional SaturatePositive, BCELReady and ZeroSlack, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (12)

PNP.DirectWire.physicalNormalizationPass_equivalent
PNP.DirectWire.physicalNormalizationPass_exact_accounting
PNP.DirectWire.PhysicalNormalizationGain.checked
PNP.DirectWire.nextPhysicalNormalizationStep_checked
PNP.DirectWire.PhysicalNormalizationTrace.checked
PNP.DirectWire.runPhysicalNormalization_checked
PNP.DirectWire.runPhysicalNormalization_of_quiescent
PNP.DirectWire.runPhysicalNormalization_idempotent
PNP.DirectWire.runPhysicalNormalization_referenceMinimum
PNP.DirectWire.runPhysicalNormalization_residualSlack
PNP.DirectWire.runPhysicalNormalization_gainIterations_le_residualSlack
PNP.DirectWire.physicalClosureNormalizer_checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-248: formal artefact coverage becomes 224 of 226; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed arbitrary-support literal NAND replacement and topological compilation

For all finite raw NAND graphs, M249 computes a topological order from the actual source fields or rejects the unresolved cyclic remainder. The ordered program has one position for every original node, exact size and complete output semantics for every solution of the original equations. For arbitrary finite terminal support records, it then constructs the actual literal splice from the canonical exterior gates, computed boundary and interface, replacement word and every original ordered output. Every accepted splice has exactly the exterior size plus replacement size; an equivalent replacement preserves all outputs, and a strict local physical saving yields a strict whole-program saving. Actual production saturation derives a primary-input-only boundary and hence unconditional compilation success, without a supplied frame, order, wiring map or acyclicity certificate. Its result agrees in size and semantics with the existing production physical constructor. Twenty-four interfaces have exactly reviewed dependencies contained in propext and Quot.sound.

Arbitrary raw port compatibility and equal open Boolean functions do not by themselves guarantee acyclic literal wiring. The regression gives an equivalent replacement with a raw graph solution but a genuine dependency cycle, which the compiler rejects. This is a physical substitution and well-formedness result, not a contradiction of the manuscript's unconstructed complete carrier premises. Full-profile preservation, the manuscript carrier and R5/R6-R8 obligation lifecycle, arbitrary-support Pull/Expand materializer identities, complete Package E and complete normalization remain open. No semantic minimum is computed, no unconditional global route is supplied, and a finite node-count termination argument is not a total encoded-size polynomial runtime theorem. Unconditional SaturatePositive, BCELReady and ZeroSlack, exact polynomial PCCMin, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global gate closes; P = NP is not proved.

Reviewed theorem interfaces (24)

PNP.DirectWire.RawNandCompilationState.readSource_sound
PNP.DirectWire.RawNandCompilationState.readGate_sound
PNP.DirectWire.RawNandReadyStep.apply_remaining_lt
PNP.DirectWire.RawNandCompilationStop.unresolved_predecessor
PNP.DirectWire.RawNandCompilationStop.complete_of_wellFounded
PNP.DirectWire.CompiledRawNandGraph.wellFounded
PNP.DirectWire.compileRawNandGraph_success_iff
PNP.DirectWire.compileRawNandGraph_failure_iff
PNP.DirectWire.CompiledRawNandGraph.candidate_gateCount
PNP.DirectWire.CompiledRawNandGraph.candidate_semantics
PNP.DirectWire.ArbitrarySupportSplice.result_gateCount
PNP.DirectWire.ArbitrarySupportSplice.compile_success_iff
PNP.DirectWire.ArbitrarySupportSplice.compile_failure_iff
PNP.DirectWire.ArbitrarySupportSplice.replacementSource_eval
PNP.DirectWire.ArbitrarySupportSplice.originalSource_eval
PNP.DirectWire.ArbitrarySupportSplice.values_solution
PNP.DirectWire.ArbitrarySupportSplice.result_semantics
PNP.DirectWire.ArbitrarySupportSplice.exterior_accounting
PNP.DirectWire.ArbitrarySupportSplice.result_exact_accounting
PNP.DirectWire.ArbitrarySupportSplice.result_strict_gain
PNP.DirectWire.ArbitrarySupportSplice.graph_rank_decreases
PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_primaryBoundary
PNP.DirectWire.ArbitrarySupportSplice.production_compiles
PNP.DirectWire.ArbitrarySupportSplice.production_agreement

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-249: formal artefact coverage becomes 225 of 227; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed wire-backed carrier preservation under physical normalization and replacement

For all finite implementations with an ordered tuple of literal computational field sources, M250 exposes ordinary outputs followed by every field without adding NAND gates. Exact pack/unpack identities retain the program and ordered sources. The actual three-pass physical normalizer preserves every ordinary output and field value, has exact trace accounting, reaches common quiescence and is idempotent. Every selected field producer belongs to the computed support interface, even when no ordinary output uses it. The actual arbitrary-support splice compiler preserves both observation classes under equality of the complete extracted open function, counts every exterior and replacement gate, transfers strict local savings and rejects cyclic literal wiring. Production predecessor closure is derived from the combined physical program without a supplied observer, order, map or successful result. Sixteen interfaces have exactly reviewed dependencies contained in propext and Quot.sound.

This represents and transports wire-backed computational fields; the wire bindings are actual input data, not a derivation of the complete manuscript carrier or every noncomputational record, role and history. Proof-only records do not become Boolean sources. The empty additional abstract profile in the physical specialization does not assert that the full manuscript profile is empty. R5/R6-R8 obligation creation and discharge, arbitrary-support Pull/Expand materializer identities, complete Package E and N1-N10, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact PCCMin and total encoded-size polynomial bounds remain open. Equal local Boolean functions do not guarantee acyclic arbitrary literal splicing; the compiler can reject them. No semantic minimum is executed, no fixed weighted checkpoint or global gate closes, deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (16)

PNP.DirectWire.WireCarrier.exposed_unpack
PNP.DirectWire.WireCarrier.unpack_exposed
PNP.DirectWire.WireCarrier.normalize_output
PNP.DirectWire.WireCarrier.normalize_field
PNP.DirectWire.WireCarrier.normalize_exact_accounting
PNP.DirectWire.WireCarrier.normalize_quiescent
PNP.DirectWire.WireCarrier.normalize_idempotent
PNP.DirectWire.WireCarrier.field_producer_visible
PNP.DirectWire.WireCarrier.splice_output
PNP.DirectWire.WireCarrier.splice_field
PNP.DirectWire.WireCarrier.splice_exact_accounting
PNP.DirectWire.WireCarrier.splice_strict_gain
PNP.DirectWire.WireCarrier.splice_checked
PNP.DirectWire.WireCarrier.splice_failure_iff
PNP.DirectWire.WireCarrier.production_boundary_isInput
PNP.DirectWire.WireCarrier.production_compiles

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-250: formal artefact coverage becomes 226 of 228; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed lost-wire projection obligations and fully charged restoration

For every finite wire-backed carrier and finite keep mask, M251 computes the actual projected NAND word and one shared materializer for all forgotten computational fields. Literal common-input concatenation restores every ordinary output and every ordered field for all valuations, with exact projected-plus-materializer physical gate charge and an output gate-count bound of twice the original. The mask derives exactly the forgotten coordinates, each with an original-source-bound R5 creation and actual restored-source-bound full-value R8 discharge. The computed independent event ledger creates and discharges every lost coordinate once and closes under replay; whole-trace identity validation rejects reusing an already discharged identity. Gain detection pays the complete materializer before requiring a strict decrease. No observer, restoration program, discharge trace or correctness certificate is supplied. Twenty-two interfaces have exactly reviewed dependencies contained in propext and Quot.sound.

This is the computational lost-wire slice of the manuscript's projection and R5/full-R8 requirements, not the full carrier or complete finite-kernel rewrite and obligation calculus. The keep mask is an input, not a derived global route. Noncomputational records, R6/R7 cancellation, arbitrary obligation-dependency DAGs, complete Package E and N1-N10, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact PCCMin and total encoded-size polynomial runtime remain open. Quotient padding is not full-field agreement. Restoration need not be a net gain or a semantic minimum. The twice-original gate bound is only an output-size fact, not a total polynomial execution or certificate-size theorem. No fixed weighted checkpoint or global gate closes, deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (22)

PNP.DirectWire.WireObligationRestoration.projected_output
PNP.DirectWire.WireObligationRestoration.projected_kept_field
PNP.DirectWire.WireObligationRestoration.materializer_forgotten_field
PNP.DirectWire.WireObligationRestoration.join_output
PNP.DirectWire.WireObligationRestoration.join_kept_field
PNP.DirectWire.WireObligationRestoration.join_forgotten_field
PNP.DirectWire.WireObligationRestoration.restored_output
PNP.DirectWire.WireObligationRestoration.restored_field
PNP.DirectWire.WireObligationRestoration.restored_exact_gate_charge
PNP.DirectWire.WireObligationRestoration.restored_gate_bound
PNP.DirectWire.WireObligationRestoration.created_exact
PNP.DirectWire.WireObligationRestoration.discharged_exact
PNP.DirectWire.WireObligationRestoration.mem_forgottenCoordinates_iff
PNP.DirectWire.WireObligationRestoration.creation_iff
PNP.DirectWire.WireObligationRestoration.discharge_iff
PNP.DirectWire.WireObligationRestoration.replay_closed
PNP.DirectWire.WireObligationRestoration.dischargeR8_full_value
PNP.DirectWire.WireObligationRestoration.gain?_isSome_iff
PNP.DirectWire.WireObligationRestoration.gain_checked
PNP.DirectWire.WireObligationRestoration.created_nodup
PNP.DirectWire.WireObligationRestoration.discharged_nodup
PNP.DirectWire.WireObligationRestoration.replay_rejects_duplicate_ids

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-251: formal artefact coverage becomes 227 of 229; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed quotient replacement lift with matched materializer costs

For every finite computational wire carrier, finite keep mask and replacement satisfying local quotient agreement on all ordinary outputs and every kept field, M252 constructs the literal replacement-plus-shared-materializer word. All ordinary outputs and all ordered computational fields agree with the original for every valuation. The same derived materializer gives exact natural gate charges and matched integer cost differences for the reference lift and the replacement expansion. Cancellation transports a saving only against the lifted reference; an original-circuit gain separately requires the full replacement-plus-materializer cost to be strictly smaller than the original. Lost-field discharges bind the original R5 source to the actual expanded source and derive full-value witnesses without any agreement about the replacement's forgotten fields. The computed gain test retains the local quotient premise and returns a complete equivalent strict gain with every field preserved. Seventeen general interfaces have exact reviewed dependencies propext and Quot.sound.

This is a computational word-level quotient lift, not arbitrary-support Pull/Expand or an embedding of the reference lift into the original circuit. The keep mask, replacement and local quotient agreement are inputs; the construction does not discover replacements or derive that local agreement. The lifted reference can exceed the original gate count, and a relative saving can leave no original gain. It does not complete the manuscript carrier, R6/R7 and general obligation-dependency DAG calculus, N1-N10, Package E, global routing, unconditional SaturatePositive, BCELReady or ZeroSlack, exact PCCMin or total encoded-size polynomial construction, runtime, output and certificate bounds. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (17)

PNP.DirectWire.WireQuotientLift.expanded_reference
PNP.DirectWire.WireQuotientLift.referenceLift_charge
PNP.DirectWire.WireQuotientLift.expanded_charge
PNP.DirectWire.WireQuotientLift.referenceLift_charge_difference
PNP.DirectWire.WireQuotientLift.expanded_charge_difference
PNP.DirectWire.WireQuotientLift.matched_materializer_charge
PNP.DirectWire.WireQuotientLift.relative_saving_iff
PNP.DirectWire.WireQuotientLift.original_gain_iff
PNP.DirectWire.WireQuotientLift.expanded_output
PNP.DirectWire.WireQuotientLift.expanded_kept_field
PNP.DirectWire.WireQuotientLift.expanded_forgotten_field
PNP.DirectWire.WireQuotientLift.expanded_field
PNP.DirectWire.WireQuotientLift.expanded_equivalent
PNP.DirectWire.WireQuotientLift.discharge_source_exact
PNP.DirectWire.WireQuotientLift.discharge_full_value
PNP.DirectWire.WireQuotientLift.checkedGain_isSome_iff
PNP.DirectWire.WireQuotientLift.CheckedGain.checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-252: formal artefact coverage becomes 228 of 230; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed original-accounted frontier replacement

For every finite computational wire carrier and keep mask, M253 computes the predecessor cone of ordinary and kept observations, then extracts its complete interface from the original fully exposed carrier. Selected forgotten field producers and exterior consumers participate in that frontier. Predecessor closure derives a primary-input-only boundary and actual replacement compiler success without a supplied support, order or success certificate. Every original exterior gate is retained exactly once. Original and expanded gate counts split into pulled or replacement gates plus the same actual exterior charge, giving matched integer differences and an exact original-saving equivalence. Equality with the complete extracted open function derives all ordinary and ordered computational field values and full discharges bound to the actual expanded sources. The computed proper-gain query separately requires proper support and strict local saving, then returns an actual original-circuit equivalent strict gain with every field preserved. Eighteen general interfaces have exact reviewed dependencies propext and Quot.sound.

