Follow verified milestones and corrections.

Update type: Correction, not an earned milestone.

Source-bound limitation: The global stopping theorem uses the exhaustive semantic reference minimum as a mathematical witness and requires a proof of global no-gain at a chain endpoint. It does not generate a route, derive global absence from a finite scan, construct the report ZeroSlack certificate, or establish polynomial runtime.

Compiled correction evidence:

• PNP.DirectWire.JointAsymmetricBound.zero_budget_read_once in PNP.NANDJointAsymmetricBound; audited axioms: Quot.sound, propext.
• PNP.DirectWire.JointAsymmetricBound.asymmetric_bound in PNP.NANDJointAsymmetricBound; audited axioms: Quot.sound, propext.
• PNP.DirectWire.JointAsymmetricBound.two_positions_permutation in PNP.NANDJointAsymmetricBound; audited axioms: Quot.sound, propext.
• PNP.DirectWire.JointAsymmetricBound.two_output_positions_bound in PNP.NANDJointAsymmetricBound; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineSupportMinimum.first_only_minimum in PNP.NANDGuardedSpineSupportMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineSupportMinimum.both_ends_minimum in PNP.NANDGuardedSpineSupportMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineSupportMinimum.proper_minimum in PNP.NANDGuardedSpineSupportMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineBoundedQuiet.proper_of_small_support in PNP.NANDGuardedSpineBoundedQuiet; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineBoundedQuiet.bounded_quiet in PNP.NANDGuardedSpineBoundedQuiet; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineBoundedQuiet.scan_none in PNP.NANDGuardedSpineBoundedQuiet; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineBoundedQuiet.quiet_with_strict_gain in PNP.NANDGuardedSpineBoundedQuiet; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineBoundedQuiet.quiet_nonminimum_exists in PNP.NANDGuardedSpineBoundedQuiet; audited axioms: Quot.sound, propext.
• PNP.DirectWire.GuardedSpineBoundedQuiet.no_uniform_zero_slack_limit in PNP.NANDGuardedSpineBoundedQuiet; audited axioms: Quot.sound, propext.

Core source: commit 0c98b51d6eb1a14f51cc612a69a1705c30a78ad1, tree cf2b90ab65bf4f95bf27506163bd26137086c64d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-280.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

A correction does not create an earned milestone or award proof-completion credit. Any score change must come from the canonical fixed-checkpoint ledger.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record. These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Update type: Correction, not an earned milestone.

Source-bound limitation: The unrestricted raw-port-complete compatible-support slack inequality is refuted by a kernel-checked eleven-gate counterexample: the whole word is minimum with slack zero, while its actual proper nine-gate cut has independent open minimum eight and slack one. Its smaller equivalent literal splice is cyclic. This does not refute the checked acyclic framed law or a correctly restricted full/admissible-support law. Complete source-derived full-profile admissibility, first-loss routing and the global proof obligations remain open. This correction adds no earned positive publication row or fixed checkpoint credit.

Compiled correction evidence:

• PNP.DirectWire.CompatibleSupportSlackObstruction.formula_exact in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.baseline in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.no_output_is_first_nand in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.gate_lower_bound in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.original_is_minimum in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.original_reference_minimum in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.global_slack_zero in PNP.NANDCompatibleSupportSlackMinimum; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.boundary_exact in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.interface_exact in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.selected_gate_count in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.smaller_formula_exact in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.same_open_function in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.comparison_reference_minimum in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.open_baseline in PNP.NANDCompatibleSupportSlackObstruction; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.local_reference_minimum in PNP.NANDCompatibleSupportSlackObstruction; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.local_slack_one in PNP.NANDCompatibleSupportSlackObstruction; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.global_slack_law_violation in PNP.NANDCompatibleSupportSlackObstruction; audited axioms: Quot.sound, propext.
• PNP.DirectWire.CompatibleSupportSlackObstruction.literal_splice_is_cyclic in PNP.NANDCompatibleSupportSlackComparison; audited axioms: Quot.sound, propext.

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-280.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

A correction does not create an earned milestone or award proof-completion credit. Any score change must come from the canonical fixed-checkpoint ledger.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record. These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computed-closed-support-nested-positivity

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 36

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-280.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computed-whole-support-minimum-bridge

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 22

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-279.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computed-closed-support-full-profile-gain

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 27

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-278.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computed-closed-support-profile-squares

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 24

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-277.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computed-wire-profile-exact-field-cost

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 72

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-276.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-profile-restoration-cost

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 19

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-275.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-profile-exposure-balance

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 35

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-274.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: source-derived-zero-cost-exposure

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 22

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-18-273.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computational-recoding-program-integration

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 88

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-18-272.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: structural-open-program-integration

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 63

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-271.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: structural-reindexing-support-transport

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 108

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-270.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: open-obligation-programs

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 144

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-269.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: proper-descendant-certificates

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 33

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-268.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: descendant-history-ownership

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 84

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-267.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: source-derived-history-ownership

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 78

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-266.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: computed-r7-history

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 41

Core source: commit f14cb7a87004ebedfa55351f6ba20d68a333cc18, tree 1cbaf64d8a7303b154848ec73f38e85e406defca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-265.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-history-arbitrary-support

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 24

Core source: commit 029153fc5d8bfc84c61d33858d0472bcbf3d3a73, tree d725f0e14d1a4625c0ce991364fa4481ef3c032a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-264.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-obligation-history

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 46

Core source: commit 029153fc5d8bfc84c61d33858d0472bcbf3d3a73, tree d725f0e14d1a4625c0ce991364fa4481ef3c032a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-263.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-causal-expansion

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 29

Core source: commit c3d4d9a115a357b44ee8104d129ee15e3174ec7f, tree 7bd3bc5854b0307330e9e405b5857de658eba54e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-262.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: context-aware-square-transport

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 14

Core source: commit c3d4d9a115a357b44ee8104d129ee15e3174ec7f, tree 7bd3bc5854b0307330e9e405b5857de658eba54e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-261.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: source-bounded-physical-boundary

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 23

Core source: commit c3d4d9a115a357b44ee8104d129ee15e3174ec7f, tree 7bd3bc5854b0307330e9e405b5857de658eba54e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-260.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-zero-unary-closure

