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"pipelineCompilerCorrectKernelTypeSha256": "e1ccd198403d41933324af1c52048c865943947c5bbd40dd94e11827b08c2303", "pipelineVerdictTheorem": "PNP.Concrete.PipelineCompiler.pipeline_boundedDecide_eq", "pipelineVerdictKernelTypeSha256": "1bafe91bba94e65a7ad654f4624f305c0ae01b3e6d656af0dd2e752d373ce87e", "pipelineMachineOutputTheorem": "PNP.Concrete.PipelineCompiler.pipeline_machineOutput_eq", "pipelineMachineOutputKernelTypeSha256": "45e02fa1e6e6b0bcbc422c3b4fd797608b875727d22b79d6f7814e1f4f0d3da7", "pipelineNoTimeoutTheorem": "PNP.Concrete.PipelineCompiler.pipeline_ne_timeout", "pipelineNoTimeoutKernelTypeSha256": "ed95c33d4fa998d79057537cd2adf847548a79b7ee9a45020b01620868273b3a", "pipelineAcceptsTheorem": "PNP.Concrete.PipelineCompiler.pipeline_accepts_iff", "pipelineAcceptsKernelTypeSha256": "94e43c664b4d185e48553ab25541925830fec7086fcbbab5215dacdcde1af6a6", "pipelineAllInputStuckTimeoutTheorem": "PNP.Concrete.PipelineCompiler.pipeline_timeout_of_stuck_rawRunExact", "pipelineAllInputStuckTimeoutKernelTypeSha256": "a6edef0532eb89036d0e6813cffb94b321f9160a08035671eb411c813ef0a3de", "pipelineCompilerAxiomClosure": [], "pipelineSequentialNamespaceFormalized": true, "pipelineSequentialNamespaceAxiomAuditPassed": true, "pipelineSequentialNamespaceAuditedDeclarationCount": 26, "pipelineSequentialNamespaceAxiomClosure": [], "pipelineSequentialCompilationFormalized": true, "pipelineSequentialCompilerAxiomAuditPassed": true, "pipelineSequentialCompilerAuditedDeclarationCount": 31, "pipelineSequentialVerdictAndOutputPreservationFormalized": true, "pipelineSequentialExternalInputSizePolynomialFormalized": true, "pipelineSequentialStuckFirstTimeoutFormalized": true, "pipelineSequentialCorrectTheorem": "PNP.Concrete.PipelineSequentialCompiler.sequential_correct", "pipelineSequentialCorrectKernelTypeSha256": "8943f2f2c396dfb2e6e8232244b9ecb386fe3a7259590ed96cedb82d1cc7b22a", "pipelineSequentialVerdictTheorem": "PNP.Concrete.PipelineSequentialCompiler.sequential_boundedDecide_eq", "pipelineSequentialVerdictKernelTypeSha256": "dd282c364787b165c9be9ca80b712c3ebf61ac95d097218300a65433a690e386", "pipelineSequentialMachineOutputTheorem": "PNP.Concrete.PipelineSequentialCompiler.sequential_machineOutput_eq", "pipelineSequentialMachineOutputKernelTypeSha256": "8d954e0e65847ff071a3a79a7be1c7f7d5a2f1696e3f94be3a7288500598b9d7", "pipelineSequentialNoTimeoutTheorem": "PNP.Concrete.PipelineSequentialCompiler.sequential_ne_timeout", "pipelineSequentialNoTimeoutKernelTypeSha256": "116c522c8a64988fd815b32bad08df882534b94b87cfa42a705fd1d8158d45af", "pipelineSequentialAcceptsTheorem": "PNP.Concrete.PipelineSequentialCompiler.sequential_accepts_iff", "pipelineSequentialAcceptsKernelTypeSha256": "7a6d0d03c735c83a2fb0c764a174a79402ec196a98169614b15dbee442df099e", "pipelineSequentialStuckFirstTimeoutTheorem": "PNP.Concrete.PipelineSequentialCompiler.sequential_timeout_of_stuck_first_rawRunExact", "pipelineSequentialStuckFirstTimeoutKernelTypeSha256": "5f5f0889b807ea0ccefdfb911ba8b583de9999f2a627745bc9317c0c6ff21a34", "pipelineSequentialCompilerAxiomClosure": [], "pipelineSequentialOutputSizePolynomial": "Bseq(m) = m + p(m) + 1", "pipelineSequentialRawTimePolynomial": "Rseq(m) = PipelineRaw(p)(m) + 6 + PipelineRaw(q)(m + p(m) + 1)", "pipelineRefinementAxiomAuditPassed": true, "pipelineRefinementAuditedDeclarationCount": 16, "pipelineRefinementAxiomClosure": [], "functionProgramRecursiveCompilationFormalized": true, "decisionProgramRecursiveCompilationFormalized": true, "polynomialTimeDeciderRawCompilationFormalized": true, "functionProgramCompileHaltsTheorem": "PNP.Concrete.FunctionProgram.RawRefinement.compile_haltsWithin", "functionProgramCompileHaltsKernelTypeSha256": "53bd33de652a55facc74179863672a789f40f9ba6dea293c2de29fcc866b5a3d", "functionProgramCompileOutputTheorem": "PNP.Concrete.FunctionProgram.RawRefinement.compile_output_eq", "functionProgramCompileOutputKernelTypeSha256": "e3bb23c7f245cb516803a91468e3a3b220338c36a11790ffa5045b8c41332a24", "decisionProgramCompileHaltsTheorem": "PNP.Concrete.DecisionProgram.RawRefinement.compile_haltsWithin", "decisionProgramCompileHaltsKernelTypeSha256": "4057fc9d48be85dd7f961ce7acf5bef68ddb4ed0c8b6798617b31deb9da8c7c5", "decisionProgramCompileVerdictTheorem": "PNP.Concrete.DecisionProgram.RawRefinement.compile_verdict_eq", "decisionProgramCompileVerdictKernelTypeSha256": "8b390dd6677d6e789499b7b713855652a5e1db2c64809ddf43d079deb4099965", "polynomialTimeDeciderCompileAcceptsTheorem": "PNP.Concrete.PolynomialTimeDecider.compileToMachine_accepts_iff", "polynomialTimeDeciderCompileAcceptsKernelTypeSha256": "ebc638eb12e60d97a7d33b0cdce5a6322594342547f65128c0a3f11503fa35ba", "standardComplexityModelFormalized": true, "concreteComplexityMachineLinkDischarged": true, "cookLevinRawTapeBridgeFormalized": true, "cookLevinRawTapeBridgeAxiomAuditPassed": true, "cookLevinRawTapeBridgeAuditedDeclarationCount": 54, "cookLevinSemanticReductionCorrectnessFormalized": true, "cookLevinSemanticTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormula_mem_CNFSAT_iff_language", "cookLevinSemanticTheoremType": "{language : PNP.Concrete.Language} (problem : PNP.Concrete.CookLevin.VerifierTableauProblem language) : PNP.Concrete.CNFSAT problem.encodedFormula ↔ language problem.input", "cookLevinSemanticKernelTypeSha256": "985c8d12419343045c76abbcfa6def7d4e01ce816d97180dca14d7bf5c0be34d", "cookLevinRawTapeBridgeAxiomClosure": [ "Classical.choice", "Quot.sound", "propext" ], "cookLevinProjectAxiomClosure": [], "cookLevinEncodedFormulaSizePolynomialFormalized": true, "cookLevinFormulaConstructionRuntimePolynomialFormalized": false, "cookLevinPolynomialReductionFormalized": true, "cookLevinFormulaSizeAxiomAuditPassed": true, "cookLevinFormulaSizeAuditedDeclarationCount": 108, "cookLevinEncodedFormulaSizeTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.encodedFormula_size_le", "cookLevinEncodedFormulaSizeTheoremType": "{language : PNP.Concrete.Language} (problem : PNP.Concrete.CookLevin.VerifierTableauProblem language) : problem.encodedFormula.size ≤ (PNP.Concrete.CookLevin.encodedFormulaSizePolynomial problem.verifier).eval problem.input.size", "cookLevinEncodedFormulaSizeKernelTypeSha256": "c2b0a4afd8793022739cde9904d379a3c807fba07f0db0ab23e3b0b0563ed699", "cookLevinFormulaSizeAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinFormulaSizeProjectAxiomClosure": [], "cookLevinEncodedFormulaSizePolynomial": "O(m) = 2 * ((V(m) + 1) + Q(m) * (2 + (V(m) + 4) * (V(m) + 1)) + 1) + 1", "cookLevinFormulaScheduleFormalized": true, "cookLevinFormulaScheduleAxiomAuditPassed": true, "cookLevinFormulaScheduleAuditedDeclarationCount": 79, "cookLevinFormulaScheduleAnswerIndependent": true, "cookLevinFormulaScheduleExactEmissionFormalized": true, "cookLevinFormulaScheduleExactLengthPolynomialFormalized": true, "cookLevinFormulaScheduleLengthTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSchedule_length", "cookLevinFormulaScheduleLengthTheoremType": "{language : PNP.Concrete.Language} (problem : PNP.Concrete.CookLevin.VerifierTableauProblem language) : problem.formulaBitSchedule.length = (PNP.Concrete.CookLevin.encodedFormulaSizePolynomial problem.verifier).eval (PNP.Concrete.BitString.size problem.input)", "cookLevinFormulaScheduleLengthKernelTypeSha256": "7460e8b8c59a2356dc8ece81571e7bcb76faf71a5ae0492d034b1d8c5d2408c4", "cookLevinFormulaScheduleEmitTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSchedule_emit_eq_encodedFormula", "cookLevinFormulaScheduleEmitTheoremType": "{language : PNP.Concrete.Language} (problem : PNP.Concrete.CookLevin.VerifierTableauProblem language) : PNP.Concrete.CookLevin.FormulaSchedule.emit problem.formulaBitSchedule = problem.encodedFormula", "cookLevinFormulaScheduleEmitKernelTypeSha256": "2376179dbf80f6e0bb76d8a6026518aa0d042e1eb79f3ec567474a730f742943", "cookLevinFormulaScheduleAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinFormulaScheduleProjectAxiomClosure": [], "cookLevinFormulaScheduleConstantTimeRawInterpretationFormalized": false, "cookLevinRawFormulaBuilderFormalized": false, "cookLevinFormulaScheduleFunctionProgramRawRefinementFormalized": false, "cookLevinFormulaCursorFormalized": true, "cookLevinFormulaCursorAxiomAuditPassed": true, "cookLevinFormulaCursorAuditedDeclarationCount": 129, "cookLevinFormulaCursorDirectCoordinateLookupFormalized": true, "cookLevinFormulaCursorNestedOptionSemanticsFormalized": true, "cookLevinFormulaCursorExactTraversalFormalized": true, "cookLevinFormulaCursorExactLengthPolynomialFormalized": true, "cookLevinFormulaCursorTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaConstraintSlotDirect_eq": "46a46409172b2443dcc6eb4dccf939737ce3fb25583a957acfdfb34dde7c0edc", "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaClauseSlotDirect_eq": "0ed670f82237e1984c35dec8edbc2b3ad392759310b5ba0b12311fc799531a98", "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaTokenSlotDirect_eq": "4675f18d3c1f1fa7fb16c2dec7b1e370589ef6977367eb8e4da97b2a03452d1a", "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSlotDirect_eq": "6a3c74f3924ed7defe38713b118e0fecc8a1e71f50b20d2ac1dc0c6535bf6e2c", "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSlotCountDirect_eq_polynomial": "d052a795eb5e0222326ef849c5e75ced764d2a5b74578da3e8ffdb290d731744", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_prefix": "5672cb875db23988aaf749a0890d3f08128b2e9276a969572dbf5b3e404b25a4", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_to_end": "2690d352f8f9072a49db1ba6e585ea5fd68b7952a96296938f44118747e06963", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_full": "d54831f37ccf2283f0ad8fe79a413232964587f85fdbc983983a17f64c9c6f7d", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.step_at_end": "624fcdaccb799650b10aa88c54da820c3de33c67600f1207d5a7d540717d7288", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_one_step_short": "699d81f19687395eaa6c82629cceb0c27fa58b1da009ffe2317e8b1840a309f1", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.step_after_one_step_short": "e6b99c99d82e9edce84ecafe5584d4dcb310221adf0ab171013479c90fe61807", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_excess": "9bdcf90c8a8628fcb4c49d6b358f5d19d7cf6e88a2bedf8e532b577d2fc5f063", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_full_emit_eq_encodedFormula": "2637f4e27b2a6e40a7e774b10fac91d379daebe9ff6930c72de43ee23bd054d0", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaTokenCursor.step_at_end": "4c5507901831dc9a683645271296f346499409ffbf7d6775b36db2382af9d887", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaTokenCursor.step_of_done": "72a7018658fadc646c07637bc07792502fdcab845760af862081e618f879732e", "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaTokenCursor.step_of_lt": "8d0bc1d099f14e3764d3d01a3f7e54b21c962538012dfd8dcd04eb282434a90b" }, "cookLevinFormulaCursorDirectBitTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSlotDirect_eq", "cookLevinFormulaCursorDirectBitTheoremType": "{language : PNP.Concrete.Language} (problem : PNP.Concrete.CookLevin.VerifierTableauProblem language) (index : Nat) : problem.formulaBitSlotDirect index = problem.formulaBitSchedule[index]?", "cookLevinFormulaCursorPolynomialTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.formulaBitSlotCountDirect_eq_polynomial", "cookLevinFormulaCursorPolynomialTheoremType": "{language : PNP.Concrete.Language} (problem : PNP.Concrete.CookLevin.VerifierTableauProblem language) : problem.formulaBitSlotCountDirect = (PNP.Concrete.CookLevin.encodedFormulaSizePolynomial problem.verifier).eval (PNP.Concrete.BitString.size problem.input)", "cookLevinFormulaCursorFullTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_full", "cookLevinFormulaCursorOneStepShortTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_one_step_short", "cookLevinFormulaCursorExcessTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_excess", "cookLevinFormulaCursorEmitTheorem": "PNP.Concrete.CookLevin.VerifierTableauProblem.FormulaBitCursor.run_full_emit_eq_encodedFormula", "cookLevinFormulaCursorAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinFormulaCursorProjectAxiomClosure": [], "cookLevinFormulaCursorConstantTimeRawInterpretationFormalized": false, "cookLevinFormulaCursorRawBuilderFormalized": false, "cookLevinFormulaCursorFunctionProgramRawRefinementFormalized": false, "cookLevinBuilderInputLengthFormalized": true, "cookLevinBuilderInputLengthAxiomAuditPassed": true, "cookLevinBuilderInputLengthAuditedDeclarationCount": 39, "cookLevinBuilderInputLengthCompiledRawMachineFormalized": true, "cookLevinBuilderInputLengthExternalInputSizePolynomialFormalized": true, "cookLevinBuilderInputLengthMalformedInternalInputTimeoutFormalized": true, "cookLevinBuilderInputLengthConnectedToTotalInputFramerEndpointFormalized": true, "cookLevinBuilderInputLengthRuleCount": 19, "cookLevinBuilderInputLengthWorkTimePolynomial": "2 * inputLength^2 + 4 * inputLength + 2", "cookLevinBuilderInputLengthRawTimePolynomial": "12 * inputLength^2 + 24 * inputLength + 12", "cookLevinBuilderInputLengthTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderInputLength.finalTape_represents": "824e9a4f2785da71c1b5810e4995984e220b131bf643bd4f0271ed53628970dd", "PNP.Concrete.CookLevin.BuilderInputLength.inputTape_eq_totalInputFramerFinalTape": 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"3fdcf061036fc5b1c6caf667cda8718c9d738a7281d30be9785841b40f034c16", "PNP.Concrete.CookLevin.BuilderInputLength.work_one_step_short_timeout": "9a70e81fe0f85ea22e9fd2b41166dc4f7281245501f8cd70bbac7895936bfa4d" }, "cookLevinBuilderInputLengthFinalTapeTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.finalTape_represents", "cookLevinBuilderInputLengthFramerEndpointTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.inputTape_eq_totalInputFramerFinalTape", "cookLevinBuilderInputLengthMalformedTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.malformedScanSymbol_timeout", "cookLevinBuilderInputLengthRawTimeTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.rawTimeBound_exact", "cookLevinBuilderInputLengthCompiledRunTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.run_compile", "cookLevinBuilderInputLengthTallySizeTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.tallySizeBound_exact", "cookLevinBuilderInputLengthAcceptTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.workBoundedDecide_accept", "cookLevinBuilderInputLengthExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.workRunExact", "cookLevinBuilderInputLengthFramerRunTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.workRunExact_after_totalInputFramer", "cookLevinBuilderInputLengthOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderInputLength.work_one_step_short_timeout", "cookLevinBuilderInputLengthAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderInputLengthProjectAxiomClosure": [], "cookLevinBuilderFormulaBitsEmittedFormalized": true, "cookLevinBuilderDirectCursorRawInterpretationFormalized": true, "cookLevinCompleteRawFormulaBuilderFormalized": true, "cookLevinBuilderFunctionProgramRawRefinementFormalized": true, "cookLevinBuilderInputPrefixFormalized": true, "cookLevinBuilderInputPrefixAxiomAuditPassed": true, "cookLevinBuilderInputPrefixAuditedDeclarationCount": 