This is a computational frontier lift for one input-derived visible predecessor cone, not arbitrary-support Pull/Expand across all manuscript traces. The keep mask, replacement and complete local open-function agreement are inputs. Ordinary-output or quotient-only agreement does not imply the stronger completed-frontier premise. No replacement search or automatic local agreement is proved. A whole-support saving is not a proper-support certificate. The construction does not complete the full manuscript carrier, noncomputational profile fields, R6/R7 and general obligation-dependency DAG calculus, N1-N10, Package E, global routing, unconditional SaturatePositive, BCELReady or ZeroSlack, exact PCCMin or total encoded-size polynomial construction, runtime, output and certificate bounds. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (18)

PNP.DirectWire.WireFrontierLift.ordinary_output_selected
PNP.DirectWire.WireFrontierLift.kept_field_selected
PNP.DirectWire.WireFrontierLift.records_predecessor_closed
PNP.DirectWire.WireFrontierLift.selected_field_in_frontier
PNP.DirectWire.WireFrontierLift.primary_boundary
PNP.DirectWire.WireFrontierLift.original_charge
PNP.DirectWire.WireFrontierLift.compile_isSome
PNP.DirectWire.WireFrontierLift.expanded_charge
PNP.DirectWire.WireFrontierLift.matched_original_charge
PNP.DirectWire.WireFrontierLift.original_gain_iff
PNP.DirectWire.WireFrontierLift.expanded_output
PNP.DirectWire.WireFrontierLift.expanded_field
PNP.DirectWire.WireFrontierLift.expanded_equivalent
PNP.DirectWire.WireFrontierLift.discharge_source_exact
PNP.DirectWire.WireFrontierLift.discharge_full_value
PNP.DirectWire.WireFrontierLift.proper_iff_exterior_positive
PNP.DirectWire.WireFrontierLift.checkedProperGain_isSome_iff
PNP.DirectWire.WireFrontierLift.ProperGain.checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-253: formal artefact coverage becomes 229 of 231; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed full-mode wire cancellation

For every finite computational wire carrier and keep mask, M254 computes canonical retained representatives by literal source identity in the original ordinary outputs and kept fields. The precise local quotient-agreement premise derives each matched forgotten wire's full value in the actual replacement. A computed resolved mask selects one actual shared materializer for the remaining unresolved wires, with an explicit zero-gate case when all fields resolve. The expanded word preserves every ordinary output and ordered computational field, and has exactly replacement gates plus its actual materializer charge. Computed R6 cancellations and R8 restorations carry full-value witnesses bound to that expanded source. Their generated R5/discharge ledger covers exactly the forgotten coordinates, closes with no pending obligations and rejects creation-identity reuse across the whole transcript, including already discharged entries. The fully paid whole-word gain query compares the actual expansion with the original gate count. Twenty-six general interfaces have reviewed propext-only or propext-and-Quot.sound dependencies.

This is an original-source-identity computational R6 case, not every semantic cancellation or the complete manuscript obligation calculus. The keep mask, replacement and precise local quotient agreement are inputs; forgotten-field equality, supplied representatives, materializer weights and global correctness certificates are not. Syntactically different but semantically equal wires may remain unresolved. No universal comparison with independently normalized earlier materializers is proved. A whole-word strict gain is not a proper-support Package E certificate. The full manuscript carrier, noncomputational profile fields, R7 and arbitrary dependency DAGs, all-trace N1-N10 normalization, complete Package E, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact PCCMin and total encoded-size polynomial construction, runtime, output and certificate bounds remain open. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (26)

PNP.DirectWire.WireMatchedCancellation.representative_isSome_iff
PNP.DirectWire.WireMatchedCancellation.observation_value
PNP.DirectWire.WireMatchedCancellation.Representative.full_value
PNP.DirectWire.WireMatchedCancellation.allResolved_sound
PNP.DirectWire.WireMatchedCancellation.charge_allResolved
PNP.DirectWire.WireMatchedCancellation.missing_unresolved_field
PNP.DirectWire.WireMatchedCancellation.charge_bound
PNP.DirectWire.WireMatchedCancellation.visible_resolved_field
PNP.DirectWire.WireMatchedCancellation.expanded_charge
PNP.DirectWire.WireMatchedCancellation.expanded_output
PNP.DirectWire.WireMatchedCancellation.expanded_field
PNP.DirectWire.WireMatchedCancellation.expanded_equivalent
PNP.DirectWire.WireMatchedCancellation.Discharge.full_value
PNP.DirectWire.WireMatchedCancellation.discharge_source_exact
PNP.DirectWire.WireMatchedCancellation.discharge_isR6_iff
PNP.DirectWire.WireMatchedCancellation.discharge_full_value
PNP.DirectWire.WireMatchedCancellation.checkedGain_isSome_iff
PNP.DirectWire.WireMatchedCancellation.CheckedGain.checked
PNP.DirectWire.WireMatchedCancellation.created_exact
PNP.DirectWire.WireMatchedCancellation.discharged_exact
PNP.DirectWire.WireMatchedCancellation.creation_iff
PNP.DirectWire.WireMatchedCancellation.discharge_iff
PNP.DirectWire.WireMatchedCancellation.created_nodup
PNP.DirectWire.WireMatchedCancellation.discharged_nodup
PNP.DirectWire.WireMatchedCancellation.replay_closed
PNP.DirectWire.WireMatchedCancellation.replay_rejects_duplicate_ids

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-254: formal artefact coverage becomes 230 of 232; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed unary full-word realization

For every unary computational wire carrier, with arbitrary original gate count, ordered ordinary outputs and computational fields, M255 derives both unary observation values from the actual source and constructs a complete zero-or-one-gate realization. Constants and the input cost zero gates; every negated observation shares the same actual NOT gate. The result preserves every ordinary output and computational field at every unary valuation. Its exact gate formula is minimal among all equivalent full computational carriers: a zero-gate source cannot negate the only boundary input. The constructor accepts no replacement, truth table, local agreement or minimizer. Source-exact R7 discharge witnesses for original R5 identities refer to the actual computed program and the original full field values. The whole-word strict-gain query succeeds whenever any equivalent full unary carrier is smaller. Eighteen general interfaces have reviewed axiom closures: five are axiom-free and thirteen use only propext and Quot.sound.

This is a complete unary computational word realization component for manuscript R7, not an arbitrary ambient-cut embedding, every R7 case or the complete manuscript obligation calculus. Minimum size is relative to all exposed computational observations, not ordinary outputs alone. A whole-word strict gain is not a proper-support Package E certificate. The keep mask and source-bound R5 identity are used only by the discharge interface; no supplied full-value agreement is a construction premise. There is no enumeration of implementations, but evaluating two unary inputs with recursive Program.eval does not prove polynomial encoded runtime. The full manuscript carrier, noncomputational profile fields, arbitrary obligation dependency DAGs, all-trace N1-N10 normalization, complete Package E, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and total encoded-size polynomial construction, runtime, output and certificate bounds remain open. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (18)

PNP.DirectWire.WireUnaryRealization.observation_value
PNP.DirectWire.WireUnaryRealization.needsNegation_iff
PNP.DirectWire.WireUnaryRealization.implementation_value
PNP.DirectWire.WireUnaryRealization.realize_output
PNP.DirectWire.WireUnaryRealization.realize_field
PNP.DirectWire.WireUnaryRealization.realize_equivalent
PNP.DirectWire.WireUnaryRealization.realize_full_equivalent
PNP.DirectWire.WireUnaryRealization.realize_gateCount
PNP.DirectWire.WireUnaryRealization.negation_requires_gate
PNP.DirectWire.WireUnaryRealization.realize_minimal
PNP.DirectWire.WireUnaryRealization.realize_nonincrease
PNP.DirectWire.WireUnaryRealization.realize_gate_bound
PNP.DirectWire.WireUnaryRealization.R7Discharge.full_value
PNP.DirectWire.WireUnaryRealization.dischargeR7_source_exact
PNP.DirectWire.WireUnaryRealization.dischargeR7_full_value
PNP.DirectWire.WireUnaryRealization.checkedGain_isSome_iff
PNP.DirectWire.WireUnaryRealization.checkedGain_complete
PNP.DirectWire.WireUnaryRealization.CheckedGain.checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-255: formal artefact coverage becomes 231 of 233; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed constant and unary frontier replacement

For arbitrary computational wire carriers, original gate counts, ordered ordinary outputs, computational fields and keep masks, M256 computes the visible predecessor cone and its completed full frontier. When the actual incoming boundary has zero or one port, it derives a zero-gate constant word or the minimum complete unary word, preserving every local output at every open valuation. No replacement, truth table, semantic agreement, wire map, compilation order, compiler result or minimizer is supplied. The actual primary-boundary compiler substitutes this word into the original exterior, retained exactly once. Every ordinary output and computational field is preserved, including forgotten selected frontier fields and exterior fields depending on other ambient inputs. The result has exact replacement-plus-exterior gate count and cannot increase the original count. Source-bound R7 witnesses discharge original R5 identities with their full values in the actual expanded program. The proper-gain query computes boundary recognition, positive actual exterior and strict local saving separately; it succeeds whenever any complete local realization is smaller on such a proper recognized cone. Thirty general interfaces have reviewed axiom closures: two are axiom-free, one uses only Quot.sound and twenty-seven use only propext and Quot.sound.

This is source-derived constant/unary R7 realization for the computed visible predecessor cone, not every arbitrary ambient support or an external-gate boundary. Minimum size is relative to the complete fixed local frontier, not all ambient circuits with different exteriors. A whole-support saving is not a proper-support Package E certificate. More-than-unary boundaries are rejected rather than supplied with correctness certificates. Finite source evaluation and actual compiler termination are not encoded-size polynomial runtime theorems. The full manuscript carrier, noncomputational profile fields, arbitrary obligation dependency DAGs, every R5-R8 interaction, all-trace N1-N10 normalization, complete Package E, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and total encoded-size polynomial construction, runtime, output and certificate bounds remain open. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (30)

PNP.DirectWire.WireUnaryFrontier.constantWord_value
PNP.DirectWire.WireUnaryFrontier.constantWord_gateCount
PNP.DirectWire.WireUnaryFrontier.unaryWord_value
PNP.DirectWire.WireUnaryFrontier.unaryWord_minimal
PNP.DirectWire.WireUnaryFrontier.unaryWord_gate_bound
PNP.DirectWire.WireUnaryFrontier.localWord_value
PNP.DirectWire.WireUnaryFrontier.localWord_minimal
PNP.DirectWire.WireUnaryFrontier.localWord_nonincrease
PNP.DirectWire.WireUnaryFrontier.localWord_gate_bound
PNP.DirectWire.WireUnaryFrontier.replacement_agreement
PNP.DirectWire.WireUnaryFrontier.replacement_minimal
PNP.DirectWire.WireUnaryFrontier.replacement_nonincrease
PNP.DirectWire.WireUnaryFrontier.replacement_gate_bound
PNP.DirectWire.WireUnaryFrontier.replacement_zero_gateCount
PNP.DirectWire.WireUnaryFrontier.expanded_output
PNP.DirectWire.WireUnaryFrontier.expanded_field
PNP.DirectWire.WireUnaryFrontier.expanded_equivalent
PNP.DirectWire.WireUnaryFrontier.expanded_charge
PNP.DirectWire.WireUnaryFrontier.expanded_nonincrease
PNP.DirectWire.WireUnaryFrontier.expanded_gain_iff
PNP.DirectWire.WireUnaryFrontier.attempt_isSome_iff
PNP.DirectWire.WireUnaryFrontier.attempt_output
PNP.DirectWire.WireUnaryFrontier.attempt_field
PNP.DirectWire.WireUnaryFrontier.attempt_nonincrease
PNP.DirectWire.WireUnaryFrontier.attempt_charge
PNP.DirectWire.WireUnaryFrontier.dischargeR7_source_exact
PNP.DirectWire.WireUnaryFrontier.dischargeR7_full_value
PNP.DirectWire.WireUnaryFrontier.checkedProperGain_isSome_iff
PNP.DirectWire.WireUnaryFrontier.checkedProperGain_complete
PNP.DirectWire.WireUnaryFrontier.ProperGain.checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-256: formal artefact coverage becomes 232 of 234; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed constant and unary replacement on arbitrary completed supports

For arbitrary finite computational wire carriers, original gate counts, ordered ordinary outputs, computational fields and finite terminal-record supports, M257 derives the complete boundary and frontier from the actual exposed program. Every actual zero- or one-port boundary has a computed minimum complete local word with at most one shared NOT gate. General open-evaluation prefix causality proves that a selected frontier gate before the sole external boundary gate is represented by a literal constant. A rank derived from original gate indices then proves well-foundedness and successful compilation of this actual replacement, without a supplied rank, acyclicity certificate, order, agreement, replacement program or compiler result. Empty and primary-input boundaries are covered as well as a sole external-gate boundary. The actual exterior is retained exactly once. Every ordinary output and computational field is preserved at every ambient valuation, with exact replacement-plus-exterior charge, nonincrease and equivalent strict local-to-global saving. Source-exact full-value R7 witnesses discharge the original R5 identities. The proper-gain query computes boundary recognition, positive exterior and strict local saving, and succeeds whenever any complete local realization is smaller on a recognized proper support. Thirty-one general interfaces have reviewed axiom closures: one is axiom-free, one uses only Quot.sound and twenty-nine use only propext and Quot.sound.