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 27

Core source: commit c3d4d9a115a357b44ee8104d129ee15e3174ec7f, tree 7bd3bc5854b0307330e9e405b5857de658eba54e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-259.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-unary-support-search

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 36

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-258.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-unary-arbitrary-support

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 31

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-257.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-unary-frontier

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 30

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-256.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-unary-realization

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 18

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-255.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-matched-cancellation

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 26

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-254.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-frontier-lift

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 18

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-253.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-quotient-lift

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 17

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-252.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-obligation-restoration

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 22

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-251.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: wire-carrier-transport

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 16

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-250.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: arbitrary-support-splice

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 24

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-249.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-physical-normalization-closure

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-248.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-constant-propagation

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-247.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-dead-support-full-mode

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 8

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-246.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-dead-support-context

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 20

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-245.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-output-cone-pruning

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-244.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-final-report-bridge

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-243.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-constructive-nand-sharing

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 9

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-242.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-physical-ownership

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-241.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-independent-materializer-cost

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-240.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-gain-profile-firewall

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-239.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-physical-gain

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-238.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-saturated-support-context

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-237.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-physical-charge-ledger

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-236.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-physical-saturation-accounting

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-235.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-saturation-trace-fidelity

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-234.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-profile-locality

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-233.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-profile-dependency-semantics

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 3

Core source: commit 6296c6e1130fbae674548ccbf949f6e608b996c7, tree 78648f5978d16ff5055c5b493e5bb97ff4cd7cac, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-232.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cnf-np-completeness

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 2

Core source: commit e4af115a66cd5a6715a9363abea7a2008238d401, tree 28bf3e0bb8f4afccf308859c5f42f9c27b14edbb, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-231.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-complete-builder

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 6

Core source: commit a5e6b44e1345b5b1ca124391a5e57f02f95742dd, tree 48938071581c3242c612573da1f0eb2f2e3f967e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-10-230.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-all-route-body-remainder-split

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 3676a3f291193221e4ee3537aaf6023fba95ace0, tree c3dec3c8d169780bc507ed247bd9e3aebdedd430, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-05-229.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-all-route-derived-finish-split

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 79d36936abf796a3f306cede1b762aabc6907cd2, tree 21ad74de9008a4bed3466407ceaab4f5f8879322, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-05-228.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-all-route-staged-request-mirrored-dispatch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 87495e636bb33140921cf582925cc395f10ad128, tree d2e6efdeb1a005cc5ad6a557c54d7dc41e6a0255, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-04-227.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-terminal-join

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 9a81dd86dc92260f3cdc56b6a463b78c651cfad6, tree 4d7c4a0f8bf28a4b73a512055e65764117b88514, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-03-226.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-all-body-staged-request-mirrored-dispatch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 8a9c372156eea1b0f8bc47bd0c7b139b3a2f17b3, tree 9a706b16567f6a5d666fa2a4ee42e365402136e1, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-03-225.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-first-body-separator-mirrored-dispatch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 752be777ca2c366aa16bb8ff4bf9120a984f25b6, tree 9e4247b91b927fa976a1988b901f1e56c794eb5d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-03-224.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-finish-mirrored-dispatch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit c789e32045c712add73d4e89ac6a13e03d4b5dd2, tree 603a9c158a6768b8d1bf8ac711a390edda76eadd, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-02-223.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-finish-workspace-orientation

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit e792920a9ab18bdc22fae8cd090d792255889437, tree d0b2fbc81ac2fe417f6c2efbbb4d3fc46008d375, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-02-222.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-finish-request

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 71199826f380c39fa59796f0d9025651e34e1fe0, tree 15f633710cb9c5b2acaf441be1b5c1ff0e39f45a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-02-221.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-classifier-pipeline

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit c674c21b994284cdf6df40b43bf1a22920d0ec98, tree e2ca8c554b0a60061ebc1532c6a6b7ea9603f171, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-220.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-finish-request

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 4ccb40cb06ceeb2c375f072f16826a3fd4ae945f, tree 7f0074c44f5b21b37d313af797bf48f9c916827c, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-219.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-dispatch-schedule

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 4d5a16953633943eaaea7605aff1ad04f1a65424, tree 55f16431378b7fbd297ac35c1d0ca4741bb11802, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-218.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-physical-optional-token-dispatch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 5278e27d3ecbfde4ef6d635552ab687c08a9b12d, tree 42c17cda671b9a8d9edd105f1bb03b8051aacad9, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-01-217.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-complete-schedule-iteration

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 32cccbf7af9761dffac7d5139e3f10a87b98358c, tree d7ff15bb4efb7cf2e659e9b18faa664948254018, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-31-216.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-post-divider-selected-token-launch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 76bd4815a3294b3642db76f1737ffd3e0e31266e, tree 475421b175cab1931d913bcd59a6fc17a82dcc85, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-31-215.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-post-divider-raw-route-classifier

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 1f749eec50cb57c0595b1fa1e8dfc8ccd497c2e8, tree 2b1a8949087773d9ca1d100e3a099412cac3edcd, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-31-214.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-post-header-raw-tape-bridge

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit f5d42870ee50c903ebcff8a71da05a74256be59d, tree fdbf10651b1f160988ff0c03015c5bc0eba302f5, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-213.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-post-header-raw-launch

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 3d2cc2eda40f6dcaa7758e96af14b203f69c55cb, tree 781d8e0fad18dd115109ba7d669286b441066b48, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-212.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-post-header-raw-divider

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 9f009edfa7588f47df90a338880bbdd9ce25ac93, tree 9ffe9ae07144c88164062f915f3de2addc36682b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-211.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-arbitrary-slot-post-header-decoder

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 228e9d3b249870ad59fa7042656827f35a535abc, tree d8ea3358fee8544f797138038802836eeb88f419, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-30-210.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-arbitrary-slot-header-router

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 8529753cac12243c0a618facfca31e2287368469, tree e55427ff8450582ca1ec781084082896d40121e6, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-209.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cook-levin-builder-full-schedule-cursor-controller