40, "cookLevinBuilderInputPrefixCompiledRawMachineFormalized": true, "cookLevinBuilderInputPrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderInputPrefixMalformedScanSymbolTimeoutFormalized": true, "cookLevinBuilderInputPrefixLiteralFramerLaunchFormalized": true, "cookLevinBuilderInputPrefixWorkTimePolynomial": "totalInputFramerWorkSteps(input) + 1 + 2 * inputLength^2 + 4 * inputLength + 2", "cookLevinBuilderInputPrefixRawTimePolynomial": "18 * inputLength^2 + 63 * inputLength + 93", "cookLevinBuilderInputPrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderInputPrefix.boundedDecide_compile_accept": "6fbd596723b2a97d405d1d8129e20901d51008c773af5d80b4633a819fead57d", "PNP.Concrete.CookLevin.BuilderInputPrefix.finalTape_represents": "14cba9d7647fcef8f062c2ab6e3d16e84eed233e1ec53491382991421795e2cc", "PNP.Concrete.CookLevin.BuilderInputPrefix.finalTape_tally_length": "92f992615d4bde8569d585f54ec0d7963cb5ec043e81b410433c1d3f6e190dfe", "PNP.Concrete.CookLevin.BuilderInputPrefix.findWorkRule_framer_of_some": "3e82d88005087443565389d5dda84a673b4eaecf637e60eff5cc4cb414679b18", "PNP.Concrete.CookLevin.BuilderInputPrefix.findWorkRule_tally_of_some": "e88f5a2d04ae75d874e6be87f837e3eb73a70aaad095ef44c8bc40383ac90dab", "PNP.Concrete.CookLevin.BuilderInputPrefix.framerState_ne_tallyState": "b37cc329b82a3489b6cbbf59f49d6f85494e1cba3b6d74afd111177f882691f0", "PNP.Concrete.CookLevin.BuilderInputPrefix.launch_workStep": "7ddf442477605b69a2a48fa9de34c9d3e231fc125fb2ffbe2f862464c0646bd9", "PNP.Concrete.CookLevin.BuilderInputPrefix.malformedTallyScanSymbol_timeout": "e6799395b2907abc1740c4fd7d96fc9ac8f1ee24670e4b7aceb39a0927fbdd66", "PNP.Concrete.CookLevin.BuilderInputPrefix.rawTimeBound_eval": "d875640901af586ab3e6ab4507d62c25b94e34ef8c87082fb35fcf58c757dc1c", "PNP.Concrete.CookLevin.BuilderInputPrefix.rawTimeBound_le": "0bb31c2ccec14489cb58eef73d58cd55053f684ece8105a311c516723178fd1d", 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"cookLevinBuilderCompleteHeaderExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.workRunExact", "cookLevinBuilderCompleteHeaderFormulaHeaderTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.finalTokenBits_eq_encodedFormula_header", "cookLevinBuilderCompleteHeaderRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.rules_length", "cookLevinBuilderCompleteHeaderRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.rules_pairwise_query_distinct", "cookLevinBuilderCompleteHeaderCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.run_compile_exact", "cookLevinBuilderCompleteHeaderCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.run_compile_rawTimeBound", "cookLevinBuilderCompleteHeaderAcceptTheorem": "PNP.Concrete.CookLevin.BuilderCompleteHeader.boundedDecide_compile_accept", "cookLevinBuilderCompleteHeaderNoTimeoutTheorem": 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"cookLevinBuilderBodyStartPrefixWorkTime": "BuilderCompleteHeader.workSteps(input) + 1 + BuilderUnaryPolynomial.workSteps(nextTokenSlotPolynomial verifier, input) + 1 + BuilderTokenAppender.workSteps(input, headerTokens problem)", "cookLevinBuilderBodyStartPrefixRawTimePolynomial": "BuilderCompleteHeader.rawTimeBound + 72 + 6 * BuilderUnaryPolynomial.workTimePolynomial(nextTokenSlotPolynomial verifier) + 24 * inputLength + 12 * FormulaWidth", "cookLevinBuilderBodyStartPrefixRuleCount": "440 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(nextTokenSlotPolynomial verifier)", "cookLevinBuilderBodyStartPrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.appenderState_injective": "c33488f7f1255236fb0d631f8c1fd46544ffb76277a4ee0305cc9bca84e85d08", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.appender_workRunExact": "9c755f18d1dfe5355dbcf902acaf35977213ffb721f9df5c2705994d812384ad", 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"6809ad9a3e53224190763f0c3f1a44cf6b51be71589ad1db4a1426cc6e5cee29", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerState_ne_appenderState": "a726e1857388047de6829f0d4744e2282bd6b503e2f4d3b26fba0e3ff77929b8", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.headerState_ne_cursorState": "a14587342fefedd1abe19190211c2198e70d3a4297a3f76f371c1beb28c21a60", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.header_workRunExact": "b9187bd36473966d53ec087bf6788e710366362fa0adaedac4330a9617c228bd", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.machine_acceptState_ne_rejectState": "584a79687212d3a0c0f22ffd89696ea8c523d7788c5f45b34ddf3054f2e622a7", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.malformedAppenderOutput_timeout": "134078d25b71b04071ed3960be3d9e25b1a9f73efc388820278e86629bad6b24", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.malformedAppenderTally_timeout": "63ff37a7325ec92751d394c9509a930c818076a6e0d9c134ff6e087184b7b0af", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.nextBitCursor_nextSlot": "789119bb75142ff180043965e0a89c1e16f6269167b650a0b38966b234deb29b", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.nextTokenSlot_eq_formulaVariableSlotBound_add_two": "d6646001b71db25b02190c75b55d3c767aa331244379504421cb3813166a82ba", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rawTimeBound_eval": "8a0f33f895ef550741b2feed3e685fbd4b205c78b027f3377a0cd5eb5b9eb50d", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rawTimeBound_le": "1e97432ba79e7e51458fc31b9424913d4c31a9150a7a14d44a1fdd79a03fff21", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rule_source_ne_acceptState": "95e62c04caa14e105e8c778c3cd955dc0000090dc7ccbed3ab61d0c41a22277f", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rule_source_ne_rejectState": "aebee131cad6a94d3ef8a037528a696fee64258cd409be40df0624049d872b29", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rules_length": "1027191f94c78b274c3d8740ecd7bc83c709b965c99230e83a8a3a877adc2aa3", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rules_pairwise_query_distinct": "32143d0b5fde6d61fb853795510732563dcff935baf2a35a55299771686be708", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_exact": "ce708c4288c6117267344b9473c7825dd5ec80553391f9b079b1f96dedcfc41b", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_rawTimeBound": "d294007089f681f74f48aa64f16edc92ff17a1621a42af227b6b5dd4474fe1c4", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_rawTimeBound_blankEquivalent": "fbde3d053b6737cc5d6ad8279befd985b3aaab68510c3b6ef2b6f997fc20d344", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.workBoundedDecide_accept": "9353985e12fbb3de51ed35fd77ac781e25cd0df7346454626f5a744f73b22a6a", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.workRunExact": "a1aa7b3af052b6311cdf177874aed2cf7a76fb427f88272d31d40cde4eb4a2db", "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.work_one_step_short_timeout": "0577a56507618c8358f7c233f355f831f690868fe0e8777a2b5daf735985d0ca" }, "cookLevinBuilderBodyStartPrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.workRunExact", "cookLevinBuilderBodyStartPrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.bodyStartTokens_eq_canonical_prefix", "cookLevinBuilderBodyStartPrefixNextTokenCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.nextTokenSlot_eq_formulaVariableSlotBound_add_two", "cookLevinBuilderBodyStartPrefixSeparatorSlotTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.firstBodyTokenSlotDirect_eq_separator", "cookLevinBuilderBodyStartPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.finalTokenBits_eq_encodedFormula_bodyStart", "cookLevinBuilderBodyStartPrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rules_length", "cookLevinBuilderBodyStartPrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.rules_pairwise_query_distinct", "cookLevinBuilderBodyStartPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_exact", "cookLevinBuilderBodyStartPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.run_compile_rawTimeBound", "cookLevinBuilderBodyStartPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.boundedDecide_compile_accept", "cookLevinBuilderBodyStartPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderBodyStartPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderBodyStartPrefix.work_one_step_short_timeout", "cookLevinBuilderBodyStartPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderBodyStartPrefixProjectAxiomClosure": [], "cookLevinBuilderFirstLiteralPrefixFormalized": true, "cookLevinBuilderFirstLiteralPrefixAxiomAuditPassed": true, "cookLevinBuilderFirstLiteralPrefixAuditedDeclarationCount": 74, "cookLevinBuilderFirstLiteralPrefixCompiledRawMachineFormalized": true, "cookLevinBuilderFirstLiteralPrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFirstLiteralPrefixExactFormulaBitsFormalized": true, "cookLevinBuilderFirstLiteralPrefixRetainedNextTokenCoordinateFormalized": true, "cookLevinBuilderFirstLiteralPrefixInputPrefixAppenderComposed": true, "cookLevinBuilderFirstLiteralPrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFirstLiteralPrefixWorkTime": "BuilderBodyStartPrefix.workSteps(input) + 1 + BuilderUnaryPolynomial.workSteps(nextTokenSlotPolynomial verifier, input) + 1 + BuilderTokenAppender.workSteps(input, bodyStartTokens problem) + 1 + BuilderTokenAppender.workSteps(input, firstLiteralSignTokens problem)", "cookLevinBuilderFirstLiteralPrefixRawTimePolynomial": "BuilderBodyStartPrefix.rawTimeBound + 174 + 6 * BuilderUnaryPolynomial.workTimePolynomial(nextTokenSlotPolynomial verifier) + 48 * inputLength + 24 * FormulaWidth", 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"PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.nextTokenSlot_eq_formulaVariableSlotBound_add_four", "cookLevinBuilderFirstLiteralPrefixSignSlotTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.firstLiteralSignSlotDirect_eq_t", "cookLevinBuilderFirstLiteralPrefixZeroTerminatorSlotTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.firstLiteralZeroTerminatorSlotDirect_eq_f", "cookLevinBuilderFirstLiteralPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_firstLiteral", "cookLevinBuilderFirstLiteralPrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rules_length", "cookLevinBuilderFirstLiteralPrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.rules_pairwise_query_distinct", "cookLevinBuilderFirstLiteralPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.run_compile_exact", "cookLevinBuilderFirstLiteralPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.run_compile_rawTimeBound", "cookLevinBuilderFirstLiteralPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.boundedDecide_compile_accept", "cookLevinBuilderFirstLiteralPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderFirstLiteralPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFirstLiteralPrefix.work_one_step_short_timeout", "cookLevinBuilderFirstLiteralPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFirstLiteralPrefixProjectAxiomClosure": [], "cookLevinBuilderFirstClausePrefixFormalized": true, "cookLevinBuilderFirstClausePrefixAxiomAuditPassed": true, "cookLevinBuilderFirstClausePrefixAuditedDeclarationCount": 79, "cookLevinBuilderFirstClausePrefixCombinedAuditedDeclarationCount": 80, "cookLevinBuilderFirstClausePrefixCompiledRawMachineFormalized": true, 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"PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.formulaVariableSlotBound_at_least_three": "df6876815223d99af21f1a5b45427486718bb51e9c22186f38d1efac2ff13343", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.launch_workStep": "c43657a609c6f60730395877f6b731f326758e8fd35571ce82dd712a7a4ecee8", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.machine_acceptState_ne_rejectState": "2dbdb022faf1c6d0d8330bc72ca83012c5263c98275913314ba8ce42155b8b64", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.malformedCountdownRoot_timeout": "caa63372fc9c8849501f35c5551be51e369c07817a745e5c57b39b5a6ee31815", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.malformedCountdownScratch_timeout": "f4bbb61e24a3dd26a57d172cecfa41a5d45e0173cbcbdcb53755ef4a49d8f247", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.paddingSlot_direct_eq_padding": "6741e59e9ee38871c591ce02391cf45dc09cc670985679c3665204f007e55618", 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"PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.workBoundedDecide_accept": "a10b7df091f941dd40f42e69ec94306deda2bdcfa02daf6f59294956ff969b9c", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.workRunExact": "a023c1357be86f78812d0c237385168e0118446d37a7f7d975dcb303e49a6bd5", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.work_one_step_short_timeout": "acf0af0b30b9f36c737d02adc55054f9ff2607fe3907fe981ff2ae7039e39985", "PNP.Concrete.CookLevin.BuilderCompleteHeader.HeaderController.workRunExact_of_unit_or_separator": "8976755a7cd89869e4821eecc80f47fb278a39be59b2bdbf679cb530d4aaf6cf" }, "cookLevinBuilderFirstClausePaddingRunExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.workRunExact", "cookLevinBuilderFirstClausePaddingRunSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.specification_padding_run", "cookLevinBuilderFirstClausePaddingRunTargetSpecificationTheorem": 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cursorWord.length", "cookLevinBuilderSecondClauseFirstLiteralPrefixRuleCount": "1610 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier)", "cookLevinBuilderSecondClauseFirstLiteralPrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.machine_acceptState_ne_rejectState": "100d797c35b0c6669b7073cdb854d4081c9d53d8688205e876159170ec7db7ec", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rule_source_ne_acceptState": 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"PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.specification_firstLiteral_sign_step", "cookLevinBuilderSecondClauseFirstLiteralPrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step", "cookLevinBuilderSecondClauseFirstLiteralPrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.specification_next_step", "cookLevinBuilderSecondClauseFirstLiteralPrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.secondClauseFirstLiteralTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondClauseFirstLiteralPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_secondClauseFirstLiteral", "cookLevinBuilderSecondClauseFirstLiteralPrefixAdvancedCoordinateTheorem": 