Arbitrary support refers to the choice of finite physical support in a computational wire carrier, not arbitrary boundary width or the full manuscript carrier. Boundaries with more than one incoming port are rejected. The minimum is over complete local open realizations for the fixed extracted frontier, not over all ambient circuits or different exteriors. A whole-support saving is not a proper-support Package E certificate. Prefix causality and the source-derived rank prove termination of this compiler, not uniformly polynomial encoded-size execution. Noncomputational profile fields, arbitrary obligation dependency DAGs, every R5-R8 interaction, all-trace N1-N10 normalization, complete Package E, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and total encoded-size polynomial construction, runtime, output and certificate bounds remain open. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (31)

PNP.DirectWire.terminalOpenGateEvaluation_prefix_congr
PNP.DirectWire.terminalOpenGateEvaluation_single_gate_prefix
PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_singleGateBoundary
PNP.DirectWire.WireUnaryArbitrarySupport.constantWord_source
PNP.DirectWire.WireUnaryArbitrarySupport.unaryWord_source_of_constant
PNP.DirectWire.WireUnaryArbitrarySupport.localWord_source_of_constant
PNP.DirectWire.WireUnaryArbitrarySupport.replacement_agreement
PNP.DirectWire.WireUnaryArbitrarySupport.replacement_gate_bound
PNP.DirectWire.WireUnaryArbitrarySupport.replacement_minimal
PNP.DirectWire.WireUnaryArbitrarySupport.replacement_nonincrease
PNP.DirectWire.WireUnaryArbitrarySupport.replacement_early_constant
PNP.DirectWire.WireUnaryArbitrarySupport.graph_wellFounded
PNP.DirectWire.WireUnaryArbitrarySupport.compile_isSome
PNP.DirectWire.WireUnaryArbitrarySupport.original_charge
PNP.DirectWire.WireUnaryArbitrarySupport.expanded_output
PNP.DirectWire.WireUnaryArbitrarySupport.expanded_field
PNP.DirectWire.WireUnaryArbitrarySupport.expanded_equivalent
PNP.DirectWire.WireUnaryArbitrarySupport.expanded_charge
PNP.DirectWire.WireUnaryArbitrarySupport.expanded_nonincrease
PNP.DirectWire.WireUnaryArbitrarySupport.expanded_gain_iff
PNP.DirectWire.WireUnaryArbitrarySupport.proper_iff_exterior_positive
PNP.DirectWire.WireUnaryArbitrarySupport.attempt_isSome_iff
PNP.DirectWire.WireUnaryArbitrarySupport.attempt_output
PNP.DirectWire.WireUnaryArbitrarySupport.attempt_field
PNP.DirectWire.WireUnaryArbitrarySupport.attempt_nonincrease
PNP.DirectWire.WireUnaryArbitrarySupport.attempt_charge
PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_source_exact
PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_full_value
PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_isSome_iff
PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_complete
PNP.DirectWire.WireUnaryArbitrarySupport.ProperGain.checked

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-257: formal artefact coverage becomes 233 of 235; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed complete search for proper constant and unary R7 gains

For arbitrary finite computational wire carriers, original gate counts, ordinary outputs and full computational fields, M258 computes a complete family of proper zero/unary support-gain candidates from the actual program. Optional boundary choices use only source wires actually consumed by gates, plus no boundary. For each choice and omitted gate, a topological maximal scan derives a support with at most one actual incoming wire and a nonempty exterior; canonical singleton supports handle one-gate savings. Any arbitrary proper zero/unary support is contained in the corresponding maximal candidate, and extraction is invariant under repeated or metadata records selecting the same gates. A support with at least two gates yields a strict saving because the complete zero/unary frontier word uses at most one shared NOT; a one-gate saving transfers to its canonical singleton. The carrier-only executable search is therefore complete whenever any proper zero/unary support admits a strictly smaller equivalent complete local word, without a supplied support family, replacement, rank, order, compiler result or completeness certificate. An accepted result constructs the actual expanded carrier, preserves every ordinary output and computational field at every valuation, charges the original exterior once, gives a strict fully paid saving and retains source-exact full-value R7 discharges for original R5 identities. A negative result excludes every such gain in this exact class. With g original gates, the computed family has at most (2*g+1)*g+g entries, each containing at most g gate records.

Completeness is for proper physical supports with zero or one actual incoming boundary in a computational wire carrier. It is not completeness for all boundary widths, every R7 case or all ambient circuit optimizations. A negative search result is not global minimality or unconditional ZeroSlack; a guarded two-boundary duplicate fixture has an explicit smaller global realization while this scoped search correctly returns no gain. A whole-support saving is not a proper-support Package E certificate. Boundary-choice enumeration excludes unused declared inputs, but inherited physical-port extraction and compilation retain their own execution costs. The physical candidate and record counts are not a theorem of total uniformly polynomial encoded-input-size execution, output size or certificate size. The full manuscript carrier, noncomputational profile fields, arbitrary obligation dependency DAGs, every R5-R8 interaction, all-trace N1-N10 normalization, complete Package E, global routing, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and its complete polynomial bounds remain open. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (36)

PNP.DirectWire.WireUnarySupportSearch.maximalSelection_admissible
PNP.DirectWire.WireUnarySupportSearch.maximalSelection_contains
PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected_iff
PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected
PNP.DirectWire.WireUnarySupportSearch.admissible_boundary
PNP.DirectWire.WireUnarySupportSearch.admissible_boundary_small
PNP.DirectWire.WireUnarySupportSearch.candidateRecords_boundary
PNP.DirectWire.WireUnarySupportSearch.candidateRecords_proper
PNP.DirectWire.WireUnarySupportSearch.consumedWires_length
PNP.DirectWire.WireUnarySupportSearch.boundary_mem_consumedWires
PNP.DirectWire.WireUnarySupportSearch.boundaryChoices_length
PNP.DirectWire.WireUnarySupportSearch.candidateFamily_length
PNP.DirectWire.WireUnarySupportSearch.candidateFamily_maximal_mem
PNP.DirectWire.WireUnarySupportSearch.candidateFamily_singleton_mem
PNP.DirectWire.WireUnarySupportSearch.supportChoice_wire_mem
PNP.DirectWire.WireUnarySupportSearch.supportChoice_of_mem
PNP.DirectWire.WireUnarySupportSearch.supportChoice_external
PNP.DirectWire.WireUnarySupportSearch.supportChoice_mem
PNP.DirectWire.WireUnarySupportSearch.support_admissible
PNP.DirectWire.WireUnarySupportSearch.support_contained_in_candidate
PNP.DirectWire.WireUnarySupportSearch.selected_length_mono
PNP.DirectWire.WireUnarySupportSearch.selected_length_le
PNP.DirectWire.WireUnarySupportSearch.candidateFamily_entry_length
PNP.DirectWire.WireUnarySupportSearch.extracted_gateCount_mono
PNP.DirectWire.WireUnarySupportSearch.singleton_selection
PNP.DirectWire.WireUnarySupportSearch.checkedGain_selection_invariant
PNP.DirectWire.WireUnarySupportSearch.candidateFamily_complete
PNP.DirectWire.WireUnarySupportSearch.findGain_complete
PNP.DirectWire.WireUnarySupportSearch.findGain_member
PNP.DirectWire.WireUnarySupportSearch.findGain_records_bound
PNP.DirectWire.WireUnarySupportSearch.GainResult.checked
PNP.DirectWire.WireUnarySupportSearch.findGain_none_excludes
PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_source_exact
PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_full_value
PNP.DirectWire.WireUnarySupportSearch.findReplacement_isSome
PNP.DirectWire.WireUnarySupportSearch.findReplacement_sound

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-258: formal artefact coverage becomes 234 of 236; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed full-field zero/unary descent and normalization closure

For every finite computational wire carrier, M259 computes a whole-span zero/unary saving branch and combines it with the complete proper-support search. The whole-span branch selects all physical gates, has zero exterior charge and is kept distinct from proper-support R7. The combined carrier-only search is complete whenever any support with zero or one actual incoming boundary admits a strictly smaller equivalent complete local word; neither a support family nor a replacement or completeness certificate is supplied by the caller. Every accepted branch builds the actual smaller carrier and preserves all ordinary outputs and every computational field at every valuation, with exact original-gate accounting. A well-founded executable closure repeatedly performs physical normalization, searches for a proper or whole-span gain, expands an accepted gain and restarts normalization. Its derived trace proves termination, full-field preservation, common physical quiescence and absence of every gain in this scoped zero/unary class. It proves exact gate savings, bounds normalization and gain iterations by the retired gates, bounds search calls including the final negative call, and proves output idempotence. Semantic reference minima occur only in specifications: their invariance yields exact residual-slack retirement and corresponding iteration and search-call bounds, without reference-minimum enumeration in the algorithm.

The stopping result is restricted to physical normalization and zero/one-actual-boundary computational gains. It is not global minimality: a guarded physically quiescent common fixed point has an explicit smaller equivalent carrier and strictly positive global residual slack. Whole-span descent is not relabelled as a proper-support Package E certificate. Preserving every computational field does not reconstruct the full manuscript carrier, noncomputational profile fields or arbitrary obligation dependency DAGs. Wider boundaries, every R5-R8 interaction, all-trace N1-N10 normalization, complete Package E, global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and complete encoded-size polynomial runtime, output and certificate bounds remain open. A gate-decrease or search-call bound is not a total polynomial execution theorem; inherited extraction, compilation and candidate-search costs still require their own bounds. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (27)

PNP.DirectWire.WireZeroUnaryClosure.whole_selected
PNP.DirectWire.WireZeroUnaryClosure.whole_exterior
PNP.DirectWire.WireZeroUnaryClosure.whole_gateCount
PNP.DirectWire.WireZeroUnaryClosure.whole_not_proper
PNP.DirectWire.WireZeroUnaryClosure.all_gates_of_zero_exterior
PNP.DirectWire.WireZeroUnaryClosure.WholeGain.checked
PNP.DirectWire.WireZeroUnaryClosure.wholeGain_isSome_iff
PNP.DirectWire.WireZeroUnaryClosure.wholeGain_complete
PNP.DirectWire.WireZeroUnaryClosure.Gain.full_field
PNP.DirectWire.WireZeroUnaryClosure.Gain.branch_boundary
PNP.DirectWire.WireZeroUnaryClosure.Gain.exact_accounting
PNP.DirectWire.WireZeroUnaryClosure.nextGain_isSome_iff
PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_iff
PNP.DirectWire.WireZeroUnaryClosure.nextGain_complete
PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_excludes
PNP.DirectWire.WireZeroUnaryClosure.normalization_accounting
PNP.DirectWire.WireZeroUnaryClosure.normalization_iterations
PNP.DirectWire.WireZeroUnaryClosure.Trace.checked
PNP.DirectWire.WireZeroUnaryClosure.Trace.searchCalls_le
PNP.DirectWire.WireZeroUnaryClosure.run_checked
PNP.DirectWire.WireZeroUnaryClosure.run_of_stopped
PNP.DirectWire.WireZeroUnaryClosure.run_idempotent
PNP.DirectWire.WireZeroUnaryClosure.run_no_smaller_zeroUnary
PNP.DirectWire.WireZeroUnaryClosure.run_referenceMinimum
PNP.DirectWire.WireZeroUnaryClosure.run_residualSlack
PNP.DirectWire.WireZeroUnaryClosure.run_gainIterations_le_residualSlack
PNP.DirectWire.WireZeroUnaryClosure.run_searchCalls_le_residualSlack

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-259: formal artefact coverage becomes 235 of 237; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-bounded ordered physical boundary extraction

For arbitrary finite program dimensions and any list of terminal primitive records, M260 computes the incoming physical boundary from nonconstant sources of actual gates. It filters those occurrences with the existing physical crossing predicate, removes duplicates and sorts by the canonical primary-input-before-gate-output coordinate. Every boundary crossing is derived from an actual gate source. The resulting list is proved exactly equal, including order and multiplicity, to the former ambient-wire filtered reference. Source occurrences and the emitted boundary each have length at most twice the physical gate count, independent of unused declared input slots. The active terminalBoundaryPorts implementation uses this source-driven construction. Public reference, length, duplicate-free and order theorems preserve the existing physical extraction and downstream support interfaces. A generic finite-list canonicalizer proves exact equality with any ordered duplicate-free reference under an injective coordinate map, without enumerating the ambient type. Guarded execution exercises exact small reference lists and sparse programs with a billion declared inputs; those large fixtures do not execute the ambient reference.