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 1d4e562bef4d03c54f22a01983a3842198aef0ae, tree 3e8e049b73a1daee34d11bfbf62955b41830eb75, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-208.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-pkgc-restoration-coverage-charge-descent

Classification: formalized-pccmin-checked-packet-pkgc-restoration-coverage-charge-descent

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit ab5ed194e1420eb801dfdbf98b27a5fcc4fd4b98, tree edbd5b558f778238abb46b5d7d54ce662a06b9fa, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-207.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-pkgc-restoration-coverage-bn6-bcel-route

Classification: formalized-pccmin-checked-packet-pkgc-restoration-coverage-bn6-bcel-route

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 2a2c3bdab876d430f462bd357b76d0f2e21fc023, tree 7df5204b9a591e1f4edd88b9644e2cc028b4acc5, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-29-206.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-restoration-coverage-bn6-ledger

Classification: formalized-residual-terminal-pkgc-restoration-coverage-bn6-ledger

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 385df6cc15cf963a19c2ec5ea96b2e22fcbe76b9, tree 9dc5f189d244ccc08181963a3c94d99d53b7a094, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-205.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-restoration-coverage-ambient-route

Classification: formalized-residual-terminal-pkgc-restoration-coverage-ambient-route

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit a08ab544b3d609ffd1793227635a9ac7a18394a4, tree 0ff0cddbd35d35767f437d12d780e46ca5657190, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-204.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-pkgc-ambient-bn4-extraction-route

Classification: formalized-pccmin-checked-packet-pkgc-ambient-bn4-extraction-route

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 171a90983820e1c6bba2fcf85203843b4bd3f5da, tree 513bbcf670bdfb02ae2640949aa8ba37c372fbcd, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-203.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-pkgc-bn6-bcel-source-route

Classification: formalized-pccmin-checked-packet-pkgc-bn6-bcel-source-route

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit a3115c0e42924db4e9c400268d63b942360e71a0, tree e91e8f657ba7b13504350521b32db32cccb03533, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-28-202.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-bn6-positive-cellization

Classification: formalized-residual-terminal-pkgc-bn6-positive-cellization

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit e0d08b9d0f294b64d41035125ce0dab1ee6188d8, tree b835319af691a07d8770f19cf6e5d0cba4c26c56, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-201.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-bcel-sparse-activation-route

Classification: formalized-pccmin-checked-packet-bn6-bcel-sparse-activation-route

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit e355f1c93ef17f7d8069cc128b204a351b4792b7, tree 2c1d5db7d1cb9da674411ae48016ec110c3510ea, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-200.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-bcel-canonical-constant-cut-basis

Classification: formalized-pccmin-checked-packet-bn6-bcel-canonical-constant-cut-basis

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 02a8fc9ea8fb7c338b9c6a484020fe6dfc754872, tree cbb00cdfdd0e002dfd0db55594dc5f0e997f0866, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-199.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-bcel-canonical-cut-ledger

Classification: formalized-pccmin-checked-packet-bn6-bcel-canonical-cut-ledger

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit ebebf9356116e3b8dca9fbae6999826c026fa18b, tree d76d40eea44b8b38c07080f0159d5d157acd3b67, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-27-198.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-bcel-canonical-grouping

Classification: formalized-pccmin-checked-packet-bn6-bcel-canonical-grouping

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 54aa7d8c2fa0a728e6e0af9349c78f27f510d989, tree bf5ebec44a12204145478b17397048b94594a725, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-26-197.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-bcel-derived-family

Classification: formalized-pccmin-checked-packet-bn6-bcel-derived-family

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit eb631703727b4121447eab01060712343b5e22f1, tree 7ef662f771f3bbe5c2940fe0a5e630a53ddd597b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-26-196.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-bcel-activation-route

Classification: formalized-pccmin-checked-packet-bn6-bcel-activation-route

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit b9523fe7ea939cd90dba5671aa627986e1f22f18, tree d17e62bdcfc1b2e8aadbb48a1e27771f0c2f82cc, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-26-195.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-bn6-hb-zeroslack-bridge

Classification: formalized-pccmin-checked-packet-bn6-hb-zeroslack-bridge

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 821f05facdda1d41e6c1fb7b2e5206b2e2703715, tree 9c6ac637e739ca23fcd30ae31d6d414475e406a3, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-194.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-hb-zeroslack-bridge

Classification: formalized-pccmin-checked-packet-hb-zeroslack-bridge

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 9f2e7f022d1483702a1ead06392ac2dafe86120b, tree 97749e342254a6ab3d798a73c6282ad3902f1c97, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-193.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-checked-packet-ranked-selector

Classification: formalized-pccmin-checked-packet-ranked-selector

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 15bd5d38829657bd0fd50954ec32df485f07f196, tree d1fb6974132d90ccc9717385a9377fe4f4ff92d1, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-192.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-rank-ordered-oracle

Classification: formalized-pccmin-rank-ordered-oracle

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 0dbad6e14d82bf1f6f1d7b315dc896bdceb325a6, tree 8f3893c6ff351315be7a4ca8b7fff8c5d5f3cd0a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-191.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-normalize-oracle-composition

Classification: formalized-pccmin-normalize-oracle-composition

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit c912b110f14386d335d58bb89b1bb9bb643bffb4, tree 42d5414571038517da97b3ba59a334790144b928, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-25-190.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: pccmin-total-oracle-loop

Classification: formalized-pccmin-total-oracle-loop

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 6e7124f7edf19b2ab077b9b52ed267cb6ecb00e3, tree ca4fab1d10d275a6639c980140f4c6c62fdec040, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-24-189.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: typed-pccpack-reflection

Classification: formalized-typed-pccpack-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 37bbbd1d978df770087a0cd675b90eba2cfc50ad, tree 3e21dbdb8b3c15c11121901d5cbf55ac0d6999c4, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-24-188.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-residual-band-compatibility

Classification: formalized-concrete-residual-band-compatibility

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 7dc26600f55762bf7a65b3fc6512a76aba23d9d0, tree e5d2dc08084b68b455b7249c4add156ef8e05651, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-24-187.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-legacy-locked-nand-compatibility

Classification: formalized-concrete-legacy-locked-nand-compatibility

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 6

Core source: commit 63ba53d76da0878b0d3b2834b891afcc6ef0fe0e, tree 98103f568ccb68561094d5516ada08c099f770a7, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-186.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-finite-bcel-packet-activation-obstruction

Classification: formalized-residual-terminal-finite-bcel-packet-activation-obstruction

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 6

Core source: commit edcf84c74280b455ca656ee57653d6fb07cfcc30, tree d8187018fb200e9ad9b8877988c8584f86bbafe7, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-185.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-finite-bcel-packet-carrier-coherence

Classification: formalized-residual-terminal-finite-bcel-packet-carrier-coherence

Verified scope: 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.