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"3579e039b667ea12cbbd2f1a0fcb2d142956188a00e0b421d41a0d6d59226746", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.trueFalseSuffix_workRunExact": "ed059e54f87c9b6773d86e6ec2f94c7fcbd05969c87baf0fd778bfa4d5bc9507", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryAppenderCursor_launch_workStep": "0e1f2080fe9bf89c6ba58b64b168227ae2f7c5a396161be6ce37005d4209b8b4", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryAppenderEndpoint_before_cursor_launch_timeout": "78458ed1e79d4d681219fe61635cc9cd66c191b4e9581df8c18461898a390958", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryCursorEndpoint_before_terminator_launch_timeout": "e0c29ad519cc50be3a8c107b9838e22032c3c98ede036ec1b8c416067937017f", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.unaryTokenCursor_workRunExact": "23414bcc9c451db68c05d5a25bea509f59642bba5130894a1dd20c8a8be9f86b", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.workBoundedDecide_accept": "9b0d11bd94ed812f99b31b6c5071dac0dd9d18b4b3e8f079f2bea6107f317554", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.workRunExact": "f21f548fedbfd5f24ecbf212501084502a6a216a621a82569be93954292404b8", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.work_one_step_short_timeout": "7c680eae6fe8ca4f6d2800d87f8dba0a7750d4280d7caa42351d1ffcf18e8bf0" }, "cookLevinBuilderSecondClauseSecondLiteralPrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.workRunExact", "cookLevinBuilderSecondClauseSecondLiteralPrefixSignSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_secondLiteral_sign_step", "cookLevinBuilderSecondClauseSecondLiteralPrefixUnaryUnitSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_secondLiteral_unaryUnit_step", "cookLevinBuilderSecondClauseSecondLiteralPrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_secondLiteral_terminator_step", "cookLevinBuilderSecondClauseSecondLiteralPrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.specification_next_step", "cookLevinBuilderSecondClauseSecondLiteralPrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondClauseSecondLiteralTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondClauseSecondLiteralPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalTokenBits_eq_encodedFormula_secondClauseSecondLiteral", "cookLevinBuilderSecondClauseSecondLiteralPrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.finalTokenSlot_eq_secondClauseStart_add_six", "cookLevinBuilderSecondClauseSecondLiteralPrefixSignTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralSignSlot_direct_eq_f", "cookLevinBuilderSecondClauseSecondLiteralPrefixUnaryUnitTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralUnaryUnitSlot_direct_eq_t", "cookLevinBuilderSecondClauseSecondLiteralPrefixTerminatorTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.secondLiteralTerminatorSlot_direct_eq_f", "cookLevinBuilderSecondClauseSecondLiteralPrefixNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.nextTokenSlot_direct_eq_finish", "cookLevinBuilderSecondClauseSecondLiteralPrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rules_length", "cookLevinBuilderSecondClauseSecondLiteralPrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.rules_pairwise_query_distinct", "cookLevinBuilderSecondClauseSecondLiteralPrefixTrueTokenCursorRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length", "cookLevinBuilderSecondClauseSecondLiteralPrefixTrueFalseSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length", "cookLevinBuilderSecondClauseSecondLiteralPrefixSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length", "cookLevinBuilderSecondClauseSecondLiteralPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.run_compile_exact", "cookLevinBuilderSecondClauseSecondLiteralPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.run_compile_rawTimeBound", "cookLevinBuilderSecondClauseSecondLiteralPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.boundedDecide_compile_accept", "cookLevinBuilderSecondClauseSecondLiteralPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedSignAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedSignAppenderTally_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedSignAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedSignAppenderOutput_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedUnaryAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedUnaryAppenderTally_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedUnaryAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedUnaryAppenderOutput_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedTerminatorAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedTerminatorAppenderTally_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedTerminatorAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedTerminatorAppenderOutput_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedSignCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedSignCursorScratch_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedUnaryCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedUnaryCursorScratch_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixMalformedTerminatorCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.malformedTerminatorCursorScratch_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.work_one_step_short_timeout", "cookLevinBuilderSecondClauseSecondLiteralPrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderSecondClauseSecondLiteralPrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderSecondClauseSecondLiteralPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondClauseSecondLiteralPrefixProjectAxiomClosure": [], "cookLevinBuilderSecondClausePrefixFormalized": true, "cookLevinBuilderSecondClausePrefixAxiomAuditPassed": true, "cookLevinBuilderSecondClausePrefixAuditedDeclarationCount": 57, "cookLevinBuilderSecondClausePrefixCompiledRawMachineFormalized": true, "cookLevinBuilderSecondClausePrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondClausePrefixExactFormulaBitsFormalized": true, "cookLevinBuilderSecondClausePrefixCompleteSecondClauseFormalized": true, "cookLevinBuilderSecondClausePrefixClauseTerminatorFormalized": true, "cookLevinBuilderSecondClausePrefixRetainedFirstPaddingCoordinateFormalized": true, "cookLevinBuilderSecondClausePrefixRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondClausePrefixInputPrefixAppenderComposed": true, "cookLevinBuilderSecondClausePrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondClausePrefixWorkTime": "BuilderSecondClauseSecondLiteralPrefix.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, secondClauseSecondLiteralTokens problem) + 1 + CursorAdvance.advanceWorkSteps(cursorWord problem)", "cookLevinBuilderSecondClausePrefixRawTimePolynomial": "BuilderSecondClauseSecondLiteralPrefix.rawTimeBound + 390 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderSecondClausePrefixRuleCount": "2098 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier)", "cookLevinBuilderSecondClausePrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.machine_acceptState_ne_rejectState": "c92ef301f714bebdfe7524e5cc6c2cfa753ba472dcee929636e806ab21bc1969", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rule_source_ne_acceptState": "e653092c4b310f8a8514b74bd8cf42f0f95e4e46ab6cbf778072dd070ff5a1d7", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rules_length": "6ad06c9953ddbf0f2a89a691370014b413047e245f4daac510c0533036c79859", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rules_pairwise_query_distinct": "1b6050b2237706ea1f262f0a4fac2134e0fec2d493d75cef02acc910a734a758", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.appenderEndpoint_before_cursor_launch_timeout": "e35dbab8d230099bece5f0e2dfc0784bf402b94acf4bed6c53bcff987e37902f", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.appender_workRunExact": "729edebb0d87989b6a48d66e786ae4007afa2f627b42f3c15a9b74ad013234f9", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.boundedDecide_compile_accept": "7ff18ece4c5faa4253103657c391cc2725fbd5409886220e8787da29140230c9", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.boundedDecide_compile_ne_timeout": "72d53addfeeb64519f63f2bd5386c833e92ac2447cd4594a01dc591873e29e31", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.clauseTerminatorSlot_direct_eq_finish": "d7e761fee2cfed73e104e481a810cc43956d37026c193c86afcbd3e9fa2269a4", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.cursor_workRunExact": "c41f968ea22b71746151e21fe902d244e870cb1f7ed0f215fe01bdea9cb4c917", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalConfiguration_state": "8c884ec1ab79fd4b9a37da4ae8a4f9d81344f7fd1d48bb68209258946221e12d", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalOutside_contains_finalTokenSlot": "3c6d7acd8631b3496257021a1ba2681bf95a05b49e026b1e89913414c6c263f5", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTape_represents": "424695b161d5e2c6e85dda3ef82bba02fe6d110bb8077da84afa38b2faf3282a", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTokenBits_eq_encodedFormula_secondClause": "89155cfc9f2690463d40d18fbb583e2d7114a7ea1452a1bb09a1c3f8611838a7", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTokenSlot_eq_secondClauseStart_add_seven": "7a6dad36e00cfe8fcbe4e0f33cc8342d94a1e67f628b390eb20fb3d23b73df3a", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finishTokenCursor_launch_workStep": "c7553d415b963f721ceeccf11c55a172cfaa585967c13d785f1a1394eae49fd4", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.machine_acceptState_ne_rejectState": "0080495a18fac7a71dace5e7ad23cc2785fced8672ee8b6f41e5048f6075a0c1", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedAppenderOutput_timeout": "facc9ffc626d76637c794e20cd222ab2e8326ffc92e2c0e19eee61fa7bb70b4b", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedAppenderTally_timeout": "4c0828846ac3dc16c83ec58e627134755784f0efe25c6aec9a2a6522082dd143", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedCursorScratch_timeout": "597f1c8fd8e136d412e4bd970fa2a5989526b3bceb84e7aedfe70a2bf4dd4030", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.nextTokenSlot_direct_eq_padding": "2986d1bf8c4d10b71ba9deed762ab6c0f073b50acf4c2f8503c9ff79c5db87e6", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.prefixEndpoint_before_launch_timeout": "04fb9ae42f1326437788608d0bddb58bcb83ce02140b6238d7330b65a2bcaf10", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.prefixFinish_launch_workStep": "cf78b77bb5663a43e32510f4625f031c80af7cc3ee7379b74dd3ec0f03534ce2", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.prefix_workRunExact": "a3b9b5619487f16c7891a16e21e1d0daf05586f8f40e3cf60b018cc6f90ec933", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rawTimeBound_eval": "c8fd020e5a95df4849ae73af2634f081ab9bd54fcef9e89a337b72ef84bc1aae", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rawTimeBound_le": "d53a117102d056edf4dae59981cb92269dceadf6d416a205d48b0452a7d35c19", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rule_source_ne_acceptState": "4a5b7b66480a16262b24f209122c0b7799c24f5f92f893d8339fbfbdf77ca7ed", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rules_length": "7550fa5770ba848aacbceb558f95324be3a8e2bcfbcddf3618e56a9e2d79a684", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rules_pairwise_query_distinct": "da5dd9b4c5336a5f5e77f38e2a0b1cf4e492d61c1092534c63749f3e8f686556", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_exact": "cd0e9aa6bb6822d06d7caf195f15d729c4e76febe1e06231a8bf9267cb10ef3d", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_rawTimeBound": "2da8b5eb7ecbc3d30396ededf15ec2cd929707db131f63cdb4d7f008c2972f2d", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_rawTimeBound_blankEquivalent": "4b783be22065343707a37662810fbdf7d4285dcf98af296746117a44f5f83e70", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.secondClauseTokens_eq_canonical_formula_prefix": "3ed7b48cecd3468ee7e5bf71fbbbe6e423c926ffe5d9983fc4ee77e846e4cc9e", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.specification_next_step": "fe8e0a7076e5f4f86dc345478b1b5423dbb9c4d81bac9b1cb136db37cf1dba25", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.specification_terminator_step": "edc48c47e4adf6e67bccb378eca4169ac1829b3baa597cf7786a4d9f5bf0cfe6", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.suffix_workRunExact": "c39a6c60938fad838aec1b4fc66e0bde9b38a9a7e06c2b3d62d402cc110c2602", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.workBoundedDecide_accept": "05f3ee214b1493a51f149da6274efd4690a96c821ea2d1bac97d3dc489623de1", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.workRunExact": "998dde8748b1b84c8333f43326fa8b4b152d8a0d44c3cf24a31e6a32f14e79b3", "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.work_one_step_short_timeout": "7c837ea2afb2ba39fa9f54f1e3b9f8daad9a5c7168c2a6545b4693a29368b671" }, "cookLevinBuilderSecondClausePrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.workRunExact", "cookLevinBuilderSecondClausePrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.specification_terminator_step", "cookLevinBuilderSecondClausePrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.specification_next_step", "cookLevinBuilderSecondClausePrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.secondClauseTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondClausePrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTokenBits_eq_encodedFormula_secondClause", "cookLevinBuilderSecondClausePrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.finalTokenSlot_eq_secondClauseStart_add_seven", "cookLevinBuilderSecondClausePrefixTerminatorTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.clauseTerminatorSlot_direct_eq_finish", "cookLevinBuilderSecondClausePrefixNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.nextTokenSlot_direct_eq_padding", "cookLevinBuilderSecondClausePrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rules_length", "cookLevinBuilderSecondClausePrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.rules_pairwise_query_distinct", "cookLevinBuilderSecondClausePrefixFinishTokenCursorRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.FinishTokenCursor.rules_length", "cookLevinBuilderSecondClausePrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_exact", "cookLevinBuilderSecondClausePrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.run_compile_rawTimeBound", "cookLevinBuilderSecondClausePrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.boundedDecide_compile_accept", "cookLevinBuilderSecondClausePrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondClausePrefixMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedAppenderTally_timeout", "cookLevinBuilderSecondClausePrefixMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedAppenderOutput_timeout", "cookLevinBuilderSecondClausePrefixMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.malformedCursorScratch_timeout", "cookLevinBuilderSecondClausePrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePrefix.work_one_step_short_timeout", "cookLevinBuilderSecondClausePrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderSecondClausePrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderSecondClausePrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondClausePrefixProjectAxiomClosure": [], "cookLevinBuilderSecondClausePaddingRunFormalized": true, "cookLevinBuilderSecondClausePaddingRunAxiomAuditPassed": true, "cookLevinBuilderSecondClausePaddingRunAuditedDeclarationCount": 68, "cookLevinBuilderSecondClausePaddingRunCompiledRawMachineFormalized": true, "cookLevinBuilderSecondClausePaddingRunExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondClausePaddingRunExactFormulaBitsFormalized": true, "cookLevinBuilderSecondClausePaddingRunRemainingPaddingCountFormalized": true, "cookLevinBuilderSecondClausePaddingRunDirectPaddingBlockFormalized": true, "cookLevinBuilderSecondClausePaddingRunThirdClauseStartFormalized": true, "cookLevinBuilderSecondClausePaddingRunNoEmissionSpecificationFormalized": true, "cookLevinBuilderSecondClausePaddingRunInputPrefixAppenderComposed": true, "cookLevinBuilderSecondClausePaddingRunFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondClausePaddingRunWorkTime": "BuilderSecondClausePrefix.workSteps(problem) + 1 + BuilderUnaryPolynomial.workSteps(remainingPaddingPolynomial verifier, input) + 1 + PaddingCountdown.loopSteps(countControllerPrefixLength, remainingPaddingCount) + 1 + BuilderUnaryPolynomial.workSteps(thirdClauseStartPolynomial verifier, input)", "cookLevinBuilderSecondClausePaddingRunRawTimePolynomial": "BuilderSecondClausePrefix.