Occurrence and output bounds are structural size bounds, not total encoded-input-size polynomial execution theorems. The reference equality preserves the existing physical semantics; it does not establish a new global minimization result. The old ambient enumeration remains only as a theorem-side specification, never the active boundary implementation. No caller-supplied boundary or completeness certificate is introduced. The full manuscript carrier, arbitrary obligation dependency DAGs, every normalization and gain interaction, complete Package E and global route coverage remain open. These results do not prove unconditional SaturatePositive, BCELReady or ZeroSlack, exact general PCCMin, or total polynomial runtime, output and certificate bounds for the complete construction. Runtime execution is regression evidence, not theorem authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (23)

PNP.DirectWire.SourceListOrder.mem_unique
PNP.DirectWire.SourceListOrder.unique_nodup
PNP.DirectWire.SourceListOrder.unique_length_le
PNP.DirectWire.SourceListOrder.mem_canonical
PNP.DirectWire.SourceListOrder.canonical_nodup
PNP.DirectWire.SourceListOrder.canonical_length_le
PNP.DirectWire.SourceListOrder.canonical_ordered
PNP.DirectWire.SourceListOrder.ordered_eq_of_mem
PNP.DirectWire.SourceListOrder.canonical_eq_reference
PNP.DirectWire.TerminalSupportWire.orderCode_injective
PNP.DirectWire.allTerminalSupportWires_strictOrder
PNP.DirectWire.Source.mem_terminalWireOccurrences_iff
PNP.DirectWire.Source.terminalWireOccurrences_length
PNP.DirectWire.terminalSourceWireOccurrences_length
PNP.DirectWire.terminalBoundaryWire_mem_sourceOccurrences
PNP.DirectWire.terminalBoundaryPortsSourceDriven_eq_reference
PNP.DirectWire.terminalBoundaryPortsSourceDriven_length
PNP.DirectWire.terminalBoundaryPortsSourceDriven_nodup
PNP.DirectWire.terminalBoundaryPortsSourceDriven_ordered
PNP.DirectWire.terminalBoundaryPorts_reference
PNP.DirectWire.terminalBoundaryPorts_length
PNP.DirectWire.terminalBoundaryPorts_nodup
PNP.DirectWire.terminalBoundaryPorts_ordered

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-260: formal artefact coverage becomes 236 of 238; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Context-aware nested open-support and four-corner transport

For arbitrary finite candidate dimensions, terminal record lists and ordinary selected-gate inclusions, M261 computes a smaller open boundary valuation from the larger support evaluator. A wire internalized in the larger support receives its computed gate value, not an independent ambient bit. For every valuation on the larger open boundary, selected gates and retained interface producers have exactly the same Boolean values after this substitution. The complete valuation maps satisfy identity and three-support composition. Actual support-square inclusions derive the four leg maps, and both join-to-meet paths agree as valuation functions. Retained output values agree for extracted implementations, arbitrary valid full realizations and the actual canonical full and quotient local-minimum families. These semantic maps come from the original open carrier, not invented internal gates of a minimum realization. The existing unconstrained-ambient coherence classifier and its exact mismatch results are preserved as a different relation.

The theorem covers arbitrary larger open-boundary valuations, not only whole-circuit executions, and introduces no caller-supplied transport or correctness certificate. Retained Boolean-output transport does not prove equality of arbitrary implementation-dependent observers or profiles, physically glue minimum circuits, or establish coherent charge and obligation ownership. Canonical finite reference minima supply specification-level comparison objects, not an efficient executable minimizer. The full manuscript carrier, arbitrary obligation dependency DAGs, complete Package E and global route coverage remain open. This result does not prove unconditional SaturatePositive, BCELReady or ZeroSlack, exact general PCCMin, or total encoded-input-size polynomial runtime, output and certificate bounds for the complete construction. Runtime fixtures are regression evidence, not proof authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (14)

PNP.DirectWire.terminalOpenGateEvaluation_pullback
PNP.DirectWire.terminalOpenSupportSemantics_pullback
PNP.DirectWire.terminalBoundaryPullback_identity
PNP.DirectWire.terminalBoundaryPullback_compose
PNP.DirectWire.TerminalOptimumLegTransport.selectedGateTransport
PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_left
PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_right
PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_square
PNP.DirectWire.TerminalOptimumLegTransport.extracted_retained_semantics
PNP.DirectWire.TerminalOptimumLegTransport.realization_retained_semantics
PNP.DirectWire.TerminalFourCornerOptimumFamily.full_retained_semantics
PNP.DirectWire.TerminalFourCornerOptimumFamily.quotient_retained_semantics
PNP.DirectWire.TerminalFourCornerCarrier.canonicalFull_retained_semantics
PNP.DirectWire.TerminalFourCornerCarrier.canonicalQuotient_retained_semantics

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-261: formal artefact coverage becomes 237 of 239; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Total source-ordered charged arbitrary-support expansion

For arbitrary finite candidate, support, replacement and computational-field dimensions, M262 derives an actual acyclic raw NAND graph and executable compiled expansion from source data. Each exterior gate is retained once and each distinct retained physical interface producer owns one complete replacement copy. Primary and earlier gate boundary ports retain actual values; only later gate-valued ports are deliberately masked, and a computed source rank decreases along every actual edge. Compilation requires no supplied rank, order, semantic or compiler-success certificate. Under complete local open-function equality, masking preserves the selected output for every open boundary valuation, the derived graph valuation satisfies every NAND equation, and every original ordered output and computational field retains its full value. Repeated literal references share the same actual compiled source. Exterior and copy ownership are injective and disjoint and cover every emitted gate. Existing R5 creations retain their coordinate and original full source value. Actual cost is E + K * R and strict original-size saving is equivalent to K * R < S, with properness S < G separately required.

This is a source-derived physical construction at arbitrary finite widths, not matched-kappa Pull/Expand or unrestricted CompatibleReplacement/SlackLaw from merely R < S. Full local open-function agreement is required for semantics; quotient-only or ordinary-output-only equality does not suffice for full computational fields. Distinct equal-valued physical producers are not merged, and repeated physical copies are not free. The inherited cyclic literal splice remains rejected; existing cone and unary constructions retain their own bounds. Literal R5 binding transport is not the complete R5–R8 event calculus or an arbitrary semantic obligation DAG. Arbitrary implementation-dependent observers, profile histories, the full manuscript carrier, complete Package E, global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and total encoded-input-size polynomial runtime, output and certificate bounds remain open. Runtime fixtures are regression evidence, not proof authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (29)

PNP.DirectWire.WireCausalExpansion.graph_rank_decreases
PNP.DirectWire.WireCausalExpansion.graph_wellFounded
PNP.DirectWire.WireCausalExpansion.compile_success
PNP.DirectWire.WireCausalExpansion.compiled_spec
PNP.DirectWire.WireCausalExpansion.expanded_gateCount
PNP.DirectWire.WireCausalExpansion.masked_replacement_output
PNP.DirectWire.WireCausalExpansion.replacementSource_eval
PNP.DirectWire.WireCausalExpansion.originalSource_eval
PNP.DirectWire.WireCausalExpansion.values_solution
PNP.DirectWire.WireCausalExpansion.expanded_semantics
PNP.DirectWire.WireCausalExpansion.expanded_smaller_iff
PNP.DirectWire.WireCausalExpansion.single_interface_smaller
PNP.DirectWire.WireCausalExpansion.interface_nodup
PNP.DirectWire.WireCausalExpansion.interface_owner_injective
PNP.DirectWire.WireCausalExpansion.exteriorPosition_injective
PNP.DirectWire.WireCausalExpansion.copyPosition_injective
PNP.DirectWire.WireCausalExpansion.exteriorPosition_ne_copyPosition
PNP.DirectWire.WireCausalExpansion.raw_node_ownership
PNP.DirectWire.WireCausalExpansion.expanded_gate_ownership
PNP.DirectWire.WireCausalExpansion.expanded_source
PNP.DirectWire.WireCausalExpansion.expanded_source_equal
PNP.DirectWire.WireCausalExpansion.expandedCarrier_output
PNP.DirectWire.WireCausalExpansion.expandedCarrier_field
PNP.DirectWire.WireCausalExpansion.expandedCarrier_gateCount
PNP.DirectWire.WireCausalExpansion.expandedCarrier_smaller_iff
PNP.DirectWire.WireCausalExpansion.expandedCarrier_proper_and_smaller
PNP.DirectWire.WireCausalExpansion.expandedCarrier_source_equal
PNP.DirectWire.WireCausalExpansion.expandedR5Creation_coordinate
PNP.DirectWire.WireCausalExpansion.expandedR5Creation_fullWitness

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-262: formal artefact coverage becomes 238 of 240; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed dependency-ordered physical obligation histories

For arbitrary finite input, output, computational-field and event dimensions, M263 computes a complete dependency order from raw event identities, explicit predecessors and intrinsic creation references. Duplicate identities, missing references and cyclic graphs reject. The scheduler succeeds exactly when the actual finite dependency relation is well-founded. The history constructor executes one evolving physical carrier from the original source, without caller-supplied order, rank, state, full-value witness or charge data. R5 captures the actual pre-drop carrier; physical normalization preserves open snapshots; source-identity R6 computes a visible representative; R8 appends and charges the complete materializer from the matching creation snapshot. Full reads require an available field, and final open obligations reject. Every successful history executes every event exactly once in dependency order, every creation discharges strictly later with its full source binding, and every ordinary output and computational field retains its original value for every valuation. Final physical gates plus actual normalization removals equal initial physical gates plus all appended materializer charges.