Recorded milestone 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 539040537eb91c62ca405c048f0be95067596f5e, tree 5155f087f5243d0e4b44b3c9e34766dfbb420c9c, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-184.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-finite-bcel-ready-composition

Classification: formalized-residual-terminal-finite-bcel-ready-composition

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit 74d7f531bebe302cba08ad992fd4d48d46a8b29e, tree 0744ba3a38151338dada4171453093b05e4af3a2, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-183.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-zeroslack-packet-selector-hb-coherence

Classification: formalized-residual-terminal-zeroslack-packet-selector-hb-coherence

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit f6f78026f9ff3be2f45b8fce859d2c09b6a8d764, tree c6feae0f7d20a0c80c561e822f6db85252563585, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-23-182.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-bcel-packet-no-lower-zeroslack-sidecar

Classification: formalized-residual-terminal-bcel-packet-no-lower-zeroslack-sidecar

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit a9559242cd6171e217e9917c9c70f99a98ca7757, tree 9d24021681b86580c96dab85e80aec98263abf70, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-22-181.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-budget-no-lower-zeroslack-sidecar

Classification: formalized-residual-terminal-packet-budget-no-lower-zeroslack-sidecar

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 54305498ca55425a39cfee7892b40181e250bbdd, tree 82fe3fa227ef1c48f70369bdcadcdaaefe40c8ab, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-22-180.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-selector-hb-zeroslack-sidecar

Classification: formalized-residual-terminal-selector-hb-zeroslack-sidecar

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 29279d1a9608a97832b7ad05e69a3fea05f39dd3, tree 1cf0190b5994fb14d4316c0c7852a15240d9d483, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-22-179.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-budget-zeroslack-sidecar

Classification: formalized-residual-terminal-budget-zeroslack-sidecar

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 98da0c0ad5614d69f5f5b50f629a759dc5c29fb9, tree 359c4da36a69e7c9ea0f1b95b8ec6448e40f4b89, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-22-178.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hresolve-zeroslack-sidecar

Classification: formalized-residual-terminal-hresolve-zeroslack-sidecar

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 337e07e725f72ddd832c2a7885d505e9044838be, tree 0432aef434d94ab43847aeec7730b76f739c5d05, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-22-177.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hresolve-certified-path-family

Classification: formalized-residual-terminal-hresolve-certified-path-family

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit ca501ca3df44c8d19933e59fe132612bea5422c2, tree ceab2cfa341b7437c01a98772912a464902451eb, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-21-176.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hn-bwl-certified-path-minimum

Classification: formalized-residual-terminal-hn-bwl-certified-path-minimum

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 15

Core source: commit fe62125f12511d042b119c9f17ceb202d03448bb, tree 680292d98320fa9a60bfff9abb2bac5bcd4333ca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-21-175.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hresolve-maximal-h-disjoint-family

Classification: formalized-residual-terminal-hresolve-maximal-h-disjoint-family

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit b1b93861a2205deec70452df3db8d66a5cf8a8d5, tree 8602575fed235009bd4b8ea4e988b77799066950, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-21-174.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-budget-no-lower-composition

Classification: formalized-residual-terminal-packet-budget-no-lower-composition

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit f3dd861bf522e9fca2a3c1ba4a4c3e78f5454b4a, tree 855b8c6001b757836b65b80e1107f1043131251e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-21-173.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-budget-no-lower-ledger

Classification: formalized-residual-terminal-budget-no-lower-ledger

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 8

Core source: commit 2d66e5a7c3468b51e019c638f43780e7acfb8f93, tree ee59e6669ba9aa9df52997cf86aa68e73415d349, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-21-172.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-budget-envelope-resolver

Classification: formalized-residual-terminal-budget-envelope-resolver

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 6d598d9ef6a866f475bcc0fa0e5d1f65061524d4, tree 5fcde27e914cfe44410a28b9b9755aefa4cdc27d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-21-171.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hresolve-support-resolver

Classification: formalized-residual-terminal-hresolve-support-resolver

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 7080186d2b2701c9b472071cc14c04292a5dff6f, tree 4f42045af939c79fdb3f5bfd6f2ed8ea4c70ef9c, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-20-170.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hresolve-coverage-ledger

Classification: formalized-residual-terminal-hresolve-coverage-ledger

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit ed0ba30a44abb27dbd4e5914541b9fcc8bd82950, tree c5b783f5bb02e59a5601921b294c7c4872d29ed5, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-20-169.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-no-lower-ledger

Classification: formalized-residual-terminal-packet-no-lower-ledger

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit 8b074cc2e8f840009a4ee064dd9dc6299c278004, tree 50d363cc8746af0a4e19f5a5467923bcd463e39b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-19-168.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-descent-no-lower-binding

Classification: formalized-residual-terminal-packet-descent-no-lower-binding

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit 7a3308520a68b5553cc95a7b56c560a20508111a, tree 792ed1354928bb38a9582af0f7c57d18992fe85f, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-19-167.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-semantic-hn-activity-binding

Classification: formalized-residual-terminal-packet-semantic-hn-activity-binding

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit fe6c20fe6929c9e57c5ab7c483f7c56bfa9e9832, tree 71bf1d7b3b7b0cfa4ed35065404277258e52d118, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-19-166.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-budget-hb-activity-binding

Classification: formalized-residual-terminal-packet-budget-hb-activity-binding

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 9f26c50f8e8bfbda9cb15a8142c6191482148220, tree 8eb9cf577a94722f3f805a463fcdf7072e60a4d2, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-19-165.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-budget-route-reflection