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps", "cookLevinBuilderSecondClausePaddingRunRuleCount": "2150 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier)", "cookLevinBuilderSecondClausePaddingRunTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le": 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"PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.machine_acceptState_ne_rejectState": "f9e17b81e926146d85a2eb9229315a8488b2288ab75828a76418056cfe63f4d2", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.malformedCountdownRoot_timeout": "4196f68a2bfd23c516eb1dcebe368a8cab1a1488a3dc8ca77c5ae7a8a15f8ef0", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.malformedCountdownScratch_timeout": "88839c44b6ef92aafffeb2e9a675bae541814fca8849b043ab118bedf6ed7b13", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.paddingSlot_direct_eq_padding": "4cd1101e05b508bd86726220c119276d53b570e1e3ef99e6e8725024df1a7d82", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.predecessorSlot_add_remainingPaddingCount": "5bd50e6159f09af08b231fa85725e89c3ad359a1b9fdca3fa4f0e60335b3609c", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.prefixEndpoint_before_launch_timeout": "b175b7b55a12726f907c6947ef67d64dbb3dd3a278b63a9cf87de884f265646b", 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"c19afcb79c517e2e5e7f0774b4374355c5de535e1a3d37933235e372776f00b8", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rules_length": "7356c01f33dbcf3630631afb14cb71b1531541442755ecf6971d2328f88c7acd", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rules_pairwise_query_distinct": "d46ee4a24be5e5d5e092142ca96e63aa6a255a02a0450613ffcf726fa7b03f4e", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_exact": "3fa0ca7054d9563a88488dc97e60d97cbfc6dc654abbb8fc5e8a040161487ec9", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_rawTimeBound": "c2f0857602baa434e36126c55b87ecaad5fa79904c8b432255adf1eead3de1a4", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_rawTimeBound_blankEquivalent": "e57460bfcf11e0f6b186936a2ccc4f235f0edb05bb0c5b61533c90acf8982c94", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.specification_padding_run": "2e750bcd50273ce84d67c967bc858f8f48391c6af63c4ea990dea28cddad7904", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.specification_target_step": "9cac7fffd995e0f6f4fc4794759257e3c77aff54ee9cdbfa1c49702451e2f2a2", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.targetEvaluator_workRunExact": "fb5877140490d31de813cb234f25c7269dbf351c9ecc1e7cc87e5b65750038f6", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.thirdClauseStart_direct_eq_sep": "490e8fef586147e9804a8d9075c60861522433002558de06324459923841d418", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.thirdClauseStart_eq": "c3a85a0d06934ff58874f9241daa9c7a6932dd62dc02549f0da7fb2057f86d05", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.workBoundedDecide_accept": "8a56178f1b2be071c434be96d5c522f3421e4e325b39ace4ad34f0ecde4dd4b8", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.workRunExact": "c224517433caa01b1e94882a88bd538589f9ee801070e9e8bd053ffe46e4b48e", "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.work_one_step_short_timeout": "b35db2da7e6d91bfcfb2696a74f6b41233788dd178f306fb3838f182e049a772" }, "cookLevinBuilderSecondClausePaddingRunExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.workRunExact", "cookLevinBuilderSecondClausePaddingRunPaddingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.specification_padding_run", "cookLevinBuilderSecondClausePaddingRunTargetSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.specification_target_step", "cookLevinBuilderSecondClausePaddingRunFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalTokenBits_eq_encodedFormula_secondClause", "cookLevinBuilderSecondClausePaddingRunRemainingCountTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_seven", "cookLevinBuilderSecondClausePaddingRunThirdClauseCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.finalTokenSlot_eq_thirdClauseStart", "cookLevinBuilderSecondClausePaddingRunDirectPaddingTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.paddingSlot_direct_eq_padding", "cookLevinBuilderSecondClausePaddingRunDirectSeparatorTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.thirdClauseStart_direct_eq_sep", "cookLevinBuilderSecondClausePaddingRunRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rules_length", "cookLevinBuilderSecondClausePaddingRunRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.rules_pairwise_query_distinct", "cookLevinBuilderSecondClausePaddingRunCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_exact", "cookLevinBuilderSecondClausePaddingRunCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.run_compile_rawTimeBound", "cookLevinBuilderSecondClausePaddingRunAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.boundedDecide_compile_accept", "cookLevinBuilderSecondClausePaddingRunNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondClausePaddingRunMalformedRootTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.malformedCountdownRoot_timeout", "cookLevinBuilderSecondClausePaddingRunMalformedScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.malformedCountdownScratch_timeout", "cookLevinBuilderSecondClausePaddingRunOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondClausePaddingRun.work_one_step_short_timeout", "cookLevinBuilderSecondClausePaddingRunAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondClausePaddingRunProjectAxiomClosure": [], "cookLevinBuilderThirdClauseSeparatorStepFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepAxiomAuditPassed": true, "cookLevinBuilderThirdClauseSeparatorStepAuditedDeclarationCount": 56, "cookLevinBuilderThirdClauseSeparatorStepCompiledRawMachineFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepExactFormulaBitsFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepThirdClauseSeparatorFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepInputPrefixAppenderComposed": true, "cookLevinBuilderThirdClauseSeparatorStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderThirdClauseSeparatorStepWorkTime": "BuilderSecondClausePaddingRun.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, secondClauseTokens problem) + 1 + CursorAdvance.advanceWorkSteps(cursorWord problem)", "cookLevinBuilderThirdClauseSeparatorStepRawTimePolynomial": "BuilderSecondClausePaddingRun.rawTimeBound + 330 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderThirdClauseSeparatorStepRuleCount": "2272 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier)", "cookLevinBuilderThirdClauseSeparatorStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": 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"PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.appenderEndpoint_before_cursor_launch_timeout": "3c7d516545e52f84a697d3fc76b4e95f9f3c3b512da286ff7ab06b1ecfa8d669", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.appender_workRunExact": "8d2a05243ed841aaef9ae166df6b942d2c21d591d2f50b5b20f10b3ee4f5040f", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.boundedDecide_compile_accept": "e7aab491624afd81b65c59d3dadaef7afd40a495e9e0fffa009d5944c7fa8267", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.boundedDecide_compile_ne_timeout": "8ca44e82291aa99fcb918b4e4b98ff8815ae8b742de3245b36e529659582ac6c", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.cursor_workRunExact": "f252365f166141d91b067b9b713650987cc10cbc74152b2909ce653a089fb12d", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalConfiguration_state": "822176ed69223c098ffe06b2fc5187c70b8c8e950cb516edff48b6608901ea9f", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalOutside_contains_finalTokenSlot": "b228338a40b4e0c1543fc18ea99aae9ca49a0762faf8eef6f8a2e6059a1c37e6", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTape_represents": "760750c3f1194cb9eee2377777b950b9ebac7e542783cc3e7a6e8c864921d091", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTokenBits_eq_encodedFormula_thirdClauseStart": "85d5bb8c8d33475f46e8501b810e375d64db6c81d1a6177c9f246863c6dac8f9", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTokenSlot_eq_thirdClauseStart_add_one": "155a77cd94f583aea6f7932071615ec360680e4d258afaffff06ebc83bff8246", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.machine_acceptState_ne_rejectState": "7bebac4c742c7d56a6021bd383b32b33e4bd2f3f3d082c1fa340f58721aac7ee", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedAppenderOutput_timeout": "193170fa9ffa8556d8611a132a3dabd71338107efd85a273cdb45f6d218e2a8f", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedAppenderTally_timeout": "09ed62823965d59ce2a07d6b579212d663ba930b85e5131fb62bd4907a347085", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedCursorScratch_timeout": "e5b87fb34a6564e480f1df45c987879ba9db3f13879fc20ef15493dd426e589b", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.nextTokenSlot_direct_eq_f": "c3f905ac4e0b3c8b33037ba867bac27e1ec1fdca19d1fee221e0e5aa0d5a4408", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.prefixEndpoint_before_launch_timeout": "2c5a665669bdfb7052e5ab9b8b5f2875f567d35c7058390da2ae1e17081e8e21", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.prefixSeparator_launch_workStep": "97bb27aab4e553fae8df89075fe65e25db1bc92b4e0ab14e7fa2a1064df975bb", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.prefix_workRunExact": "7bb2cfe206f16a72dd85123954c1544483ce15ecc1cd92513e5d19ab978c21f5", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rawTimeBound_eval": "26455a47a169f2ab21aa86619bb14c22d852a5474416617186aada9c0a45fcbb", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rawTimeBound_le": "abd8c20e8f57369d14d0e71004279aa81aa926f9c9f962f7517c1404625b90df", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rule_source_ne_acceptState": "75ee6db8b58b2b3cdc04b16788fb3e5f90ac5267d4b05624105a84c5dd419d9a", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rules_length": "7e4e36172ba08839d194b54ea20ce54465d7cbbd635fbc498d669711ffa97ee0", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rules_pairwise_query_distinct": "28b241ffa6d977b311bc06bfc08b9787981c44edcf1cc3287a12c9fd7a50d3c2", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_exact": "a0033107c250aaf5a4045c8c1e60fba5d7ea68ae2bbb82b874acfcc2fd727522", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_rawTimeBound": 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"d3a1d340250aba265a75676baf27e41a7d66d3f4a75e49553eb6083c994c9f66", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.workBoundedDecide_accept": "a9792042832f1ca6bb8c66f2b35d21c866858cdad9aa5e306a51e39d204f15c7", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.workRunExact": "af4a88cbefc4d741864dfa237e619ba257f585842dba8c8ae7c52fdf9c704ff1", "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.work_one_step_short_timeout": "545fdd856efa6b261596bf853d98eb82a38a618b75ec70e7751d6b5a2ba2449f" }, "cookLevinBuilderThirdClauseSeparatorStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.workRunExact", "cookLevinBuilderThirdClauseSeparatorStepSeparatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.specification_separator_step", "cookLevinBuilderThirdClauseSeparatorStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.specification_next_step", "cookLevinBuilderThirdClauseSeparatorStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.thirdClauseStartTokens_eq_canonical_formula_prefix", "cookLevinBuilderThirdClauseSeparatorStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTokenBits_eq_encodedFormula_thirdClauseStart", "cookLevinBuilderThirdClauseSeparatorStepAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.finalTokenSlot_eq_thirdClauseStart_add_one", "cookLevinBuilderThirdClauseSeparatorStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.nextTokenSlot_direct_eq_f", "cookLevinBuilderThirdClauseSeparatorStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rules_length", "cookLevinBuilderThirdClauseSeparatorStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.rules_pairwise_query_distinct", "cookLevinBuilderThirdClauseSeparatorStepSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length", "cookLevinBuilderThirdClauseSeparatorStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_exact", "cookLevinBuilderThirdClauseSeparatorStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.run_compile_rawTimeBound", "cookLevinBuilderThirdClauseSeparatorStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.boundedDecide_compile_accept", "cookLevinBuilderThirdClauseSeparatorStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderThirdClauseSeparatorStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedAppenderTally_timeout", "cookLevinBuilderThirdClauseSeparatorStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedAppenderOutput_timeout", "cookLevinBuilderThirdClauseSeparatorStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.malformedCursorScratch_timeout", "cookLevinBuilderThirdClauseSeparatorStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSeparatorStep.work_one_step_short_timeout", "cookLevinBuilderThirdClauseSeparatorStepPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderThirdClauseSeparatorStepPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderThirdClauseSeparatorStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderThirdClauseSeparatorStepProjectAxiomClosure": [], "cookLevinBuilderThirdClauseFirstLiteralPrefixFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixAxiomAuditPassed": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixAuditedDeclarationCount": 87, "cookLevinBuilderThirdClauseFirstLiteralPrefixCompiledRawMachineFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixExactFormulaBitsFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixCompleteFirstNegativeLiteralFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixInputPrefixAppenderComposed": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderThirdClauseFirstLiteralPrefixWorkTime": "BuilderThirdClauseSeparatorStep.workSteps(problem) + 