Reviewed theorem interfaces (46)

PNP.DependencyScheduler.ReadyStep.remaining_lt
PNP.DependencyScheduler.Schedule.at_injective
PNP.DependencyScheduler.Schedule.order_complete
PNP.DependencyScheduler.Schedule.order_length
PNP.DependencyScheduler.Schedule.order_nodup
PNP.DependencyScheduler.Schedule.wellFounded
PNP.DependencyScheduler.Stop.complete_of_wellFounded
PNP.DependencyScheduler.Stop.unresolved_predecessor
PNP.DependencyScheduler.compile_failure_iff
PNP.DependencyScheduler.compile_success_iff
PNP.DirectWire.WireObligationHistory.State.cancel_full_value
PNP.DirectWire.WireObligationHistory.State.cancel_gateCount
PNP.DirectWire.WireObligationHistory.State.closed_field
PNP.DirectWire.WireObligationHistory.State.create_gateCount
PNP.DirectWire.WireObligationHistory.State.create_source_snapshot
PNP.DirectWire.WireObligationHistory.State.currentAgreement
PNP.DirectWire.WireObligationHistory.State.normalize_gate_balance
PNP.DirectWire.WireObligationHistory.State.restore_full_value
PNP.DirectWire.WireObligationHistory.State.restore_gate_charge
PNP.DirectWire.WireObligationHistory.OrderedEvents.identities_nodup
PNP.DirectWire.WireObligationHistory.OrderedEvents.order_complete
PNP.DirectWire.WireObligationHistory.OrderedEvents.order_length
PNP.DirectWire.WireObligationHistory.OrderedEvents.order_nodup
PNP.DirectWire.WireObligationHistory.completeReferences_iff
PNP.DirectWire.WireObligationHistory.graph_dependency_iff
PNP.DirectWire.WireObligationHistory.orderEvents_failure_iff
PNP.DirectWire.WireObligationHistory.orderEvents_success_iff
PNP.DirectWire.WireObligationHistory.uniqueIDs_iff
PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle
PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before
PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_count
PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_identities_nodup
PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field
PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output
PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance
PNP.DirectWire.WireObligationHistory.Execution.creationsClosed_of_finalClosed
PNP.DirectWire.WireObligationHistory.Execution.pending_persists_or_discharged
PNP.DirectWire.WireObligationHistory.Execution.record_identities
PNP.DirectWire.WireObligationHistory.Execution.total_charge
PNP.DirectWire.WireObligationHistory.Execution.total_removed
PNP.DirectWire.WireObligationHistory.State.isClosed_sound
PNP.DirectWire.WireObligationHistory.Transition.charged_eq
PNP.DirectWire.WireObligationHistory.Transition.created_pending
PNP.DirectWire.WireObligationHistory.Transition.dischargeRecord_binding
PNP.DirectWire.WireObligationHistory.Transition.pending_persists_or_discharged
PNP.DirectWire.WireObligationHistory.Transition.removed_eq

This is the computational R5/R6/R8 history component, not the complete manuscript obligation calculus or Package E. Acyclicity guarantees a computed order, not a valid lifecycle or confluence of underspecified event graphs. R5 projection alone removes no physical gates; repeated restorations receive no free cross-snapshot sharing, and restoration can increase physical size. Quotient-only agreement cannot discharge a full obligation. Full R7 and other R1-R9 semantics, all N1-N10 transports, arbitrary observers and profile histories, noncomputational carrier records, matched-kappa Pull/Expand, complete Package E, global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and complete encoded-input-size polynomial runtime, output and certificate bounds remain open. Runtime fixtures are regression evidence, not proof authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-263: formal artefact coverage: 239 of 241; risk-weighted estimate: 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-derived closed-history literal arbitrary-support replacement

For arbitrary finite candidate, support and raw-event dimensions, the constructor extracts actual computational fields with zero duplicate ordinary outputs, executes the existing closed R5/R6/R8 history, and derives literal-splice acyclicity from original gate labels and actual causal bounds. The current carrier and every pending snapshot preserve those bounds through actual normalization, source-identity cancellation and paid captured restoration. The existing literal graph compiler then succeeds for every accepted closed history without a caller-supplied replacement, rank, order or semantic certificate. All ordered original outputs are preserved; every exterior gate occurs once; final gates plus actual removals equal original gates plus all actual materializer charges. Strict gain follows when removals exceed charges. The splice stage introduces no rejection beyond the actual history compiler.

Reviewed theorem interfaces (24)

PNP.DirectWire.extractTerminalSupport_causal_levels
PNP.DirectWire.extractTerminalSupport_causal_index
PNP.DirectWire.CausalBound.physical_normalization_output_bound
PNP.DirectWire.WireCarrier.normalize_causalBounds
PNP.DirectWire.WireObligationRestoration.join_causalBounds
PNP.DirectWire.WireObligationHistory.Transition.causalInvariant
PNP.DirectWire.WireObligationHistory.Execution.causalInvariant
PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant
PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound
PNP.DirectWire.WireObligationHistory.compileHistory_causal_bounds
PNP.DirectWire.ArbitrarySupportSplice.graph_causal_rank_decreases
PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_causalInterfaceBound
PNP.DirectWire.ArbitrarySupportSplice.compile_of_causalInterfaceBound
PNP.DirectWire.WireHistoryArbitrarySupport.extractedCarrier_gateCount
PNP.DirectWire.WireHistoryArbitrarySupport.extractedCarrier_fieldValue
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_equivalent
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_causalInterfaceBound
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain
PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete
PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound
PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff

This covers the existing computational R5/R6/R8 language and three-pass physical normalizer, not all manuscript R1-R9 or N1-N10 rules, full R7, arbitrary observers, noncomputational carriers, full-profile compatibility, matched-kappa Pull/Expand or complete Package E. The support records and raw history remain input data. It does not derive terminal families, a globally successful rewrite strategy, global route coverage, unconditional SaturatePositive, BCELReady or ZeroSlack, exact general PCCMin or complete encoded-input polynomial runtime/output/certificate bounds. Boolean equivalence alone is not a causal certificate. Runtime fixtures are regression evidence, not proof authority. No fixed weighted checkpoint or global gate closes; deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-264: formal artefact coverage: 240 of 242; risk-weighted estimate: 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-derived R7 discharge in raw computational histories

For arbitrary finite computational carriers, support lists and raw-event dimensions, R7 decodes every gate, boundary and interface coordinate against the immutable carrier of the identified open creation. Whole lists round-trip without dropping or substituting coordinates. Recognition succeeds exactly when decoding succeeds and the actual completed boundary has at most one port. The replacement is computed from that source's complete zero/unary open function, never from a supplied implementation, truth table or correctness certificate. Labelled dependency bounds follow the actual topological compiler and the literal replacement, not Boolean equivalence alone. The resulting full-field materializer discharges the exact captured creation, charges every appended gate, preserves ordinary outputs and other pending snapshots, and preserves the current-and-snapshot causal invariant. The extended raw R5/R6/R7/R8 history retains full lifecycle closure and exact physical accounting. Every accepted closed history still admits the literal one-copy ambient splice without an additional supplied rank, order, agreement or successful-compilation premise; strict gain requires actual removals to exceed all charges.

This is the zero/unary R7 extension of the computational history language, not the complete manuscript R1-R9 or N1-N10 calculus, arbitrary observers, noncomputational carriers, full-profile compatibility, matched-kappa Pull/Expand or complete Package E. Support coordinates and raw events remain input data; the result does not derive terminal families or a globally successful rewrite strategy. Global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and complete encoded-input polynomial runtime, output and certificate bounds remain open. Boolean soundness alone does not bound syntactic dependencies. Materialization can increase physical size, and finite runtime fixtures are regression evidence, not proof authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (41)

PNP.DirectWire.RawNandCompilationState.finish_position
PNP.DirectWire.RawNandCausalBound.compile_bounds
PNP.DirectWire.RawNandCausalBound.candidate_bound
PNP.DirectWire.ArbitrarySupportSplice.graph_dependency_bounds
PNP.DirectWire.ArbitrarySupportSplice.result_output_dependency_bound
PNP.DirectWire.WireUnaryCausalBound.implementation_output_bound
PNP.DirectWire.WireUnaryCausalBound.constantWord_output_bound
PNP.DirectWire.WireUnaryCausalBound.localWord_output_bound
PNP.DirectWire.WireUnaryCausalBound.arbitrary_replacement_output_bound
PNP.DirectWire.WireUnaryCausalBound.compiled_spec
PNP.DirectWire.WireUnaryCausalBound.replacement_dependency_bound
PNP.DirectWire.WireUnaryCausalBound.expanded_exposed_bound
PNP.DirectWire.WireUnaryCausalBound.expanded_causalBounds
PNP.DirectWire.WireUnaryCausalBound.attempt_causalBounds
PNP.DirectWire.WireObligationHistory.decodeRecord_encode
PNP.DirectWire.WireObligationHistory.decodeRecord_source
PNP.DirectWire.WireObligationHistory.decodeRecords_encode
PNP.DirectWire.WireObligationHistory.decodeRecords_source
PNP.DirectWire.WireObligationHistory.computeR7_isSome_iff
PNP.DirectWire.WireObligationHistory.R7Realization.full_field
PNP.DirectWire.WireObligationHistory.R7Realization.exact_charge
PNP.DirectWire.WireObligationHistory.R7Realization.causalBounds
PNP.DirectWire.WireObligationHistory.State.restoreR7_gate_charge
PNP.DirectWire.WireObligationHistory.State.restoreR7_full_value
PNP.DirectWire.WireObligationHistory.State.restoreR7_other_pending
PNP.DirectWire.WireObligationHistory.State.restoreR7_causalInvariant
PNP.DirectWire.WireObligationHistory.Transition.causalInvariant
PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant
PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound
PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output
PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field
PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance
PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle
PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting
PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain
PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete
PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound
PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-265: formal artefact coverage becomes 241 of 243; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-derived physical ownership through computational histories

For arbitrary finite computational carriers, selected support lists and raw-event dimensions, physical origins follow the actual constant, sharing and cone compiler branches and compose through the existing normalization trace. Every initial gate retains its source coordinate; every R7/R8 appended gate is labelled by its executing event identity and local allocation coordinate. Creation, cancellation and reads allocate no gates. The complete closed history computes a duplicate-free partition of live and removed origins into original gates and all historical charges, including allocations later removed. The actual topological compiler's computed two-sided position inverse carries those labels into the literal ambient splice, with every exterior gate present once and extracted coordinates restored to ambient positions. A source-only ownership constructor returns exactly the existing constructor's result. Its disjoint raw-event requests and fixed original-gate remainder reuse the existing ownership kernel for support-stable membership, actual extracted piece sizes and charge identities, independent open semantics and induced-boundary reconnection. No owner family, provenance map, partition proof, charge amount, topological order or successful-splice certificate is supplied.

This is source-derived physical ownership for the existing computational history language, not the complete manuscript carrier/profile universe, all R1-R9 or N1-N10 routes, arbitrary observers, matched-kappa arbitrary-support Pull/Expand or complete Package E. Support coordinates and raw events remain input data; no terminal-derived family or globally successful history is constructed. Historical allocated size and surviving owned size are distinct, and physical identity or integer accounting does not prove a runtime bound. Global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and complete encoded-input polynomial runtime, output and certificate bounds remain open. Finite runtime fixtures are regression evidence, not proof authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (78)