Classification: formalized-residual-terminal-packet-budget-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 30

Core source: commit 055325ee54abddefc595ccb826ea410dc8be2231, tree b7901a65cf63fcef9a029023761085f234b6bc5e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-19-164.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-direction-route-reflection

Classification: formalized-residual-terminal-packet-direction-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 28

Core source: commit 289ccde2874be3f2f4684470602cad073858fac0, tree f0e0d8ac1d1e538deb8ae2e75de50988c7abae48, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-18-163.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-bn4-activation-route-reflection

Classification: formalized-residual-terminal-packet-bn4-activation-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 28

Core source: commit 8978e4d55ef11b26276d3726d8eea38caa3397fe, tree 7ee8f15af0e232ffc26df9fc178f8ad10666a6b4, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-18-162.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-bn5-obligation-route-reflection

Classification: formalized-residual-terminal-packet-bn5-obligation-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 26

Core source: commit 97ca87c3588deab60b8126c204d4d63b10dc2c85, tree ad75312852cd810d4caae740e2b2c8ebbfd456cb, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-18-161.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-frontier-route-reflection

Classification: formalized-residual-terminal-packet-frontier-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 23

Core source: commit 52b77de8a79e41527b4fbab788d433ec031da459, tree de1d06adcc136c567bfb28ad337b0d34d6be023e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-18-160.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-colour-route-reflection

Classification: formalized-residual-terminal-packet-colour-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 22

Core source: commit dcba2fad66dcbdaaad5c3ebb939b0130e9a95bf8, tree a23af77ef3eb3ffade774d667a39982e6eb527ba, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-18-159.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-charge-route-reflection

Classification: formalized-residual-terminal-packet-charge-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 19

Core source: commit 83b2a786c1960e15d193404eb7a5eef14fd0cb89, tree 256aa873ed2d18e3650a5a2c22d8ea13ae960443, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-17-158.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-exact-route-reflection

Classification: formalized-residual-terminal-packet-exact-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 16

Core source: commit 26547c1a3c05de0c907021320352a46a8145dbaa, tree 9e6f148199075ef04d6d5a19405ceaa6121cd18f, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-17-157.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-rank-route-reflection

Classification: formalized-residual-terminal-packet-rank-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit 206e3d3a3fa6d173bde009a5afca0f0510759d2c, tree bdb78783c739ac72c1dfd368dee60917e03fa276, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-17-156.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-descent-route-reflection

Classification: formalized-residual-terminal-packet-descent-route-reflection

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 9

Core source: commit 60ac6413b5329650b68cac8f6fefcee2f7a430f4, tree 61bb9ad09c600518ab0884e26c3b85bfedc96532, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-17-155.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-first-route-semantics

Classification: formalized-residual-terminal-packet-selector-first-route-semantics

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 6

Core source: commit b69c7419158154187c2adc6991ebe31aef6538f9, tree 43afa4efa61e45a6d94c099d235b4fb691401b2c, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-17-154.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-first-route-outcome

Classification: formalized-residual-terminal-packet-selector-first-route-outcome

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 72e2509cb18080700a764dde8309060a7d9bb21c, tree c943e898cd30d1ad1c479af2a29718b3c336c583, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-17-153.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-faithfulness-table

Classification: formalized-residual-terminal-packet-selector-faithfulness-table

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 8

Core source: commit 8bc8d36fea5abf3f486e9dbfe7cfccea5c6b34e0, tree f25cf38b740b398e071a2a9c3e964d933bd26838, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-16-152.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-faithfulness-routing

Classification: formalized-residual-terminal-packet-selector-faithfulness-routing

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit b2e0b1e97744e365528b7c1a06e208a6481d7d1a, tree 28ee8cf19a2092479f2661ac5ad7cb5c54cfe734, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-16-151.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hb-executable-selector-silence-induction

Classification: formalized-residual-terminal-hb-executable-selector-silence-induction

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 0a21d196359069a09be43c489a8fe4a95f5c8cf6, tree 96c474678413f986a0fd8e58be029ba1bb860f1b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-16-150.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hb-selector-silence-closure

Classification: formalized-residual-terminal-hb-selector-silence-closure

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit f3ca3346b3cd2b33e1259321297b6149ac5c52db, tree 893ca3bf26930886e798ce69e1f846fd96460e8b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-15-149.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hb-active-dependency-closure

Classification: formalized-residual-terminal-hb-active-dependency-closure

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit ff003dc1e86367a072e783d7fb8e32d374feed05, tree 31387d243fbcfa8fa62f683377c238861b0830f9, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-15-148.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hb-dependency-table-closure

Classification: formalized-residual-terminal-hb-dependency-table-closure

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit d3794beaf85242ea6d5c4f141f74e52876261c4f, tree b870327f236eca3badc60cdd020028f90a5dcfe3, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-15-147.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-hb-blocker-graph-acyclicity

Classification: formalized-residual-terminal-hb-blocker-graph-acyclicity

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit 9835168ab80564fce8a7a66c0a2c2d0d9027ff07, tree efd51b34650f9e4fd8d91bdf7258185e8256503f, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-15-146.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-typed-realizer-contract

Classification: formalized-residual-terminal-packet-typed-realizer-contract

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 7cba7335d300b31617fde64a2c7a96c758c6fdf5, tree 96a3a0b839c0ca66d32572dd54146b1a5e773772, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-15-145.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-unit-charge-blueprint-realizer

Classification: formalized-residual-terminal-packet-unit-charge-blueprint-realizer

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 13

Core source: commit 5f2d880b953cfc1f2d26b6fc0d6a97d5a1c2b8cf, tree e5f2d5c750718a77248b7f4f84f2d80f2897d696, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-14-144.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-charge-surplus

Classification: formalized-residual-terminal-packet-charge-surplus

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 8

Core source: commit 77b275efe586e68339f6dd61abb5a2d3abcdce68, tree 4b71837f0f4c8d078a95f003264c157a5e4d33d3, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-14-143.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-gain-coverage