1 + BuilderThirdClauseFirstLiteralPrefix.suffixWorkSteps(problem)", "cookLevinBuilderThirdClauseFirstLiteralPrefixRawTimePolynomial": "BuilderThirdClauseSeparatorStep.rawTimeBound + 732 + 48 * inputLength + 24 * FormulaWidth + 24 * cursorWord.length", "cookLevinBuilderThirdClauseFirstLiteralPrefixRuleCount": "2516 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier)", "cookLevinBuilderThirdClauseFirstLiteralPrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.machine_acceptState_ne_rejectState": "100d797c35b0c6669b7073cdb854d4081c9d53d8688205e876159170ec7db7ec", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rule_source_ne_acceptState": "bf196201e146f446a56416af0eb05e5a515f1ac5832d224c313b343ca814ba15", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_length": "9a8f723b4a8b1cac430edc51c0820def765e54ced9d39e1f44d4ce3c067ddf43", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.rules_pairwise_query_distinct": "24a4a64c8cbb3a4bc76886e3ba8db047c1e5bcb5ef87e7c05029d09e09da3360", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.machine_acceptState_ne_rejectState": "2dc79ae4c9843605442a27c12d6767cab9e0e4fee9b5ea179177128ecc77ce8a", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rule_source_ne_acceptState": "e4d2f92edde5f7d135e1449a07249349da4b9bc16b173dfa5e5b66fd1d19ea2f", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_length": "a502886839be2e262df7418abf74efbc75148b689509d23f2037351a65fd5e5f", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_pairwise_query_distinct": "f4d2b3a0f1821d864b4a7878facc2f6cbe74af602aeb84ad82d289f76f4e78ed", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.boundedDecide_compile_accept": "1083fb50b85c2eb4bd8965ebe4fd5cd1add5bb3b9eb5f50f5bae5debe7a80176", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.boundedDecide_compile_ne_timeout": "b8998789592f31eaa71114aade359a23a3eeb997be108ea73db652f3d5874e49", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalConfiguration_state": "30d417308d16b7ba743c3269bf7e00e39113a17f28f8c96e0ec9fbc2e1c8abe8", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalOutside_contains_finalTokenSlot": "b0256a9f5c6455673f712da415cab56221a35f55e0ef333ae551e6396e9b957c", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTape_represents": "4ed7727092630a39d8da50060c84338c9f17d959f5817d770401b22d035cb311", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_thirdClauseFirstLiteral": "aa32c1b77b98f4c6ea952104a0a950e086b6a375e3684b4557998c05ee93d252", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTokenSlot_eq_thirdClauseStart_add_three": "53ee38e1ef7e949de3082d1cb7de3b244a6506c0729eee081c23ccb2cebc284f", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstAppenderEndpoint_before_cursor_launch_timeout": "f619484b4292b970d8968135d186cc293bf6a8eb5a37c55ebd8cf9a4ed57d682", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstAppender_workRunExact": "0aba1695fd933a81f877d1feb2b47dce1476ab4378e33d3d838a807ab8e2dcc2", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstCursorEndpoint_before_secondAppender_launch_timeout": "f3e724f24ea96a79af09d52c2501f4a1bf5f2c55a949269a1ba9f0a8388a4e70", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstCursor_workRunExact": "5b999df397c26f41bc19c40ccf72a8106ec31a2b853777d77e0c3a39e53c4762", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstFalseTokenCursor_launch_workStep": "d80f3fe3881cbe1d90d483256e1728cd7a94c192ff3e9848be57ab93a344e4bb", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstFalseTokenCursor_workRunExact": "5bb0d558c83e6c3dfcf4b035d6b791daff3a9285c22f73683277d30bf52ffcd1", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralSignSlot_direct_eq_f": "f3ade16c48fd3450c83bb34e4ee944560d30deab8885fb1a668d554092bdf96e", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralSuffix_launch_workStep": "07f2f9e32cd6032a2762815bce9602a64a56b8c53f6d1fcff3f0de9fa8f6ac4d", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralZeroTerminatorSlot_direct_eq_f": "adb17a823fefb7625c561a6f785d8e454e824703123f2efa31a79b6e01431d56", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.machine_acceptState_ne_rejectState": "36f2cb38c9eff77b43f0ba637bef01266bdee93851617073ae5aafd856095795", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstAppenderOutput_timeout": "5210d7e07b447d604ce6dad734984c91a7a5e244d8c5db8d3c6376d5acf7e336", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstAppenderTally_timeout": "5314abe6e09c3157b5e5ed525de3911a8d64aa79b8ef4345e32fbc53a43970c7", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstCursorScratch_timeout": "956b2aadd56af4bf1cf7d4aed00f765d81aa5955ff00ca2e49bb5408e49b373c", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondAppenderOutput_timeout": "aaa5e36357e90581bc5587ed5cee51a84f6ab1320774851f997888e8e3fe43ea", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondAppenderTally_timeout": "3c9e2918fcf975b25a253dfabf250974eb0bbc1ae34271248b1465141ddc8a44", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondCursorScratch_timeout": "e7fdb4759b8a0b286da96dd7bde6495427abc3512d0892eb2a70f4c8dc696092", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.nextTokenSlot_direct_eq_f": "8f7b6f1644b01d67d8d825cde4fb1096eb4f1c1c1f6b09ce7936b67c83f32ea5", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefixEndpoint_before_launch_timeout": "6ba174820755f7cf7bc5d88980ecc36776b4dc8bf9abd63b99af676c23a9318e", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefixFirstLiteral_launch_workStep": "45555fd22b4d093d59e5a3ee4bcf83c82cf72fef1bf234067b509232d41c57e7", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefix_workRunExact": "9a04a17fe4271fc78e5ceacb2b85fad1988eb42f2f01e17ff132ce0a66c39732", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rawTimeBound_eval": "391d0fbf52e06d81d81d8477daafe756384f4c427bd09a001af53928d554e86b", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rawTimeBound_le": "b1a90e2d1b4e215684406e9e158595bbc9eb753606518fb1821d22a0097fa8aa", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rule_source_ne_acceptState": "3ecddcfe51834fe3b09dd23158040bcf1921fa83d5c0712e3438e832f5d0f158", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rules_length": "b110cff2fd9b5d39c9e7453fd91410f308c83504e3e5bde451026366255cbddc", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rules_pairwise_query_distinct": "0e76455eef96aa9257fe87eeccf85cf422d8a36b5444ae6c1c6ab5ae657a592d", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_exact": "b917638bdb6d294678a6c8e6ae18d389d979cffc5d239a52195c042cb80a61a2", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_rawTimeBound": "deffe2b95b1483b37a01c0ac3fa322f50fabfaa2b064aa9e2cedf23a9d72df81", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_rawTimeBound_blankEquivalent": "b4b6ffd4b17f6e85c280b0d674f3e4eb905ff07780f18ea57f4c8864813297cc", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondAppenderEndpoint_before_cursor_launch_timeout": "9dd64d8a94d0fa736cf1860048c08ddea3c20139867af1ed14cf56a1614ae572", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondAppender_workRunExact": "bde3f77d49a9a3f27c5b9a7528f9cfe07bcf30101db006cbd09da3fe595111ac", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondCursor_workRunExact": "3ee0b6bd708584eb532a44b3a7209ca09bcbf0ec256270dd146fb343fffd94b2", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondFalseTokenCursor_launch_workStep": "25b69232c775d7a5fbffd6225345e1f7293a11bdd57be95bb3bee6b8dc953a99", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondFalseTokenCursor_workRunExact": "8567823d416bf7144828400a4b45541f3e53aa9049d0d4357b19b13e12ecc805", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_firstLiteral_sign_step": "193ecb39fec5e294efee2dbe0d24197fc94d965ba3012ebd35694edd013e2d42", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step": "789608fc7adc92e986511b827b35d119cbb4258920d3835bf3d440ee1d740194", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_next_step": "760a1f1cbd557cc4875198de16364e8cfed512a2ae87eb1bf722d208cbce7a48", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.suffix_workRunExact": "1c4fd727ca2ce5252b961eb660a50fcce613d641da14f4c069e87c5b83ac8712", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.thirdClauseFirstLiteralTokens_eq_canonical_formula_prefix": "7021e06ba4475f4cf8bb6427d6ecd80eb4b9a48c4d6c1e941ced1a838b0ccee7", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.workBoundedDecide_accept": "19e9f2d65fba85ceed2a94f62d9c4ee1bfb8b02966ae31eb64b545d8047f7562", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.workRunExact": "b325a2050c25cd0c62f451fcdcede3a53c55c36d6d878d21d2aecdec6fb9b391", "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.work_one_step_short_timeout": "5df5289a7db4588834094a4cacd58c119ada4223e0520f96adf7859558da9e8c" }, "cookLevinBuilderThirdClauseFirstLiteralPrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.workRunExact", "cookLevinBuilderThirdClauseFirstLiteralPrefixSignSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_firstLiteral_sign_step", "cookLevinBuilderThirdClauseFirstLiteralPrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step", "cookLevinBuilderThirdClauseFirstLiteralPrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.specification_next_step", "cookLevinBuilderThirdClauseFirstLiteralPrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.thirdClauseFirstLiteralTokens_eq_canonical_formula_prefix", "cookLevinBuilderThirdClauseFirstLiteralPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_thirdClauseFirstLiteral", "cookLevinBuilderThirdClauseFirstLiteralPrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.finalTokenSlot_eq_thirdClauseStart_add_three", "cookLevinBuilderThirdClauseFirstLiteralPrefixSignTokenTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralSignSlot_direct_eq_f", "cookLevinBuilderThirdClauseFirstLiteralPrefixTerminatorTokenTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstLiteralZeroTerminatorSlot_direct_eq_f", "cookLevinBuilderThirdClauseFirstLiteralPrefixNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.nextTokenSlot_direct_eq_f", "cookLevinBuilderThirdClauseFirstLiteralPrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rules_length", "cookLevinBuilderThirdClauseFirstLiteralPrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.rules_pairwise_query_distinct", "cookLevinBuilderThirdClauseFirstLiteralPrefixSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FirstLiteralSuffix.rules_length", "cookLevinBuilderThirdClauseFirstLiteralPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_exact", "cookLevinBuilderThirdClauseFirstLiteralPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.run_compile_rawTimeBound", "cookLevinBuilderThirdClauseFirstLiteralPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.boundedDecide_compile_accept", "cookLevinBuilderThirdClauseFirstLiteralPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixMalformedFirstAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstAppenderTally_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixMalformedFirstAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstAppenderOutput_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixMalformedFirstCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedFirstCursorScratch_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixMalformedSecondAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondAppenderTally_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixMalformedSecondAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondAppenderOutput_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixMalformedSecondCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.malformedSecondCursorScratch_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.prefixEndpoint_before_launch_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixFirstAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstAppenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixFirstCursorEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.firstCursorEndpoint_before_secondAppender_launch_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixSecondAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.secondAppenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseFirstLiteralPrefix.work_one_step_short_timeout", "cookLevinBuilderThirdClauseFirstLiteralPrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderThirdClauseFirstLiteralPrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderThirdClauseFirstLiteralPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderThirdClauseFirstLiteralPrefixProjectAxiomClosure": [], "cookLevinBuilderThirdClauseSecondLiteralPrefixFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixAxiomAuditPassed": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixAuditedDeclarationCount": 145, "cookLevinBuilderThirdClauseSecondLiteralPrefixCompiledRawMachineFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixExactFormulaBitsFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixCompleteSecondNegativeLiteralFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixRetainedClauseTerminatorCoordinateFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixInputPrefixAppenderComposed": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderThirdClauseSecondLiteralPrefixWorkTime": "BuilderThirdClauseFirstLiteralPrefix.workSteps(problem) + 1 + BuilderThirdClauseSecondLiteralPrefix.suffixWorkSteps(problem)", "cookLevinBuilderThirdClauseSecondLiteralPrefixRawTimePolynomial": "BuilderThirdClauseFirstLiteralPrefix.rawTimeBound + 1752 + 96 * inputLength + 48 * FormulaWidth + 48 * cursorWord.length", "cookLevinBuilderThirdClauseSecondLiteralPrefixRuleCount": "3004 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier)", 