PNP.DirectWire.PhysicalGateProvenance.constantOrigins_positions
PNP.DirectWire.PhysicalGateProvenance.sharingOrigins_positions
PNP.DirectWire.PhysicalGateProvenance.constantOrigin_alias
PNP.DirectWire.PhysicalGateProvenance.constantOrigin_injective
PNP.DirectWire.PhysicalGateProvenance.sharingOrigin_alias
PNP.DirectWire.PhysicalGateProvenance.sharingOrigin_injective
PNP.DirectWire.terminalExtractionOrigin_selected
PNP.DirectWire.terminalExtractionGateIndex_origin
PNP.DirectWire.terminalExtractionOrigin_gateIndex
PNP.DirectWire.terminalExtractionOrigin_injective
PNP.DirectWire.PhysicalGateProvenance.coneOrigin_selected
PNP.DirectWire.PhysicalGateProvenance.coneOrigin_position
PNP.DirectWire.PhysicalGateProvenance.coneOrigin_injective
PNP.DirectWire.PhysicalGateProvenance.coneOrigin_image
PNP.DirectWire.PhysicalGateProvenance.passOrigin_injective
PNP.DirectWire.PhysicalGateProvenance.traceOrigin_injective
PNP.DirectWire.PhysicalGateProvenance.normalizedOrigin_injective
PNP.DirectWire.PhysicalGateProvenance.constantOrigins_length
PNP.DirectWire.PhysicalGateProvenance.constantOrigins_nodup
PNP.DirectWire.PhysicalGateProvenance.sharingOrigins_length
PNP.DirectWire.PhysicalGateProvenance.sharingOrigins_nodup
PNP.DirectWire.PhysicalGateProvenance.passRemoved_iff
PNP.DirectWire.PhysicalGateProvenance.pass_partition
PNP.DirectWire.PhysicalGateProvenance.traceRemoved_iff
PNP.DirectWire.PhysicalGateProvenance.trace_partition
PNP.DirectWire.PhysicalGateProvenance.normalizedRemoved_iff
PNP.DirectWire.PhysicalGateProvenance.normalized_partition
PNP.DirectWire.WireObligationHistory.PhysicalOwnership.append_origin_left
PNP.DirectWire.WireObligationHistory.PhysicalOwnership.append_origin_right
PNP.DirectWire.WireObligationHistory.PhysicalOwnership.append_live
PNP.DirectWire.WireObligationHistory.PhysicalOwnership.normalize_partition
PNP.DirectWire.WireObligationHistory.PhysicalOwnership.normalize_removed_length
PNP.DirectWire.WireObligationHistory.Transition.restore_physical_positions
PNP.DirectWire.WireObligationHistory.Transition.realize_physical_positions
PNP.DirectWire.WireObligationHistory.Transition.allocations_nodup
PNP.DirectWire.WireObligationHistory.Transition.physical_charged
PNP.DirectWire.WireObligationHistory.Transition.physical_removed_length
PNP.DirectWire.WireObligationHistory.Transition.physical_conservation
PNP.DirectWire.WireObligationHistory.Execution.allocations_length
PNP.DirectWire.WireObligationHistory.Execution.physical_charged
PNP.DirectWire.WireObligationHistory.Execution.physical_removed_length
PNP.DirectWire.WireObligationHistory.Execution.physical_conservation
PNP.DirectWire.WireObligationHistory.Execution.allocations_member
PNP.DirectWire.WireObligationHistory.Execution.allocations_nodup
PNP.DirectWire.WireObligationHistory.ClosedHistory.physical_charged
PNP.DirectWire.WireObligationHistory.ClosedHistory.physical_partition
PNP.DirectWire.WireObligationHistory.ClosedHistory.physical_ownership
PNP.DirectWire.CompiledRawNandGraph.position_surjective
PNP.DirectWire.CompiledRawNandGraph.position_physicalOrigin
PNP.DirectWire.CompiledRawNandGraph.physicalOrigin_position
PNP.DirectWire.CompiledRawNandGraph.physicalOrigin_injective
PNP.DirectWire.CompiledRawNandGraph.physicalOrigin_surjective
PNP.DirectWire.CompiledRawNandGraph.physicalOrigins_nodup
PNP.DirectWire.CompiledRawNandGraph.physicalOrigins_perm
PNP.DirectWire.RawNandCompilationState.finish_physicalOrigin
PNP.DirectWire.WireHistoryAmbientOwnership.liftOrigin_injective
PNP.DirectWire.WireHistoryAmbientOwnership.original_coordinate_partition
PNP.DirectWire.WireHistoryAmbientOwnership.rawNodeOrigin_exterior
PNP.DirectWire.WireHistoryAmbientOwnership.rawNodeOrigin_history
PNP.DirectWire.WireHistoryAmbientOwnership.physicalOrigin_position
PNP.DirectWire.WireHistoryAmbientOwnership.physical_partition
PNP.DirectWire.WireHistoryAmbientOwnership.physical_ownership
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.ownership
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.semantics
PNP.DirectWire.WireHistoryAmbientOwnership.compileOwned_result
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventRequests_member
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventRequests_disjoint
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_some_iff
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.charged_origin
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.live_allocated_event
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_none_iff
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.support_membership
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.support_restrict
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_gateCount
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_chargeIdentity
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_wholeCharge
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_semantics
PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_induced

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-266: formal artefact coverage becomes 242 of 244; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Persistent physical ownership through descendant histories

For arbitrary finite source dimensions and raw stage/event lists, a source-only decoder and compiler traverse the complete list using each actual preceding descendant. Persistent physical origins relabel original positions through the existing literal ambient compiler and label allocations by computed stage position, executing raw event and local gate. The arbitrary-program theorem conserves original gates and every historical charge as a duplicate-free live/removed permutation with exact actual execution totals; later removal never erases an earlier charge. Accepted input-event keys are distinct across stages, even when local event numbers are reused, and every historical or surviving allocation traces to that raw family. Derived final owner requests are disjoint before support selection and reuse the existing extraction kernel for support-stable ownership, exact piece sizes and charges, open semantics and induced reconnection. Whole-program Boolean semantics and physical size accounting yield an optional final StrictEquivalentGain through a computed final-size comparison, permitting intermediate expansion and propagating every rejected stage. No intermediate implementation, owner family, provenance map, charge amount, rank, successful-history certificate or semantic oracle is supplied.

This covers arbitrary finite sequences of the existing closed computational-history compilations, not the full manuscript carrier/profile universe, cross-support transport of open obligations, all R1-R9 or N1-N10 rules, matched-kappa arbitrary-support Pull/Expand, proper-support VerifyDW, full ChargeSoundness or complete Package E. Raw supports and events remain inputs; no terminal-derived family or globally successful strategy is constructed. Final net gain does not require each stage to decrease, prove local minimality after rejection, bound temporary growth or establish encoded-input polynomial runtime. Global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin and complete polynomial runtime, output and certificate bounds remain open. Runtime fixtures are regression evidence, not theorem authority. No fixed weighted checkpoint or global gate closes. Deterministic CNFSAT in P and the eligible root remain absent, and P = NP is not proved.

Reviewed theorem interfaces (84)

PNP.DirectWire.WireDescendantHistory.decodeRecord_encode
PNP.DirectWire.WireDescendantHistory.decodeRecord_source
PNP.DirectWire.WireDescendantHistory.decodeRecords_encode
PNP.DirectWire.WireDescendantHistory.decodeRecords_source
PNP.DirectWire.WireDescendantHistory.decodeAction_encode
PNP.DirectWire.WireDescendantHistory.decodeAction_source
PNP.DirectWire.WireDescendantHistory.decodeEvent_encode
PNP.DirectWire.WireDescendantHistory.decodeEvent_source
PNP.DirectWire.WireDescendantHistory.decodeEvents_encode
PNP.DirectWire.WireDescendantHistory.decodeEvents_source
PNP.DirectWire.WireDescendantHistory.StageCompilation.records_source
PNP.DirectWire.WireDescendantHistory.StageCompilation.events_source
PNP.DirectWire.WireDescendantHistory.StageCompilation.existing_result
PNP.DirectWire.WireDescendantHistory.StageCompilation.semantics
PNP.DirectWire.WireDescendantHistory.StageCompilation.physicalOrigin_position
PNP.DirectWire.WireDescendantHistory.StageCompilation.physical_ownership
PNP.DirectWire.WireDescendantHistory.StageCompilation.gate_balance
PNP.DirectWire.WireDescendantHistory.StageCompilation.charged_origin
PNP.DirectWire.WireDescendantHistory.StageCompilation.event_identity_unique
PNP.DirectWire.WireDescendantHistory.compileStage_records_none
PNP.DirectWire.WireDescendantHistory.compileStage_events_none
PNP.DirectWire.WireDescendantHistory.compileStage_history_none
PNP.DirectWire.WireDescendantHistory.CompiledRun.semantics
PNP.DirectWire.WireDescendantHistory.CompiledRun.gate_balance
PNP.DirectWire.WireDescendantHistory.compile_nil
PNP.DirectWire.WireDescendantHistory.compile_cons
PNP.DirectWire.WireDescendantHistory.compile_stage_none
PNP.DirectWire.WireDescendantHistory.compile_tail_none
PNP.DirectWire.WireDescendantHistory.compile_cons_some
PNP.DirectWire.WireDescendantHistory.compile_sound
PNP.DirectWire.WireDescendantHistory.createdBefore_mono
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.initial_wellFormed
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.accounted_before
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.origin_before
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.origin_injective
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_original
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_allocated
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_injective
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.lift_originals
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_live
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_charged_length
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_removed_length
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_physicalOrigin_position
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_charge_origin
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_partition
PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_wellFormed
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_nil
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_cons
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_wellFormed
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charged_length
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_removed_length
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charge_survives
PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_nil
PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_wellFormed
PNP.DirectWire.WireDescendantHistory.CompiledRun.physical_ownership
PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_origin_injective
PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_charged_before
PNP.DirectWire.WireDescendantHistory.inputEventKeys_nil
PNP.DirectWire.WireDescendantHistory.inputEventKeys_cons
PNP.DirectWire.WireDescendantHistory.inputEventKeys_bounds
PNP.DirectWire.WireDescendantHistory.StageCompilation.rawEventIdentities_nodup
PNP.DirectWire.WireDescendantHistory.CompiledRun.inputEventKeys_nodup
PNP.DirectWire.WireDescendantHistory.CompiledRun.inputEventKeys_unique
PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charged_origin
PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_charged_origin
PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_live_allocated_event
PNP.DirectWire.WireDescendantHistory.CompiledRun.eventRequests_member
PNP.DirectWire.WireDescendantHistory.CompiledRun.eventRequests_disjoint
PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_some_iff
PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_none_iff
PNP.DirectWire.WireDescendantHistory.CompiledRun.support_membership
PNP.DirectWire.WireDescendantHistory.CompiledRun.support_restrict
PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_gateCount
PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_chargeIdentity
PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_wholeCharge
PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_semantics
PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_induced
PNP.DirectWire.WireDescendantHistory.CompiledRun.strictGain
PNP.DirectWire.WireDescendantHistory.GainResult.strictGain
PNP.DirectWire.WireDescendantHistory.GainResult.strictResidualDescent
PNP.DirectWire.WireDescendantHistory.compileGain_compile_none
PNP.DirectWire.WireDescendantHistory.compileGain_no_gain
PNP.DirectWire.WireDescendantHistory.compileGain_complete
PNP.DirectWire.WireDescendantHistory.compileGain_exists_iff

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-267: formal artefact coverage becomes 243 of 245; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Source-only proper-support certificates for descendant programs

For arbitrary finite computational wire-carrier dimensions, raw outer support records and raw descendant programs, source-only verification decodes every outer coordinate and executes the complete local program on the extracted source. Arbitrary-label dependency bounds follow actual execution and derive literal outer compilation without a supplied wiring order or successful-splice premise. Acceptance is exactly complete decoding, successful complete local execution, proper physical support and strict final local saving. The constructed one-copy ambient splice preserves all ordinary outputs and literal fields, retains the actual run and compiler receipts, and satisfies exact historical charge/removal accounting. Intermediate expansion is permitted; invalid coordinates, a failed later stage, whole support and final nondecrease reject. Every accepted certificate yields StrictEquivalentGain and strict residual descent without supplied intermediate circuits, correctness, owners, costs, ranks or semantic oracles.

This verifies offered finite programs in the existing closed computational wire-carrier language. It does not prove that every nonminimal input has an accepted certificate, construct a globally successful strategy, derive terminal families or establish local minimality after rejection. Full manuscript profiles, all R1-R9 and N1-N10 rule families, cross-support transport of open obligations, matched-kappa arbitrary-support Pull/Expand, full manuscript VerifyDW, ChargeSoundness and Package E remain open. No bound on temporary growth, encoded-input polynomial runtime, output size or certificate size is proved. Global route coverage, unconditional SaturatePositive, BCELReady and ZeroSlack, exact general PCCMin, deterministic CNFSAT in P and the eligible root remain open. Runtime fixtures are regression evidence, not theorem authority. No fixed weighted checkpoint or global gate closes, and P = NP is not proved.

Reviewed theorem interfaces (33)

PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_dependencyInterfaceBound
PNP.DirectWire.WireDescendantHistory.StageCompilation.output_dependency_bound
PNP.DirectWire.WireDescendantHistory.CompiledRun.output_dependency_bound
PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_causalInterfaceBound
PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_compiles
PNP.DirectWire.WireDescendantProperSupport.proper_iff_exterior_positive
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.open_equivalent
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.output
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.field
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gateCount
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.charge_accounting
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gain_iff_local_gain
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gain_iff_net_charges
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.strictGain
PNP.DirectWire.WireDescendantProperSupport.SplicedRun.strictResidualDescent
PNP.DirectWire.WireDescendantProperSupport.compile_complete
PNP.DirectWire.WireDescendantProperSupport.compile_exists_iff
PNP.DirectWire.WireDescendantProperSupport.compile_none_iff
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.records_source
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.proper_support
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.output
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.field
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.gateCount
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.charge_accounting
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictGain
PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictResidualDescent
PNP.DirectWire.WireDescendantCertificate.verify_complete
PNP.DirectWire.WireDescendantCertificate.verify_exists_iff
PNP.DirectWire.WireDescendantCertificate.verify_sound
PNP.DirectWire.WireDescendantCertificate.verify_decode_none
PNP.DirectWire.WireDescendantCertificate.verify_run_none
PNP.DirectWire.WireDescendantCertificate.verify_not_proper
PNP.DirectWire.WireDescendantCertificate.verify_no_gain

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-268: formal artefact coverage becomes 244 of 246; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Constructive wire-profile restoration cost and exact gain boundary

For arbitrary finite input, ordinary-output and computational-field widths, the existing concrete quotient agreement is equivalent to wire-profile quotient comparison. The actual shared hidden-wire materializer restores the computed quotient-minimum witness into a full-equivalent carrier, preserving every ordinary output and actual field at every input valuation. If F is the full minimum, Q the quotient minimum, C the actual materializer charge, D = F - Q and S the actual full-field normalization saving, the theorems prove F <= Q + C, D <= C, paid cost = F + (C - D), S <= C - D and normalized cost = F + (C - D - S). Strict improvement against the original carrier is equivalent to the remaining overhead being smaller than its full slack; the executable acceptance test checks the actual final size and yields a sound strict equivalent gain. The existing complete one-input constructor has gate count exactly F for arbitrary output and field widths, and improves the original exactly when full slack is positive. No full replacement, minimum, charge or correctness certificate is supplied to the constructed route.