Classification: formalized-residual-terminal-packet-selector-gain-coverage

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit f149a972c366b96a3db704aaa1a23679abc21b6a, tree 6b526cd25b1b871e1d6a65e20162c23d92d4b4ae, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-14-142.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-universe-gain-scan

Classification: formalized-residual-terminal-packet-selector-universe-gain-scan

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 5055eaaa82a57ee5ce0793f07e2f49ae82189169, tree 3f35e3fb250da4ed62fa68e29f69ba4bef81e6dd, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-14-141.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-gain-scan

Classification: formalized-residual-terminal-packet-selector-gain-scan

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit fa7436c2bb0efcc77f1a8b193b918c6d97d3d3b5, tree eb155a196d8e73a6d28efe23d76bc89b5df1a075, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-14-140.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-payload-realization

Classification: formalized-residual-terminal-packet-selector-payload-realization

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit 38ad00f1798b703371c4d32d1507b43268f0ea9f, tree 9f12ba9e28d68818e6ecf7f776181e80a42d1b1b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-13-139.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-codec

Classification: formalized-residual-terminal-packet-selector-codec

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit 81155a482de1e7cf1cd974cc8078dbd94d88d8ae, tree 613e81db14201e554d47a6cb56d4411a80bdff1d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-13-138.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-handles

Classification: formalized-residual-terminal-packet-selector-handles

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit d9940d34f6273831dd889f1e23073ce9bff1b039, tree 287a5b7c0ea9abb3165851028b753eb55d61dd12, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-13-137.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-universe

Classification: formalized-residual-terminal-packet-selector-universe

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 6

Core source: commit 28829559f3c2a151fb1983fa408e979296cdde76, tree 42c42a0b0add5d589c6402d27cac321465e8059e, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-13-136.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-packet-selector-seeds

Classification: formalized-residual-terminal-packet-selector-seeds

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 3

Core source: commit a98bdbcd759e80cf3953a336f9b7755e68bf29d3, tree cfc43d9c8392fb3a61f4f156c9fff6cd0f216e7f, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-13-135.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-ambient-bn4-residual-reduction

Classification: formalized-residual-terminal-pkgc-ambient-bn4-residual-reduction

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 8

Core source: commit d677d7704c29642490b9262b48139f9f3eb097dd, tree 0c92e684275589eea09c8477b9b7f670c3056b6b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-12-134.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-ambient-bn4-ledger

Classification: formalized-residual-terminal-pkgc-ambient-bn4-ledger

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit 63f38f39881dd8293e139b1687bf09688acb8e5d, tree af26f9121bd2b6e7d2df11e1d7f3152a0af6914a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-12-133.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-same-key-cancellation

Classification: formalized-residual-terminal-pkgc-same-key-cancellation

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit a46bc46175186748592af32661641fc232dae109, tree caddf0db1c54ee534653a1435047b796aac8025f, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-12-132.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-typed-restoration

Classification: formalized-residual-terminal-pkgc-typed-restoration

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 9

Core source: commit fe2c8ceb024d0a1afcb2a79a21015eb2969c37bd, tree 31e942af36667a728849744f7512fd690bbd3194, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-12-131.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-pkgc-separating-consumers

Classification: formalized-residual-terminal-pkgc-separating-consumers

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 9

Core source: commit 49c463eb734ad7c11ece63177948c9df0af8f52a, tree 4622cebf0bf937b0f4d9c9decb62383aefe9b416, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-12-130.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-bn6-hypergraph-packet

Classification: formalized-residual-terminal-bn6-hypergraph-packet

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 8

Core source: commit d77a5faf194b86fd1175065a0930fd485e16ace5, tree 34344e42d12991af68f7ed81ca575cff0307f69a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-129.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-constant-cut-hypergraph-rigidity

Classification: formalized-residual-terminal-v53-constant-cut-hypergraph-rigidity

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 8e38de05d9e1b3066484c9fc5555813997076d02, tree 1aca9eafba5ac7a0aaf6d2fe63774a479ac24126, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-128.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-consumer-antichain-normal-form

Classification: formalized-residual-terminal-v54-consumer-antichain-normal-form

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit dd7b9be6ad6d05d516da2baf48813ae608c4e46d, tree d755c0b1ab7e407e11ce03428e7f1e68a03ca645, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-127.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-bn5-full-shadow-localization

Classification: formalized-residual-terminal-bn5-full-shadow-localization

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit b829e62744c3e645726f7cba9875fe6926a6b207, tree dc1e76c188b26b9311b2a65f8a8376f497cdd69d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-126.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-bn4-activation-cancellation

Classification: formalized-residual-terminal-bn4-activation-cancellation

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 13

Core source: commit ef94583b39f7050953a78a7a6e0ad431cd2eb459, tree b82aecb1817c83a2b3ec840680aa0f9a9f31870b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-125.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-bn3-request-envelope

Classification: formalized-residual-terminal-bn3-request-envelope

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit 85c72816225bc6feab4ffc60499475419645dd73, tree 773d96dae8e14038cc35893dc85402a25bf1b655, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-124.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: global-locked-nand-threshold

Classification: formalized-concrete-locked-nand-threshold

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

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 1

Core source: commit 7445d2afa7af75375d20751b4a0aa7b87e8b8dfc, tree 7376c3d35ebfd9a80e38abb86964e60df6d4f4b3, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-11-123.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-CONCRETE-LOCKED-NAND-THRESHOLD-121.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-rank-wf

Classification: formalized-residual-terminal-rank-wf

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 18

Core source: commit dd69b94a762eb830a3b91503faffde3984cce84f, tree d06833216d204b8eca0510267654263e79752e51, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-10-121.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-RESIDUAL-RANK-WF-120.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-finite-saturate-positive-composition

Classification: formalized-residual-terminal-finite-saturate-positive-composition

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 9

Core source: commit 3f4352d190b44d34866500e672c2ef2af89e08de, tree 2133ae4be763f61dda2c6f8fcc6e194ba777feb2, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-10-120.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-FINITE-SATURATE-POSITIVE-119.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-interface-exposure-routing