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"PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length", "cookLevinBuilderThirdClauseSecondLiteralPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.run_compile_exact", "cookLevinBuilderThirdClauseSecondLiteralPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.run_compile_rawTimeBound", "cookLevinBuilderThirdClauseSecondLiteralPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.boundedDecide_compile_accept", "cookLevinBuilderThirdClauseSecondLiteralPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.prefixEndpoint_before_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixSignAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.signAppenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixSignCursorEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.signCursorEndpoint_before_firstUnary_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixFirstUnaryAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.firstUnaryAppenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixFirstUnaryCursorEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.firstUnaryCursorEndpoint_before_secondUnary_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixSecondUnaryAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondUnaryAppenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixSecondUnaryCursorEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.secondUnaryCursorEndpoint_before_terminator_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixTerminatorAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.terminatorAppenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedSignAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSignAppenderTally_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedSignAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSignAppenderOutput_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedSignCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSignCursorScratch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedFirstUnaryAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedFirstUnaryAppenderTally_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedFirstUnaryAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedFirstUnaryAppenderOutput_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedFirstUnaryCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedFirstUnaryCursorScratch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedSecondUnaryAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSecondUnaryAppenderTally_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedSecondUnaryAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSecondUnaryAppenderOutput_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedSecondUnaryCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedSecondUnaryCursorScratch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedTerminatorAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedTerminatorAppenderTally_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedTerminatorAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedTerminatorAppenderOutput_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixMalformedTerminatorCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.malformedTerminatorCursorScratch_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.work_one_step_short_timeout", "cookLevinBuilderThirdClauseSecondLiteralPrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderThirdClauseSecondLiteralPrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderThirdClauseSecondLiteralPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderThirdClauseSecondLiteralPrefixProjectAxiomClosure": [], "cookLevinBuilderThirdClausePrefixFormalized": true, "cookLevinBuilderThirdClausePrefixAxiomAuditPassed": true, "cookLevinBuilderThirdClausePrefixAuditedDeclarationCount": 57, "cookLevinBuilderThirdClausePrefixCompiledRawMachineFormalized": true, "cookLevinBuilderThirdClausePrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderThirdClausePrefixExactFormulaBitsFormalized": true, "cookLevinBuilderThirdClausePrefixCompleteThirdClauseFormalized": true, "cookLevinBuilderThirdClausePrefixClauseTerminatorFormalized": true, "cookLevinBuilderThirdClausePrefixRetainedFirstPaddingCoordinateFormalized": true, "cookLevinBuilderThirdClausePrefixRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderThirdClausePrefixInputPrefixAppenderComposed": true, "cookLevinBuilderThirdClausePrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderThirdClausePrefixWorkTime": "BuilderThirdClauseSecondLiteralPrefix.workSteps(problem) + 1 + appenderWorkSteps(problem) + 1 + cursorWorkSteps(problem)", "cookLevinBuilderThirdClausePrefixRawTimePolynomial": "BuilderThirdClauseSecondLiteralPrefix.rawTimeBound + 498 + 24 * inputLength + 12 * FormulaWidth + 12 * BuilderThirdClauseSeparatorStep.cursorWord.length", "cookLevinBuilderThirdClausePrefixRuleCount": "3126 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier)", "cookLevinBuilderThirdClausePrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.machine_acceptState_ne_rejectState": "085381a296da46be4e957d68e063026810db4855c2fe2f74a8ad13705a2c6a43", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rule_source_ne_acceptState": "c9bca6b81c8c7ef40929c045d8e7527cc5f673f645dd087785f5e677148af184", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rules_length": "13f07acc2df0542753393765f038d0a567a15fbc61e31fbd22b7407d59eb589d", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rules_pairwise_query_distinct": "14a7b49176c64cbc29d038c4cbd6f5bcade9a660e4bb2b2d308182fb3ae369c8", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.appenderEndpoint_before_cursor_launch_timeout": "5333ea3774ad1d00eaedcd2bbcd295b6c372ccccf906fa78ad196c2efd45b37c", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.appender_workRunExact": "86b7e16c9bb3ff5782deb385e0b2654a82a46b87348600d8417dfe5406da80f3", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.boundedDecide_compile_accept": "4879b56d09425763782427481cc0698af9a90ba59c54e1dd8ce461d6163334f5", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.boundedDecide_compile_ne_timeout": "fb51a3a95ccaecdba08da7ee2415f4df8cfbeaf567ae68a8f6650703da7b731b", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.clauseTerminatorSlot_direct_eq_finish": "469513eb11e5474d00e27321b86942e61dae005fefffe81c5ecd11a198cd9055", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.cursor_workRunExact": "4a3d019f45b85fb97bb24b640c943524087cfd95259083d83f82d1c53bfeefe7", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalConfiguration_state": "47f8564a92976c270f5905b67532dc6c62dd8ac1b40100e39c9602d55294c46f", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalOutside_contains_finalTokenSlot": "edbe14a3caced903a3b1ff04834d355dc8a964a4181314ad491e815166c4a1d7", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTape_represents": "19a1d224dc1815de31a20e318031cfc4dcb36fbafb5f998cb7f048ce5007d265", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTokenBits_eq_encodedFormula_thirdClause": "a8711d3a0e1d183e8a18b0d4490c753d64b07747639d50d4e96814d11133c47b", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTokenSlot_eq_thirdClauseStart_add_eight": "5751378f4a8db7806c76121fa9db3ba23bf0051d7fa58a108becc64467e2f3db", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finishTokenCursor_launch_workStep": "c27bdc9f389fc095349896236e5ff5f1086891be758029cfe8411c103e952088", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.machine_acceptState_ne_rejectState": "39df940577968fde13b2b47b606747ed2b196f08b77a2f8adbd5c06dc99a7c30", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedAppenderOutput_timeout": "85b5cfbc421c0baf4def6cb648d7a3e77dc7e62166dda88c2415cb43328d7ae2", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedAppenderTally_timeout": "e46a74465a167cb4ecb34580720b0b83c3e7a0d4591c0cf8f323c72b3d47d2ef", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedCursorScratch_timeout": "f3c43228d9fc2b650d435352117d3434df5adfacabd6d2c26183485a20009557", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.nextTokenSlot_direct_eq_padding": "cf94e231582120a0b1e638929359b7b343b32c77be2562cb3a5afd68e9681fce", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefixEndpoint_before_launch_timeout": "bf0c0daa8d899381ffd4ec937ec540e521dc17935d5b3e36f4d3ccccd40f528a", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefixFinish_launch_workStep": "f1a2da449333f7a3e872abb128448c047b2cd0f14b89bdcaaca306cfc747380d", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefix_workRunExact": "e9b6513e6a432072be40e4a6e0855e82e5a16ace99ae19d33307be0ecc37ca6d", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rawTimeBound_eval": "0fb6da98fab563b511af87602a7dc92ec646a2498619b92e53fb9e73c473fd02", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rawTimeBound_le": "0c6e16ad24372dd734027089e09167ac3e9f8b52d10a12e91cbd4ca4956d21b1", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rule_source_ne_acceptState": "9bad8e5e20457c730807972c3ef54356d066493d294318afbda32e18111d17dc", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rules_length": "5ccd5111f0e6490ca7f841abb7e3135a9059639a966d5d9a917301e9734c00af", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rules_pairwise_query_distinct": "5d2bda00893162af9c4c265d90beded2927e4cc425c7ff56649697d882bc7dab", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_exact": "386d6372459efb419def9197f97025a83daec0539177c8f6be7c7abfe247703a", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_rawTimeBound": "888185e7abf7d0158c969bc03bc47c81b03e382b1189829d679584727975caeb", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_rawTimeBound_blankEquivalent": "0b6ec6cab92f3035f0da87262007b5ebdedb6cf27bdbe5c8177ad2b4501b0975", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.specification_next_step": "a7d47c19e2a6423fa06cb6968206f527d8c0838b7bca4a6078fe014c50264867", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.specification_terminator_step": "cb975c3f55a9a9e42e94e42234e831506ad6dc3307d2fda9716a18755814b8bf", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.suffix_workRunExact": "c4cf3144bdbecb6c1ca5920afac7c992931b4b251de4e0f09ed89e58b9d15bdb", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.thirdClauseTokens_eq_canonical_formula_prefix": "adf0ef05eaf503599e482f976d8bee54ecc8158ef042ccbf5cf656457c82c765", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.workBoundedDecide_accept": "34d15063d2b9f9959a4cf20e51e73dee9bedbb93a99e09dfa66136039322f37f", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.workRunExact": "29a8862876d69b1c90f8382f325c9a4f81c906eecaf3a2e6ad74f6d07117239f", "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.work_one_step_short_timeout": "2357eca86e6707f27b61bcc0fa33e711ad024622b95263478917f280025126ea" }, "cookLevinBuilderThirdClausePrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.workRunExact", "cookLevinBuilderThirdClausePrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.specification_terminator_step", "cookLevinBuilderThirdClausePrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.specification_next_step", "cookLevinBuilderThirdClausePrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.thirdClauseTokens_eq_canonical_formula_prefix", "cookLevinBuilderThirdClausePrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTokenBits_eq_encodedFormula_thirdClause", "cookLevinBuilderThirdClausePrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.finalTokenSlot_eq_thirdClauseStart_add_eight", "cookLevinBuilderThirdClausePrefixClauseTerminatorTokenTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.clauseTerminatorSlot_direct_eq_finish", "cookLevinBuilderThirdClausePrefixNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.nextTokenSlot_direct_eq_padding", "cookLevinBuilderThirdClausePrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rules_length", "cookLevinBuilderThirdClausePrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.rules_pairwise_query_distinct", "cookLevinBuilderThirdClausePrefixFinishTokenCursorRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.FinishTokenCursor.rules_length", "cookLevinBuilderThirdClausePrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_exact", "cookLevinBuilderThirdClausePrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.run_compile_rawTimeBound", "cookLevinBuilderThirdClausePrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.boundedDecide_compile_accept", "cookLevinBuilderThirdClausePrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderThirdClausePrefixPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.prefixEndpoint_before_launch_timeout", "cookLevinBuilderThirdClausePrefixAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderThirdClausePrefixMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedAppenderTally_timeout", "cookLevinBuilderThirdClausePrefixMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedAppenderOutput_timeout", "cookLevinBuilderThirdClausePrefixMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.malformedCursorScratch_timeout", "cookLevinBuilderThirdClausePrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePrefix.work_one_step_short_timeout", "cookLevinBuilderThirdClausePrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderThirdClausePrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderThirdClausePrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderThirdClausePrefixProjectAxiomClosure": [], "cookLevinBuilderThirdClausePaddingRunFormalized": true, "cookLevinBuilderThirdClausePaddingRunAxiomAuditPassed": true, "cookLevinBuilderThirdClausePaddingRunAuditedDeclarationCount": 68, "cookLevinBuilderThirdClausePaddingRunCompiledRawMachineFormalized": true, "cookLevinBuilderThirdClausePaddingRunExternalInputSizePolynomialFormalized": true, "cookLevinBuilderThirdClausePaddingRunExactFormulaBitsFormalized": true, "cookLevinBuilderThirdClausePaddingRunRemainingPaddingCountFormalized": true, "cookLevinBuilderThirdClausePaddingRunDirectPaddingBlockFormalized": true, "cookLevinBuilderThirdClausePaddingRunFourthClauseStartFormalized": true, "cookLevinBuilderThirdClausePaddingRunNoEmissionSpecificationFormalized": true, "cookLevinBuilderThirdClausePaddingRunInputPrefixAppenderComposed": true, "cookLevinBuilderThirdClausePaddingRunFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderThirdClausePaddingRunWorkTime": "BuilderThirdClausePrefix.workSteps(problem) + 1 + BuilderUnaryPolynomial.workSteps(remainingPaddingPolynomial verifier, input) + 1 + PaddingCountdown.loopSteps(countControllerPrefixLength, remainingPaddingCount) + 1 + BuilderUnaryPolynomial.workSteps(fourthClauseStartPolynomial verifier, input)", "cookLevinBuilderThirdClausePaddingRunRawTimePolynomial": "BuilderThirdClausePrefix.