This is a cost and compatibility interface for computational wire profiles, not complete manuscript profiles or a terminal-derived family. The materializer charge only upper-bounds projection defect; equality and forced-cost transparency are not established. Physical normalization is not a semantic minimizer. A kernel-checked positive-slack example is refused by restoration plus normalization, while the existing unary route recovers it; this limits that component, not every route or the manuscript's complete route family. Returning no gain does not establish ZeroSlack. Unary completeness is restricted to one input and is reused, not newly proved for arbitrary inputs. Reference minimization is exhaustive, not a polynomial PCCMin algorithm. Complete Package E, global route coverage and rank decrease, unconditional SaturatePositive, BCELReady and ZeroSlack, exact polynomial PCCMin, encoded runtime, output and certificate bounds, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global proof gate closes, and P = NP is not proved.

Reviewed theorem interfaces (19)

PNP.DirectWire.WireProfileRestoration.quotientAgreement_iff
PNP.DirectWire.WireProfileRestoration.expanded_fullEquivalent
PNP.DirectWire.WireProfileRestoration.paidWitness_fullEquivalent
PNP.DirectWire.WireProfileRestoration.paidWitness_gateCount
PNP.DirectWire.WireProfileRestoration.fullMinimum_le_quotientMinimum_add_charge
PNP.DirectWire.WireProfileRestoration.projectionDefect_le_charge
PNP.DirectWire.WireProfileRestoration.paidWitness_exact_overhead
PNP.DirectWire.WireProfileRestoration.paidWitness_smaller_iff
PNP.DirectWire.WireProfileRestoration.paidWitness_optimal_iff
PNP.DirectWire.WireProfileRestoration.normalizedWitness_fullEquivalent
PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_accounting
PNP.DirectWire.WireProfileRestoration.reclaimed_le_overhead
PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_overhead
PNP.DirectWire.WireProfileRestoration.normalizedWitness_smaller_iff
PNP.DirectWire.WireProfileRestoration.normalizedWitness_optimal_iff
PNP.DirectWire.WireProfileRestoration.checkedGain_isSome_iff
PNP.DirectWire.WireProfileRestoration.CheckedGain.checked
PNP.DirectWire.WireProfileRestoration.unary_fullMinimum
PNP.DirectWire.WireProfileRestoration.unary_smaller_iff_fullSlack_positive

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-275: formal artefact coverage becomes 251 of 253; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed wire-profile models and exact independent-field cost

For arbitrary finite input, ordinary-output and computational-field widths, target-relative availability computes one actual constant, input or gate source that realizes a field uniformly over every input valuation. Rebinding constructs a carrier without adding gates and identifies terminal full and quotient profile minima with the corresponding wire-profile minima. The model constructor proves coherence between its base and ambient observers under unused-input padding and output rewording. A source-derived field seed and physical dependency closure yield an actual extracted support preserving every field at all ambient input valuations. For any old implementation with semantic minimum F and any natural width k, an explicit extension appends k independent NAND fields on disjoint fresh input pairs. Semantic gate retraction proves that every equivalent implementation needs at least F + k gates; the matching construction attains that bound. Its actual wire profile therefore has full minimum F + k, all-forgotten quotient minimum F, projection defect k and unchanged full slack. Three general coupling theorems establish these same exact minima and their difference inside the constructed terminal profile model, without a supplied model, minimum, field support or correctness certificate.

This is a computed model for actual computational wire fields, not the complete manuscript profile grammar or a terminal-derived governed family. The extracted support is field-preserving but is not asserted to be proper, smaller or optimal. The exact additive cost theorem concerns the explicit independent fresh-input NAND family, not arbitrary correlated, duplicated or supplied manuscript fields. The semantic retraction helper has an explicit uniform constant-value hypothesis, discharged for that family; it is not a general polynomial semantic-constant detector. The existing shared materializer charge is only bounded below by the family's projection defect, not proved equal to it. Availability checks enumerate valuations and reference minima remain exhaustive; no complete polynomial minimizer follows. Complete Package E, global route coverage and rank decrease, unconditional SaturatePositive, BCELReady and ZeroSlack, exact polynomial PCCMin, encoded runtime, output and certificate bounds, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global proof gate closes, and P = NP is not proved.

Reviewed theorem interfaces (72)

PNP.DirectWire.ComputedWireProfileCost.full_minimum
PNP.DirectWire.ComputedWireProfileCost.minimum_gap
PNP.DirectWire.ComputedWireProfileCost.quotient_minimum
PNP.DirectWire.FreshNandCost.erased_constant
PNP.DirectWire.FreshNandCost.erased_count_lower_bound
PNP.DirectWire.FreshNandCost.extend_gateCount
PNP.DirectWire.FreshNandCost.extended_equivalent
PNP.DirectWire.FreshNandCost.extended_fresh
PNP.DirectWire.FreshNandCost.extended_old
PNP.DirectWire.FreshNandCost.freshCandidate_semantics
PNP.DirectWire.FreshNandCost.freshConditions
PNP.DirectWire.FreshNandCost.freshGate_injective
PNP.DirectWire.FreshNandCost.freshGate_selected
PNP.DirectWire.FreshNandCost.freshGate_source
PNP.DirectWire.FreshNandCost.freshGate_value
PNP.DirectWire.FreshNandCost.freshValue_joinInput
PNP.DirectWire.FreshNandCost.freshValue_restricted
PNP.DirectWire.FreshNandCost.gateCount_lower_bound
PNP.DirectWire.FreshNandCost.inputNands_eval
PNP.DirectWire.FreshNandCost.oldCandidate_semantics
PNP.DirectWire.FreshNandCost.padInputs_semantics
PNP.DirectWire.FreshNandCost.profile_field
PNP.DirectWire.FreshNandCost.profile_fullMinimum
PNP.DirectWire.FreshNandCost.profile_fullSlack
PNP.DirectWire.FreshNandCost.profile_gateCount
PNP.DirectWire.FreshNandCost.profile_materializer_charge_lower_bound
PNP.DirectWire.FreshNandCost.profile_output
PNP.DirectWire.FreshNandCost.profile_projectionDefect
PNP.DirectWire.FreshNandCost.profile_quotientMinimum
PNP.DirectWire.FreshNandCost.referenceMinimum_extend
PNP.DirectWire.FreshNandCost.referenceMinimum_padInputs
PNP.DirectWire.FreshNandCost.restricted_oldInput
PNP.DirectWire.SemanticGateRetraction.gateCount_eq_sub
PNP.DirectWire.SemanticGateRetraction.gateCount_partition
PNP.DirectWire.SemanticGateRetraction.kept_gate_value
PNP.DirectWire.SemanticGateRetraction.reboundSource_value
PNP.DirectWire.SemanticGateRetraction.semantics
PNP.DirectWire.WireProfileAmbient.available_iff_exists
PNP.DirectWire.WireProfileAmbient.available_pad
PNP.DirectWire.WireProfileAmbient.available_pad_iff
PNP.DirectWire.WireProfileAmbient.available_reword
PNP.DirectWire.WireProfileAmbient.eval_paddedSource
PNP.DirectWire.WireProfileAmbient.eval_retractSource
PNP.DirectWire.WireProfileAmbient.model_observe_coherent
PNP.DirectWire.WireProfileAmbient.pad_fieldValue
PNP.DirectWire.WireProfileAmbient.pad_gateCount
PNP.DirectWire.WireProfileAvailability.available_of_source
PNP.DirectWire.WireProfileAvailability.bind_fieldValue
PNP.DirectWire.WireProfileAvailability.bind_full
PNP.DirectWire.WireProfileAvailability.bind_gateCount
PNP.DirectWire.WireProfileAvailability.bind_implementation
PNP.DirectWire.WireProfileAvailability.bind_quotient
PNP.DirectWire.WireProfileAvailability.current_available
PNP.DirectWire.WireProfileAvailability.findSource_congr
PNP.DirectWire.WireProfileAvailability.findSource_sound
PNP.DirectWire.WireProfileAvailability.full_match_iff
PNP.DirectWire.WireProfileAvailability.full_minimum
PNP.DirectWire.WireProfileAvailability.quotient_match_iff
PNP.DirectWire.WireProfileAvailability.quotient_minimum
PNP.DirectWire.WireProfileAvailability.sourceMatches_congr
PNP.DirectWire.WireProfileAvailability.sourceMatches_iff
PNP.DirectWire.WireProfileAvailability.system_congr
PNP.DirectWire.WireProfileAvailability.system_fullEquivalent
PNP.DirectWire.WireProfileFieldClosed.ambient_fieldValue
PNP.DirectWire.WireProfileFieldClosed.available
PNP.DirectWire.WireProfileFieldClosed.boundary_isInput
PNP.DirectWire.WireProfileFieldClosed.gate_value
PNP.DirectWire.WireProfileFieldClosed.source_selected
PNP.DirectWire.extractTerminalSupport_gate_evaluation
PNP.DirectWire.extractTerminalSupport_gate_induced
PNP.DirectWire.terminalPhysicalComplementRecords_gateCount_partition
PNP.DirectWire.terminalPhysicalComplementRecords_selected

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-276: formal artefact coverage becomes 252 of 254; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed closed-support observations and profile-compatible squares

For arbitrary finite input, ordinary-output and computational-field widths, the actual computed dependency-closed support observes a field exactly when it retains an original constant, input or gate source whose value agrees with that field uniformly over every input valuation. The matching table and support are computed from the circuit and ordinary seed data. For arbitrary seed pairs, observations of the computed union are the Boolean union of the separate observations. This extends to arbitrary finite families, with the empty support's observation as the base, and to seed-inclusion monotonicity. Seeding the requested profile records derives availability and uniform field-value preservation without injecting their literal original gate bindings. The actual meet, left, right and join of the constructed support square all preserve those requested computational fields and agree pairwise on their values at every ambient input valuation. Existing source extraction, structural square laws and arbitrary-context profile locality are reused, not newly claimed.

This is computational-field compatibility, not ordinary-output equivalence, the complete manuscript profile grammar, a terminal-derived governed family, or a legitimate full projection square. Field preservation does not imply a proper, smaller, minimum or positive support. A kernel-checked duplicate-circuit example has positive full slack but no proper seed in the computed model; the existing sharing pass removes that duplicate, so the example is not a normalized terminal counterexample and does not refute a manuscript theorem with additional terminal or admissibility hypotheses. Source matching and influence remain finite exhaustive computations, not polynomial algorithms. Complete Package E, forced-cost transparency, global route coverage and rank decrease, unconditional SaturatePositive, BCELReady and ZeroSlack, exact polynomial PCCMin, encoded runtime, output and certificate bounds, deterministic CNFSAT in P and the eligible root remain open. No fixed weighted checkpoint or global proof gate closes, and P = NP is not proved.

Reviewed theorem interfaces (24)

PNP.DirectWire.ClosedSupportObservation.available_eq_tableAvailable
PNP.DirectWire.ClosedSupportObservation.available_iff_retained_source
PNP.DirectWire.ClosedSupportObservation.available_of_retained_source
PNP.DirectWire.ClosedSupportObservation.boundary_isInput
PNP.DirectWire.ClosedSupportObservation.gate_value
PNP.DirectWire.ClosedSupportObservation.lift_retained_source
PNP.DirectWire.ClosedSupportObservation.mem_matchingSources
PNP.DirectWire.ClosedSupportObservation.retract_support_source
PNP.DirectWire.ClosedSupportObservation.tableAvailable_iff
PNP.DirectWire.ClosedSupportProfile.profile_available
PNP.DirectWire.ClosedSupportProfile.projected_available
PNP.DirectWire.ClosedSupportProfile.projected_fieldValue
PNP.DirectWire.ClosedSupportProfile.projected_tableAvailable
PNP.DirectWire.ClosedSupportSquare.corner_available
PNP.DirectWire.ClosedSupportSquare.corner_fieldValue
PNP.DirectWire.ClosedSupportSquare.corner_profileMember
PNP.DirectWire.ClosedSupportSquare.corners_fieldValue_equal
PNP.DirectWire.ClosedSupportUnion.available_append
PNP.DirectWire.ClosedSupportUnion.available_flatten
PNP.DirectWire.ClosedSupportUnion.available_mono
PNP.DirectWire.ClosedSupportUnion.mem_records_append
PNP.DirectWire.ClosedSupportUnion.records_mono
PNP.DirectWire.ClosedSupportUnion.retained_append
PNP.DirectWire.ClosedSupportUnion.tableAvailable_append

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-277: formal artefact coverage becomes 253 of 255; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed closed-support full-profile physical gain

For arbitrary finite wire carriers, keep masks and seed record families under the computed computational-wire-profile model, the full-profile reference minimum of the actual closed support is specialized to primary inputs and reconnected to the derived physical complement. The resulting whole carrier preserves every ordered output and computational field for every input, with exact gate and whole-carrier full-slack balance. Positive computed local full slack yields a checked strict equivalent gain; zero local full slack returns no gain. The support, minimum, source bindings and reconnection are computed, not supplied correctness data.