Classification: formalized-residual-terminal-interface-exposure-routing

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 19f43501ad87d4c5611ba109d53157fd0bd1dfdb, tree 574fa83fd6dd1b0d124770d1f577bf3f0147aaa4, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-10-119.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-10-INTERFACE-EXPOSURE-ROUTING-118.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-candidate-saturation-cost-balance

Classification: formalized-residual-terminal-candidate-saturation-cost-balance

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 17

Core source: commit ead67f4864902e667e5fd436eea21c61de2f871e, tree 072fe73440ac21f5daa7a9a3a79b51deb459aeb6, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-09-118.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-09-CANDIDATE-SATURATION-COST-BALANCE-117.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-saturation-positivity-firewall

Classification: formalized-residual-terminal-saturation-positivity-firewall

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit e6fcbad711f1bdfcc67d8e4c748f2a65d192b8a5, tree 1a326290d19798563b9ed4680228ff595b620248, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-09-117.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-09-RESIDUAL-TERMINAL-SATURATION-POSITIVITY-FIREWALL-116.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-computed-bcel-anchor-nucleus

Classification: formalized-residual-terminal-computed-bcel-anchor-nucleus

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 36

Core source: commit f0bad8053fa334d4d996abd8ee5b796138526ec8, tree 2e5ee34ffcea47219605756ef3041246996c734c, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-09-116.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-09-RESIDUAL-TERMINAL-COMPUTED-BCEL-ANCHOR-NUCLEUS-115.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-computed-bn2-square-legitimacy

Classification: formalized-residual-terminal-computed-bn2-square-legitimacy

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 20

Core source: commit ca60f66498eaa4a6242e15c86fa86a2fe62e78f9, tree 86a19d87f564dd644f78ceea604c18a30ad223ca, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-09-115.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-09-RESIDUAL-TERMINAL-COMPUTED-BN2-SQUARE-LEGITIMACY-114.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-four-corner-tight-basis-maximum

Classification: formalized-residual-terminal-four-corner-complete-tight-basis-maximum

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 28

Core source: commit fc47845928f2cafb4f7ebbafed38e5e7a8a6c25a, tree fa466d44f3d5cd15ebcd6fabe0a961582cb66c25, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-08-114.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-08-RESIDUAL-TERMINAL-FOUR-CORNER-TIGHT-BASIS-MAXIMUM-113.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-four-corner-side-tight-completion

Classification: formalized-residual-terminal-four-corner-side-tight-completion-under-local-route-silence

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 20

Core source: commit 78c8862e74f251622cdd2eed65e44fd3d0586301, tree 763dcc3b89004639f93e483e4464b3faf7ac4bf7, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-08-113.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-08-RESIDUAL-TERMINAL-FOUR-CORNER-SIDE-TIGHT-COMPLETION-112.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-four-corner-optimum-coherence-dichotomy

Classification: formalized-residual-terminal-four-corner-optimum-coherence-dichotomy

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 19

Core source: commit 34713d47d7e00298aeb532dc9d5c69e57d11f296, tree 8f141b6aa8a7300309c15430e54bf093aceead14, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-08-112.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-08-RESIDUAL-TERMINAL-FOUR-CORNER-OPTIMUM-COHERENCE-111.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-four-corner-optimum-carrier-compatibility

Classification: formalized-residual-terminal-four-corner-optimum-carrier-compatibility

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 30

Core source: commit df4f4d830f6a0fd44af51edb0be178652d1b9417, tree db7e1089cbeed18e98a48bbb5000f0985608f1c9, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-08-111.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-08-RESIDUAL-TERMINAL-FOUR-CORNER-OPTIMUM-COMPATIBILITY-110.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-four-corner-carrier-transport

Classification: formalized-residual-terminal-four-corner-carrier-transport

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 27

Core source: commit 45e828437ed335a62dbc4e9889e65ee383c53139, tree 89d37dd773ec1369ee22d97f8ee0cb3c9da41c9b, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-07-110.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-07-RESIDUAL-TERMINAL-FOUR-CORNER-CARRIER-109.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-side-tight-minimum-arithmetic

Classification: formalized-residual-terminal-side-tight-minimum-arithmetic

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 24

Core source: commit 4aad02a158f05e18809748e8a6234ea568b76bfc, tree 0781b85b3960a177bd421aff73aa88c07370af0a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-07-109.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-07-RESIDUAL-TERMINAL-SIDE-TIGHT-MINIMUM-108.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-governed-projection-square

Classification: formalized-terminal-governed-projection-square

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 23

Core source: commit 23abd2eaf8913ea91dc1cf379878f278b9ee3d10, tree 5d2486bd4233650eb4a4186ababb9db99ac57f17, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-06-108.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-06-RESIDUAL-TERMINAL-PROJECTION-SQUARE-107.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-governed-frontier-pushout

Classification: formalized-terminal-governed-frontier-pushout

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 28

Core source: commit 31937a36ecc21413e334e5e7f7f27058f0dfecc7, tree 795ca7177f7a99e301b19e4dca7c3abac914d1ef, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-06-107.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-06-RESIDUAL-TERMINAL-FRONTIER-PUSHOUT-106.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-governed-support-completion

Classification: formalized-terminal-governed-support-completion

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 26

Core source: commit c225e91eeb469cd87f0c52c9731074e8b66fc573, tree 9616b6c150124561a7f88672aa20a34bba1a4aae, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-06-106.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-06-RESIDUAL-TERMINAL-GOVERNED-SUPPORT-COMPLETION-105.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-saturated-support-square-closure

Classification: formalized-terminal-saturated-support-square-closure

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 23

Core source: commit 7e4f3a683f87f0009c2c6010678ff022638bc8b8, tree ee1727221b3600193b9f622dc1cc060c3b2c8833, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-06-105.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-06-RESIDUAL-TERMINAL-SATURATED-SUPPORT-SQUARE-CLOSURE-104.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-proper-positive-support-search

Classification: formalized-governed-proper-positive-support-search

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 22

Core source: commit bdbbabc67f20b5d4f673e11098ba86a9d10a1cf1, tree c26d7b20ab7d5241ad4fc7f214ac06b9477e78c6, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-05-104.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-05-RESIDUAL-TERMINAL-PROPER-POSITIVE-SUPPORT-SEARCH-103.

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These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-support-extraction

Classification: formalized-terminal-support-extraction

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 21

Core source: commit 5bc35c370e0d8987c69bd51f7f31e29070f7c162, tree 9f28a98946ada047b8a3beb50158239d66ecf5d9, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-05-103.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-05-RESIDUAL-TERMINAL-SUPPORT-EXTRACTION-102.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-physical-support-completion

Classification: formalized-terminal-physical-support-completion

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 14

Core source: commit 9a01a9aee903b0d76132e80d40eed9004dc4eae1, tree 10972cee78cd0c70926b2ea13fbe073e6202a43d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-05-102.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-05-RESIDUAL-TERMINAL-PHYSICAL-SUPPORT-COMPLETION-101.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-saturation-closure

Classification: formalized-terminal-saturation-closure

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 7

Core source: commit e355c176bd0e961b5db41dd11fc5b2ccfe6642fb, tree 2ab1d800d697d4f6f0fa360615f4315ff277c022, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-04-101.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-04-RESIDUAL-TERMINAL-SATURATION-100.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-projection-transfer

Classification: formalized-terminal-projection-transfer

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 4

Core source: commit aa888e54beeff5be0162415fa962f80b4b18d113, tree d3978744cfd0f86905a6bc934b012a7468e1e49f, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-04-100.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-04-RESIDUAL-TERMINAL-PROJECTION-TRANSFER-99.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-projection-minimum

Classification: formalized-terminal-projection-minimum

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 14

Core source: commit accf07e45123837661307a37a02d2119ecd7aacc, tree 79f2ab904d9c90db6aa2d10ba2931c11a036b747, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-04-99.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-04-RESIDUAL-TERMINAL-PROJECTION-MINIMUM-98.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-mode-firewall

Classification: formalized-terminal-mode-firewall

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 12

Core source: commit 1c9732052c9fbb05b7bea33887cfefea535a1c01, tree 88b8b18e0adc1e62d78d2b6b37bdfcb9d2a95332, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-04-98.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-04-RESIDUAL-TERMINAL-MODE-FIREWALL-97.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-terminal-full-carrier-bridge

Classification: formalized-terminal-full-mode-semantic-bridge

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 13

Core source: commit 1361ec17b033acc591d0bd91a7a6e7ec552a449b, tree 3fd4f4bf9d41fbc7f1a56daf28b1060766df006a, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-03-97.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-03-RESIDUAL-TERMINAL-FULL-CARRIER-BRIDGE-96.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-gain-stopping-specification

Classification: formalized-semantic-stopping-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 10

Core source: commit 1b5c1bc1f563d39c58b735c7163be661042c1356, tree 2daff0f133177f30a79e4d1ce01d44f721954124, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-03-96.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-03-RESIDUAL-GAIN-STOPPING-SPECIFICATION-95.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: residual-gain-chain-bound

Classification: formalized-iteration-bound-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 14

Core source: commit 3894e5e2dd3f34c2fe19f6eb0b9e39119ad05403, tree 83f4874213a6c2be7c182d9e33d61a0e1b250acb, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-08-03-95.

Publication: PUBLIC-SURFACE-BASELINE-2026-08-03-RESIDUAL-GAIN-CHAIN-BOUND-94.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cnf-to-nand-polynomial-reduction

Classification: formalized-polynomial-reduction

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 28

Core source: commit 3e60a7b270d4695da137a60d6a4a9ca59d3886f8, tree 04dbf61379eb4d24f1adc8419bf6e9d2dd636346, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-07-31-94.

Publication: PUBLIC-SURFACE-BASELINE-2026-07-31-CNF-TO-NAND-POLYNOMIAL-REDUCTION-93.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-cnf-to-nand-semantic-compiler

Classification: formalized-semantic-boundary

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 18

Core source: commit 95773a6583ca3d41f7b0c82090f000d9c6eb72da, tree 9890af1d8b919dd432ec00707eb5555d720000d1, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-07-31-93.

Publication: PUBLIC-SURFACE-BASELINE-2026-07-31-CNF-TO-NAND-SEMANTIC-COMPILER-92.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-locked-nand-polynomial-reduction

Classification: formalized-polynomial-reduction

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 5

Core source: commit 03f62a5465c1eacd399671121123a3891d8b3e67, tree 9ac174c23560579e75091fefda81f81e986b6cc1, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-07-30-92.

Publication: PUBLIC-SURFACE-BASELINE-2026-07-30-LOCKED-NAND-POLYNOMIAL-REDUCTION-91.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-locked-nand-target-emitter

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 22

Core source: commit 23f53b6efccee3ff50987cf55338b8b01ddad343, tree 1549519b1c971a062b5315c8146272786a407648, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-07-29-91.

Publication: PUBLIC-SURFACE-BASELINE-2026-07-29-LOCKED-NAND-TARGET-EMITTER-90.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-locked-nand-source-parser

Classification: formalized-foundation-only

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 20

Core source: commit a20c99f035eeb6bc3cafc7184bec6c40f9cbda22, tree 6114efcd6cf47f1e960eaf22bedc66e73ebb2f72, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-07-29-90.

Publication: PUBLIC-SURFACE-BASELINE-2026-07-29-LOCKED-NAND-SOURCE-PARSER-89.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.

Milestone: concrete-locked-nand-encoded-semantic-boundary

Classification: formalized-semantic-boundary

Verified scope: 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.

Recorded milestone boundary: 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.

Later milestones may close obligations described as open in this recorded boundary. See the current proof tracker and current proof boundary for today's project status.

Reviewed theorem pins: 11

Core source: commit fdd4e10c36155f079edc72f44fd59f0e8767dad6, tree 34313d90e30ff0940ce4624d6d590b0b65df7b7d, status PNP-FORMAL-RECONSTRUCTION-STATUS-2026-07-28-89.

Publication: PUBLIC-SURFACE-BASELINE-2026-07-28-LOCKED-NAND-ENCODED-SEMANTIC-BOUNDARY-88.

Site release and live deployment identity are verified separately by the release seal and deployment provenance record.

These coordinates and hashes establish artefact identity only; they do not establish theorem correctness.