The full-profile minimum, source matching and saturation influence tests remain exhaustive finite reference computations. This does not derive a proper positive support, make whole-span replacements locally VerifyDW-eligible, implement the manuscript's complete noncomputational profile grammar, establish global route coverage or unconditional SaturatePositive, BCELReady or ZeroSlack, or prove complete PCCMin polynomial runtime, output-size or certificate bounds. The eligible root theorem remains absent and P = NP is not proved.

Reviewed theorem interfaces (27)

PNP.DirectWire.ClosedSupportFullGain.ambient_output
PNP.DirectWire.ClosedSupportFullGain.boundarySource_value
PNP.DirectWire.ClosedSupportFullGain.complement_gate_value
PNP.DirectWire.ClosedSupportFullGain.fieldSource_value
PNP.DirectWire.ClosedSupportFullGain.improvement?_none_iff
PNP.DirectWire.ClosedSupportFullGain.improvement?_sound
PNP.DirectWire.ClosedSupportFullGain.improvement?_strictGain
PNP.DirectWire.ClosedSupportFullGain.inputBinding_eval
PNP.DirectWire.ClosedSupportFullGain.interface_index_exists
PNP.DirectWire.ClosedSupportFullGain.interface_index_sound
PNP.DirectWire.ClosedSupportFullGain.localFullSlack_le_global
PNP.DirectWire.ClosedSupportFullGain.offered_available
PNP.DirectWire.ClosedSupportFullGain.offered_gateCount
PNP.DirectWire.ClosedSupportFullGain.offered_gateCount_le
PNP.DirectWire.ClosedSupportFullGain.outputSource_value
PNP.DirectWire.ClosedSupportFullGain.prefixField_value
PNP.DirectWire.ClosedSupportFullGain.prefixOutput_value
PNP.DirectWire.ClosedSupportFullGain.prefixSource_value
PNP.DirectWire.ClosedSupportFullGain.restrict_extendZero
PNP.DirectWire.ClosedSupportFullGain.result_exact_accounting
PNP.DirectWire.ClosedSupportFullGain.result_fullEquivalent
PNP.DirectWire.ClosedSupportFullGain.result_fullMinimum
PNP.DirectWire.ClosedSupportFullGain.result_fullSlack_balance
PNP.DirectWire.ClosedSupportFullGain.result_gain_balance
PNP.DirectWire.ClosedSupportFullGain.result_output
PNP.DirectWire.ClosedSupportFullGain.result_strict_iff
PNP.DirectWire.ClosedSupportFullGain.retained_source_value

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-278: formal artefact coverage becomes 254 of 256; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed whole-support minimum bridge

For arbitrary finite wire carriers and keep masks, the physical whole-support seed is derived from all original gates. Its computed saturated interface contains exactly the original gate-valued ordinary outputs, while every computational field is available. Explicit size-preserving comparisons identify its full-profile reference minimum with the independent whole-carrier output-and-field minimum. The actual computed full-profile replacement attains that minimum, has zero remaining whole-carrier full slack, and returns no strict improvement exactly when the original whole-carrier full slack is zero. The seed, interface, observer, minimum and replacement are derived rather than supplied correctness data.

The whole-span reference branch remains exhaustive, including minimum search, source matching and saturation influence. Zero slack after exhaustive reference minimization is not the manuscript's unconditional ZeroSlack theorem or a polynomial PCCMin algorithm. This does not discover a proper positive support, compile arbitrary minima into proper-local VerifyDW histories, reconstruct the complete noncomputational profile grammar, derive global route coverage or unconditional SaturatePositive and BCELReady, or establish complete polynomial runtime, output-size or certificate bounds. The eligible root theorem remains absent and P = NP is not proved.

Reviewed theorem interfaces (22)

PNP.DirectWire.ClosedWholeMinimum.ambient_output_absent
PNP.DirectWire.ClosedWholeMinimum.available_all
PNP.DirectWire.ClosedWholeMinimum.forward_available
PNP.DirectWire.ClosedWholeMinimum.forward_equivalent
PNP.DirectWire.ClosedWholeMinimum.forward_gateCount
PNP.DirectWire.ClosedWholeMinimum.forward_output_none
PNP.DirectWire.ClosedWholeMinimum.forward_output_some
PNP.DirectWire.ClosedWholeMinimum.fullSlack_eq
PNP.DirectWire.ClosedWholeMinimum.full_minimum
PNP.DirectWire.ClosedWholeMinimum.gate_selected
PNP.DirectWire.ClosedWholeMinimum.global_minimum_le
PNP.DirectWire.ClosedWholeMinimum.improvement_none_iff
PNP.DirectWire.ClosedWholeMinimum.interface_iff_output
PNP.DirectWire.ClosedWholeMinimum.outputIndex_exists
PNP.DirectWire.ClosedWholeMinimum.outputIndex_none_not_interface
PNP.DirectWire.ClosedWholeMinimum.outputIndex_sound
PNP.DirectWire.ClosedWholeMinimum.result_gateCount
PNP.DirectWire.ClosedWholeMinimum.result_optimal
PNP.DirectWire.ClosedWholeMinimum.result_zero_fullSlack
PNP.DirectWire.ClosedWholeMinimum.source_retained
PNP.DirectWire.ClosedWholeMinimum.support_gateCount
PNP.DirectWire.ClosedWholeMinimum.support_minimum_le

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-279: formal artefact coverage becomes 255 of 257; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Computed nested-support cost and positivity transport

For arbitrary finite wire carriers, keep masks and two raw seed lists whose computed completed supports are physically nested, derive the exact gate difference and crossing bindings. Extend the actual full or quotient reference minimum inside the common ambient input domain, preserving the larger padded ordinary interface and exact required computational-field availability, including false values. The derived comparisons prove that either minimum grows by at most the added physical gates, that full slack and support size minus quotient minimum are monotone, and that positive full slack or projection defect remains positive in the completed larger support. Raw-seed inclusion derives the physical inclusion. No cost inequality, field-equality certificate or optimizer is supplied to the final theorem.

This compares already completed dependency-closed supports in the computational-wire-profile model. It does not prove preservation of an arbitrary raw witness's initial positivity during completion, transparency of every intermediate event, monotonicity of projection defect alone, complete manuscript profile semantics, discovery of a proper positive support, global routing or unconditional SaturatePositive, BCELReady or ZeroSlack. Reference minimization, matching and influence computations remain exhaustive; complete polynomial PCCMin runtime, output-size and certificate bounds are not proved. The eligible root theorem remains absent and P = NP is not proved.

Reviewed theorem interfaces (36)

PNP.DirectWire.ClosedSupportNestedGain.ambient_output_absent
PNP.DirectWire.ClosedSupportNestedGain.append_positive
PNP.DirectWire.ClosedSupportNestedGain.available_from_large
PNP.DirectWire.ClosedSupportNestedGain.available_from_prefix
PNP.DirectWire.ClosedSupportNestedGain.available_mono
PNP.DirectWire.ClosedSupportNestedGain.available_to_large
PNP.DirectWire.ClosedSupportNestedGain.boundarySource_value
PNP.DirectWire.ClosedSupportNestedGain.difference_boundary_interface
PNP.DirectWire.ClosedSupportNestedGain.difference_gate_value
PNP.DirectWire.ClosedSupportNestedGain.difference_selected
PNP.DirectWire.ClosedSupportNestedGain.difference_selected_iff
PNP.DirectWire.ClosedSupportNestedGain.extended_available
PNP.DirectWire.ClosedSupportNestedGain.extended_gateCount
PNP.DirectWire.ClosedSupportNestedGain.extended_source_origin
PNP.DirectWire.ClosedSupportNestedGain.full_minimum_cost_balance
PNP.DirectWire.ClosedSupportNestedGain.full_minimum_extension_bound
PNP.DirectWire.ClosedSupportNestedGain.full_minimum_le_support
PNP.DirectWire.ClosedSupportNestedGain.full_slack_le
PNP.DirectWire.ClosedSupportNestedGain.included_of_seed_subset
PNP.DirectWire.ClosedSupportNestedGain.larger_interface_in_smaller
PNP.DirectWire.ClosedSupportNestedGain.outputSource_value
PNP.DirectWire.ClosedSupportNestedGain.positive_iff_quotient_slack
PNP.DirectWire.ClosedSupportNestedGain.positive_mono
PNP.DirectWire.ClosedSupportNestedGain.prefix_source_value
PNP.DirectWire.ClosedSupportNestedGain.quotient_minimum_cost_balance
PNP.DirectWire.ClosedSupportNestedGain.quotient_minimum_extension_bound
PNP.DirectWire.ClosedSupportNestedGain.quotient_minimum_le_full
PNP.DirectWire.ClosedSupportNestedGain.quotient_slack_le
PNP.DirectWire.ClosedSupportNestedGain.retained_mono
PNP.DirectWire.ClosedSupportNestedGain.seed_full_cost_balance
PNP.DirectWire.ClosedSupportNestedGain.seed_full_slack_le
PNP.DirectWire.ClosedSupportNestedGain.seed_positive
PNP.DirectWire.ClosedSupportNestedGain.seed_quotient_cost_balance
PNP.DirectWire.ClosedSupportNestedGain.slack_decomposition
PNP.DirectWire.ClosedSupportNestedGain.support_count_decomposition
PNP.DirectWire.ClosedSupportNestedGain.support_size_le

Historical formal-review snapshot at PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-280: formal artefact coverage becomes 256 of 258; risk-weighted estimate remains 40%. Uncertainty range: 20% to 40%. Global gates: 0 of 5 closed. This is the original review, not the current project total. Original milestone record.

Concrete publication gate

Every required subcheck must be true

Gate input	Current result	Why publication stays closed
Concrete standard-model target	present, inactive	`PNP.Main.ConcretePEqualsNP` is an axiom-free definition, not a proof. Raw-machine eligibility and concrete CNF-SAT NP-completeness are established, but a deterministic polynomial-time CNF-SAT algorithm remains unproved.
Compatibility root theorem	false	`PNP.Main.p_eq_np` is absent.
Reviewed kernel fingerprints	unconfigured	Expected target/root/closure fingerprints are null; null never matches null.
Axiom closure	false	No eligible root exists to audit against the immutable Lean-standard allowlist.
Report-facing compatibility alias	present, not proof	`PNP.PEqualsNP` definitionally names the concrete target but cannot substitute for `PNP.Main.p_eq_np`.
Strict conjunction	passed = false	Theorem statement, conclusion, establishment, and emission fields derive only from this gate.

Remaining formal work

Five blockers remain; no project-specific axioms remain

Formal blockers

Formal.ConcreteSAT
Formal.ResidualBandMinimizer
Formal.ZeroSlack
Formal.PolynomialRuntimeAndCertificateBounds
Formal.RootTheoremAndAxiomAudit

Project axioms

None. The absence of project-specific axioms does not close the five mathematical gates or create the eligible root theorem.

No site wording, report digest, Boolean/string field, JavaScript checker acceptance, historical activation record, or review status clears these obligations.

Current and historical reports

Do not conflate the two documents

Current formal report

The canonical download is generated from the verified core inventory and retains the complete earned milestone ledger. For nested supports that have already been completed by the existing construction, the project now builds the comparison circuits needed to prove cost and positive-saving bounds. The bounds follow from those physical constructions instead of being assumptions.

Historical 57-page manuscript

The old direct-claim manuscript is preserved at tag final-pnp-proof-report-hardened-7072f8d, commit 7072f8d0bda6d44d240f9bb3fad624fd357e1278, with provenance in archive/legacy-v0/ARCHIVE.json. It is not current authority.