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps", "cookLevinBuilderThirdClausePaddingRunRuleCount": "3178 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier)", "cookLevinBuilderThirdClausePaddingRunTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le": "972da09f44b6d35d56ce775bd4a46687be45609dacd0670bc983d603715bf278", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact": "ff60669772a7f137755431c1300c4368e8004a05b1d36972a768b50d1846cf5a", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.boundedDecide_compile_accept": "249619b7b1570265253cdee788574d80a05aaa0242c5c3ba31a31e662d64c923", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.boundedDecide_compile_ne_timeout": "80a6a5d3c928355ad98edbea3d9675ee42269b2b8defdebef910f83b340c9263", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.countEvaluator_workRunExact": "5913f826d1190b662b8647a483e06128bcfec9de44cb36b66bdc97c552799252", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.countdownBoundPolynomial_eval": "c23d59fe9a6f879f4ba99597d155184d132e6c1b5a9df2f93c687a62db4ac4ac", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.countdown_workRunExact": "4cadccfc1078724596bae46160e344852270eea712f1bb0d245ffbb5a7974aa7", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalConfiguration_state": "98e8fc89dcc30ed871cdf756fab18f87d7b2e94dc88fe000be7259b2f2973972", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalOutside_contains_finalTokenSlot": "35a2ea6fa44b064e38abd9b96fb505e29ea50589bb4748f6466d2099da49a669", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTape_represents": "0a4457eab8230b8583001e4151c9459d60f50971dc1cd0cfbdd9711c36fe0441", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTokenBits_eq_encodedFormula_thirdClause": "2988eef4e435028d78489115eeb7c28a88334f000563c64dbe0110888c347858", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTokenSlot_eq_fourthClauseStart": "d603123516ad69a4531919b3f3b22341858323a63cdad7aa1a45517370804b59", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.fourthClauseStart_direct_eq_sep": "8bf000c7e607b87ad395dbff9d833fd4158127c97aec8b37f56d0aebe6a6071c", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.fourthClauseStart_eq": "f43ac8e50e0d1ddd14f8de0d28f1a6d3fe5386b584cc75927332c727c56db4e0", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.launch_workStep": "86b12940f025d5f9de17cfb0d8d3b81fbbbc99e26fd15a3a06a500cec7fbd5ef", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.machine_acceptState_ne_rejectState": "4c79f1781807f48a0a56e974f1ed6c649c26989dc219d5fb958465d65bc1b47f", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.malformedCountdownRoot_timeout": "04c6dcb17614f29dfc1eebe3fd8c0fce0174653c2028bab46eba5d4bdd4c807f", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.malformedCountdownScratch_timeout": "4fdb556d8158bf65a3d0e7a536475b005adc09037a58a3048d2cc24bfb97e8e4", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.paddingSlot_direct_eq_padding": "e9277e87bf95bccc32d8dab0aff308e082e481397687d863a7f09c057838e134", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.predecessorSlot_add_remainingPaddingCount": "7d7af0212477c437f6a59989757321fde88a915dc48fac55e051a439d719d0d8", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.prefixEndpoint_before_launch_timeout": "0991a439e29ee54ccb1b4d44bec5b170616c0d9034d9c7c76504173ac4e40674", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.prefix_workRunExact": "f2661ddadce96b42143d386748160fb213c56f790a74ea71456e948ea0e76529", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rawTimeBound_eval": "b5a20219d4686f94f3eca8614a2c7ccf168339aeed4ed15c8ef2d5c74004b4ca", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rawTimeBound_le": "4c2507af0df6c20bc18d90027d2cea598d3a094e1fcf0e34f87a7dce87b02c79", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_eq": "fe3b47bfbbad07a39d205644b4f84cf5c0519a577e5b82219d621192a12e6860", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_eight": "ce7bd592722a6ea242af9102abe295af9499f27678ceee935ab411c40d231229", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_positive": "d898e69b239ffdbdae05fc682c90965f126a1f1b41774c95da03af2db8e8337a", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rule_source_ne_acceptState": "00a7adbb12a9d382b1dfbdfe383965d302b11bf327059076591a44104b835ce0", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rules_length": "4e78d1ad72a2b134a42d76a22e124e493866f4d5cca9158bc85628067d01282a", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rules_pairwise_query_distinct": "e7ef104c5e23f906cf29ac34e59f0b348caee4a11343fb676a9091b85b392bf2", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_exact": "49d7e0cd137a9ca58691fe3d6cd60d8750def0da941a1e1e83239cff76053b85", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_rawTimeBound": "5ed7455a66395afbf20467693127bfdfc2a95127312336ddf64f656256201b6f", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_rawTimeBound_blankEquivalent": "2d73b2a250ea33ab11a036b72676ce1375cfc606ca7b9c3a01e581a077e90857", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.specification_padding_run": "279edcb8496ae6338653d8ec36d4439080d0bf535b988b6e780b532c852b06ee", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.specification_target_step": "828e185b5bc315c839fe74a79e0436c0e884351d78289443aa2bbf86805b6da9", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.targetEvaluator_workRunExact": "e192253998613fc225dcd6b79b3ca96659981dd35d77d5308134427ac812f967", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.workBoundedDecide_accept": "8d6703ae70de3e00dc93cc6f265ce97e372a690d9a04fdffb17ee6b9fbca8a73", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.workRunExact": "87a47c4a0da0c5f643342d9cc23e6332eb5794c6d4fb7e285af1dc4c61ee3ef8", "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.work_one_step_short_timeout": "ee53851ecb0eb5818f0eedf5da88dd61a986676940d7211ec4823875a9d2564f" }, "cookLevinBuilderThirdClausePaddingRunExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.workRunExact", "cookLevinBuilderThirdClausePaddingRunPaddingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.specification_padding_run", "cookLevinBuilderThirdClausePaddingRunTargetSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.specification_target_step", "cookLevinBuilderThirdClausePaddingRunFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTokenBits_eq_encodedFormula_thirdClause", "cookLevinBuilderThirdClausePaddingRunRemainingCountTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_eight", "cookLevinBuilderThirdClausePaddingRunFourthClauseCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.finalTokenSlot_eq_fourthClauseStart", "cookLevinBuilderThirdClausePaddingRunDirectPaddingTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.paddingSlot_direct_eq_padding", "cookLevinBuilderThirdClausePaddingRunDirectSeparatorTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.fourthClauseStart_direct_eq_sep", "cookLevinBuilderThirdClausePaddingRunRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rules_length", "cookLevinBuilderThirdClausePaddingRunRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.rules_pairwise_query_distinct", "cookLevinBuilderThirdClausePaddingRunCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_exact", "cookLevinBuilderThirdClausePaddingRunCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.run_compile_rawTimeBound", "cookLevinBuilderThirdClausePaddingRunAcceptTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.boundedDecide_compile_accept", "cookLevinBuilderThirdClausePaddingRunNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.boundedDecide_compile_ne_timeout", "cookLevinBuilderThirdClausePaddingRunMalformedRootTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.malformedCountdownRoot_timeout", "cookLevinBuilderThirdClausePaddingRunMalformedScratchTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.malformedCountdownScratch_timeout", "cookLevinBuilderThirdClausePaddingRunOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderThirdClausePaddingRun.work_one_step_short_timeout", "cookLevinBuilderThirdClausePaddingRunAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderThirdClausePaddingRunProjectAxiomClosure": [], "cookLevinBuilderFourthClauseSeparatorStepFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepAxiomAuditPassed": true, "cookLevinBuilderFourthClauseSeparatorStepAuditedDeclarationCount": 56, "cookLevinBuilderFourthClauseSeparatorStepCompiledRawMachineFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepExactFormulaBitsFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepFourthClauseSeparatorFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepInputPrefixAppenderComposed": true, "cookLevinBuilderFourthClauseSeparatorStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFourthClauseSeparatorStepWorkTime": "BuilderThirdClausePaddingRun.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, thirdClauseTokens problem) + 1 + CursorAdvance.advanceWorkSteps(cursorWord problem)", "cookLevinBuilderFourthClauseSeparatorStepRawTimePolynomial": "BuilderThirdClausePaddingRun.rawTimeBound + 426 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderFourthClauseSeparatorStepRuleCount": "3300 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier)", "cookLevinBuilderFourthClauseSeparatorStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": 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"PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.machine_acceptState_ne_rejectState": "59d3b5b9d120f5a4ad400ec786b5e91ded76db1a3a42a0acd5c27fecf9551b12", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedAppenderOutput_timeout": "072fad47fe11e0883118fbd76cdd7d62579b4cf1d5e9c2bf14d9cc51e8172339", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedAppenderTally_timeout": "f257955721f774cc27968596fcf9086cf99696e3cbad73a4d20288ef2cd64dce", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedCursorScratch_timeout": "b94dd4da07d392e1b36d9df16069c2d08f8c4e26b2b90e089fbaba278b41528b", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.nextTokenSlot_direct_eq_f": "1548a9fa843d9a27ab5a01f6963e96291a62e6be0cb881b04d5c5099cd8b8927", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.prefixEndpoint_before_launch_timeout": "1e45e9387fc47880a2b7ac9d265e48708eb86235e1fe38a24e9e387eff88b607", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.prefixSeparator_launch_workStep": "400645444248ccf6db6ad2164ff200b71ed37bb767efafc9e1c2625cb245a1a6", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.prefix_workRunExact": "596c409712a58dea94b2c94629d974d765de54406d958c345b67314370750017", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rawTimeBound_eval": "6c873cb716d26f84e9a34f040073a9f16499591e4b073cd227958770162ce48b", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rawTimeBound_le": "ef35a0073f8ebe104a81c2a83698c413aeeddfcb9495092bff920f230c35345c", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rule_source_ne_acceptState": "434439ee8ada8b595e3f13f383427a507fff515a35206c85b60fb204329af266", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rules_length": "597bc6eb8066b3165bf71c79606a648b9fe779a658c0c52bdfdaae4c83f5541b", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rules_pairwise_query_distinct": "362135763c4ecfa80c05af2b7eec1f6748c6c85594a7a11f14ea14693f1e5574", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_exact": "da621856ebe60fd28b9415879b0184d443c7a0c2b5749c998e9cdc7449984ebe", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_rawTimeBound": "af8f2c669032549e58b87d8b0cc9d836f237785adbbb047e91cba475844850d7", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_rawTimeBound_blankEquivalent": "bc3c2b6d92fdf3427e89842aa722ee568d2d1211c448fe77ca6b397e64157867", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.separatorCursor_launch_workStep": "6394c0e1101b85531da2621007d29bf8016ca1dbfe5ac67d8c8e8f7665c042a7", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.specification_next_step": "b362f4ab496d5284b80dc490248dc43bbc91b0ab701616744cb498685f056726", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.specification_separator_step": "76329e6caff5f9602529486bf8c2c6d44ca8773c620d05e3482005b0c3938211", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.suffix_workRunExact": "6f35aae20eb89b2ab2879cb55e8a98290a21834345a7a00f0035c7fb10721c1c", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.workBoundedDecide_accept": "d64b4cc454d8a1f4c9ea4de4eac80c684e68e36e2837741227b3eaad81dacaeb", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.workRunExact": "6b7cdb57771609eb203509b19a2c9af8c1983f720cfeb573428ed7a465f9a606", "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.work_one_step_short_timeout": "24c2aca571f257b69837f58221d1790f0fa8d670fcdda6164df9543c6e460626", "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.machine_acceptState_ne_rejectState": "eee6920f72c0fa3566bb3cc5fec3951b18a9b2aa1b50b5cf34436d0183ab750b", "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rule_source_ne_acceptState": "7374475130eed22d8cc19092f72edf903e2c68e024a2f87b3ab4220e8cce98ef", "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length": "f7a8b37c7c3b3404f9144c91f3ce51689b46abf2e61945b6fb89b3d865f98200", "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_pairwise_query_distinct": "c17b7f7fa8d40cb373b90f541f7700eb91c2bc21b5a0a7f5a02ba842283f879d" }, "cookLevinBuilderFourthClauseSeparatorStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.workRunExact", "cookLevinBuilderFourthClauseSeparatorStepSeparatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.specification_separator_step", "cookLevinBuilderFourthClauseSeparatorStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.specification_next_step", "cookLevinBuilderFourthClauseSeparatorStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.fourthClauseStartTokens_eq_canonical_formula_prefix", "cookLevinBuilderFourthClauseSeparatorStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalTokenBits_eq_encodedFormula_fourthClauseStart", "cookLevinBuilderFourthClauseSeparatorStepAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.finalTokenSlot_eq_fourthClauseStart_add_one", "cookLevinBuilderFourthClauseSeparatorStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.nextTokenSlot_direct_eq_f", "cookLevinBuilderFourthClauseSeparatorStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rules_length", "cookLevinBuilderFourthClauseSeparatorStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.rules_pairwise_query_distinct", "cookLevinBuilderFourthClauseSeparatorStepSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rules_length", "cookLevinBuilderFourthClauseSeparatorStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_exact", "cookLevinBuilderFourthClauseSeparatorStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.run_compile_rawTimeBound", "cookLevinBuilderFourthClauseSeparatorStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.boundedDecide_compile_accept", "cookLevinBuilderFourthClauseSeparatorStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderFourthClauseSeparatorStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedAppenderTally_timeout", "cookLevinBuilderFourthClauseSeparatorStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedAppenderOutput_timeout", "cookLevinBuilderFourthClauseSeparatorStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.malformedCursorScratch_timeout", "cookLevinBuilderFourthClauseSeparatorStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSeparatorStep.work_one_step_short_timeout", "cookLevinBuilderFourthClauseSeparatorStepPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderFourthClauseSeparatorStepPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderFourthClauseSeparatorStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFourthClauseSeparatorStepProjectAxiomClosure": [], "cookLevinBuilderFourthClauseFirstLiteralPrefixWorkTime": "BuilderFourthClauseSeparatorStep.workSteps(problem) + 1 + BuilderFourthClauseFirstLiteralPrefix.suffixWorkSteps(problem)", "cookLevinBuilderFourthClauseFirstLiteralPrefixRawTimePolynomial": "BuilderFourthClauseSeparatorStep.rawTimeBound + 1422 + 72 * inputLength + 36 * FormulaWidth + 36 * cursorWord.length", "cookLevinBuilderFourthClauseFirstLiteralPrefixRuleCount": "3666 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + 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"PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.machine_acceptState_ne_rejectState": "4dac552c93dffe9e77d712891185d1d12585926292dfb3773386e749c4a20646", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rule_source_ne_acceptState": "d94f787a19844fb8e755e09249bcc56e75751d9b2c40143e02660a62d7b4ad04", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length": "e5b32823754bf6c535394d67f89795dab7d13d83fc26601606d2d3b97ad1355d", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_pairwise_query_distinct": "b1aa2a7114f99c3a80df8a2837b9d8590374aa0c0db075381da329db16842aec", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState": "8751719f745f8345308450a6fa63c4555415c822188cbbcac76ae752890895e8", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState": "11ea0df62f1691605a85227e5f0b315f3232a811aac074053c18d465743d560b", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length": "54722218e5109a54d5d89bcf6b9011921f507daba1452870f0f22142f426de1d", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_pairwise_query_distinct": "f01f1614a6efad7479051b52b3f910046c73ad4c6b60f7275a62b0cdec42731e" }, "cookLevinBuilderFourthClauseFirstLiteralPrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.workRunExact", "cookLevinBuilderFourthClauseFirstLiteralPrefixSignSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_firstLiteral_sign_step", "cookLevinBuilderFourthClauseFirstLiteralPrefixUnaryUnitSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_firstLiteral_unaryUnit_step", "cookLevinBuilderFourthClauseFirstLiteralPrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_firstLiteral_terminator_step", "cookLevinBuilderFourthClauseFirstLiteralPrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.specification_next_step", "cookLevinBuilderFourthClauseFirstLiteralPrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.fourthClauseFirstLiteralTokens_eq_canonical_formula_prefix", "cookLevinBuilderFourthClauseFirstLiteralPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalTokenBits_eq_encodedFormula_fourthClauseFirstLiteral", "cookLevinBuilderFourthClauseFirstLiteralPrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.finalTokenSlot_eq_fourthClauseStart_add_four", "cookLevinBuilderFourthClauseFirstLiteralPrefixSignTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralSignSlot_direct_eq_f", "cookLevinBuilderFourthClauseFirstLiteralPrefixUnaryUnitTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralUnaryUnitSlot_direct_eq_t", "cookLevinBuilderFourthClauseFirstLiteralPrefixTerminatorTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.firstLiteralTerminatorSlot_direct_eq_f", "cookLevinBuilderFourthClauseFirstLiteralPrefixNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.nextTokenSlot_direct_eq_f", "cookLevinBuilderFourthClauseFirstLiteralPrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rules_length", "cookLevinBuilderFourthClauseFirstLiteralPrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.rules_pairwise_query_distinct", "cookLevinBuilderFourthClauseFirstLiteralPrefixTrueTokenCursorRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length", "cookLevinBuilderFourthClauseFirstLiteralPrefixTrueFalseSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length", "cookLevinBuilderFourthClauseFirstLiteralPrefixSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length", "cookLevinBuilderFourthClauseFirstLiteralPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.run_compile_exact", "cookLevinBuilderFourthClauseFirstLiteralPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.run_compile_rawTimeBound", "cookLevinBuilderFourthClauseFirstLiteralPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.boundedDecide_compile_accept", "cookLevinBuilderFourthClauseFirstLiteralPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedSignAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedSignAppenderTally_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedSignAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedSignAppenderOutput_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedUnaryAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedUnaryAppenderTally_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedUnaryAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedUnaryAppenderOutput_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedTerminatorAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedTerminatorAppenderTally_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedTerminatorAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedTerminatorAppenderOutput_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedSignCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedSignCursorScratch_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedUnaryCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedUnaryCursorScratch_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixMalformedTerminatorCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.malformedTerminatorCursorScratch_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseFirstLiteralPrefix.work_one_step_short_timeout", "cookLevinBuilderFourthClauseFirstLiteralPrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderFourthClauseFirstLiteralPrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderFourthClauseFirstLiteralPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFourthClauseFirstLiteralPrefixProjectAxiomClosure": [], "cookLevinBuilderFourthClauseFirstLiteralPrefixFormalized": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixAxiomAuditPassed": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixAuditedDeclarationCount": 115, "cookLevinBuilderFourthClauseFirstLiteralPrefixCompiledRawMachineFormalized": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixExactFormulaBitsFormalized": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixCompleteFirstNegativeLiteralFormalized": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixInputPrefixAppenderComposed": true, "cookLevinBuilderFourthClauseFirstLiteralPrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixAxiomAuditPassed": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixAuditedDeclarationCount": 147, "cookLevinBuilderFourthClauseSecondLiteralPrefixCompiledRawMachineFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixExactFormulaBitsFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixCompleteSecondNegativeLiteralFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixInputPrefixAppenderComposed": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFourthClauseSecondLiteralPrefixWorkTime": "BuilderFourthClauseFirstLiteralPrefix.workSteps(problem) + 1 + BuilderFourthClauseSecondLiteralPrefix.suffixWorkSteps(problem)", "cookLevinBuilderFourthClauseSecondLiteralPrefixRawTimePolynomial": "BuilderFourthClauseFirstLiteralPrefix.rawTimeBound + 2232 + 96 * inputLength + 48 * FormulaWidth + 48 * cursorWord.length", "cookLevinBuilderFourthClauseSecondLiteralPrefixRuleCount": "4154 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier)", "cookLevinBuilderFourthClauseSecondLiteralPrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": 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"cookLevinBuilderFourthClauseSecondLiteralPrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_secondLiteral_terminator_step", "cookLevinBuilderFourthClauseSecondLiteralPrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.specification_next_step", "cookLevinBuilderFourthClauseSecondLiteralPrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.fourthClauseSecondLiteralTokens_eq_canonical_formula_prefix", "cookLevinBuilderFourthClauseSecondLiteralPrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalTokenBits_eq_encodedFormula_fourthClauseSecondLiteral", "cookLevinBuilderFourthClauseSecondLiteralPrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.finalTokenSlot_eq_fourthClauseStart_add_eight", "cookLevinBuilderFourthClauseSecondLiteralPrefixSignTokenTheorem": 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"cookLevinBuilderFourthClauseSecondLiteralPrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.rules_pairwise_query_distinct", "cookLevinBuilderFourthClauseSecondLiteralPrefixTrueTokenCursorRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTokenCursor.rules_length", "cookLevinBuilderFourthClauseSecondLiteralPrefixTrueFalseSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueFalseSuffix.rules_length", "cookLevinBuilderFourthClauseSecondLiteralPrefixTrueTrueFalseSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.TrueTrueFalseSuffix.rules_length", "cookLevinBuilderFourthClauseSecondLiteralPrefixSuffixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderThirdClauseSecondLiteralPrefix.SecondLiteralSuffix.rules_length", "cookLevinBuilderFourthClauseSecondLiteralPrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.run_compile_exact", "cookLevinBuilderFourthClauseSecondLiteralPrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.run_compile_rawTimeBound", "cookLevinBuilderFourthClauseSecondLiteralPrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.boundedDecide_compile_accept", "cookLevinBuilderFourthClauseSecondLiteralPrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedSignAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSignAppenderTally_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedSignAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSignAppenderOutput_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedFirstUnaryAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedFirstUnaryAppenderTally_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedFirstUnaryAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedFirstUnaryAppenderOutput_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedSecondUnaryAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSecondUnaryAppenderTally_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedSecondUnaryAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSecondUnaryAppenderOutput_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedTerminatorAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedTerminatorAppenderTally_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedTerminatorAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedTerminatorAppenderOutput_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedSignCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSignCursorScratch_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedFirstUnaryCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedFirstUnaryCursorScratch_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedSecondUnaryCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedSecondUnaryCursorScratch_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixMalformedTerminatorCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.malformedTerminatorCursorScratch_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFourthClauseSecondLiteralPrefix.work_one_step_short_timeout", "cookLevinBuilderFourthClauseSecondLiteralPrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderFourthClauseSecondLiteralPrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderFourthClauseSecondLiteralPrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFourthClauseSecondLiteralPrefixProjectAxiomClosure": [], "cookLevinBuilderFourthClausePrefixFormalized": true, "cookLevinBuilderFourthClausePrefixAxiomAuditPassed": true, "cookLevinBuilderFourthClausePrefixAuditedDeclarationCount": 57, "cookLevinBuilderFourthClausePrefixCompiledRawMachineFormalized": true, "cookLevinBuilderFourthClausePrefixExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFourthClausePrefixExactFormulaBitsFormalized": true, "cookLevinBuilderFourthClausePrefixCompleteFourthClauseFormalized": true, "cookLevinBuilderFourthClausePrefixRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFourthClausePrefixInputPrefixAppenderComposed": true, "cookLevinBuilderFourthClausePrefixFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFourthClausePrefixWorkTime": "BuilderFourthClauseSecondLiteralPrefix.workSteps(problem) + 1 + BuilderFourthClausePrefix.suffixWorkSteps(problem)", "cookLevinBuilderFourthClausePrefixRawTimePolynomial": "BuilderFourthClauseSecondLiteralPrefix.rawTimeBound + 618 + 24 * inputLength + 12 * FormulaWidth + 12 * BuilderFourthClauseSeparatorStep.cursorWord.length", "cookLevinBuilderFourthClausePrefixRuleCount": "4276 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier)", "cookLevinBuilderFourthClausePrefixTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.machine_acceptState_ne_rejectState": "d1b4614551fca900c3a41a77cb586bc1156b49be570406646abfeca3ec746727", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rule_source_ne_acceptState": "099a4f315f2931616552f289617686a314867d012e4a6478055b82929c992066", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rules_length": "29de843b9f577f39e8c08bae3255e607304104037558a03b60bb30e086b3ce31", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rules_pairwise_query_distinct": "572715d1f7fe044eaca73872f3744cf1f802487cb6bafcc5320014ebb7bd37c1", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.appenderEndpoint_before_cursor_launch_timeout": "878b0bd1539df3f33c733cfc2a3d4eecc3aa713a35c3983e81a86a0e6940c3ac", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.appender_workRunExact": "57410537009f4a5560ce65e76aa790224dade6d960d4f0dba1e19fb80a6f3396", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.boundedDecide_compile_accept": "0e052362dd73fc59afee9e8613eb1d62a70c1e2fd66c935a9f491c8c7af14979", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.boundedDecide_compile_ne_timeout": "ff61311a7fbc601cd154d8e997adf0abfaa5e0a576728a859cf177791f7608bc", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.clauseTerminatorSlot_direct_eq_finish": "ccc4bcfa9a81572d3742c0ad56ce8eabacfb455b62b48225e336693beb722150", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.cursor_workRunExact": "5f479e9912ed28ed8a540681ca2c76d0caad8ccd669aab4986269dbd601a7169", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalConfiguration_state": "d47a5624bcfc6e2fb7460d1a739659ae18c361673e4e905144e437c63558db38", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalOutside_contains_finalTokenSlot": "e5bde3bbef097ce45663b1f17dbd56d5c223cb7ea8d3e766f30cbe328e4add75", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTape_represents": "376a03008e8179b7c3b484747c476013d4e8bae1617954f71aa2ac1cd8744aa6", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTokenBits_eq_encodedFormula_fourthClause": "52de8c80e35a85307cd97bbede5d00e8ac58ad1e3059098ae539d2a1bcd28d63", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTokenSlot_eq_fourthClauseStart_add_nine": "6b663999511ae2abe7b41b4a759b5aa91b87ca19103051b3482bc9e490a28489", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finishTokenCursor_launch_workStep": "4e32ce0265f0d7700b11c2b61288c1194b0588d29717bbfe9692a712940a5565", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.fourthClauseTokens_eq_canonical_formula_prefix": "f5af9c2feeef4c262bc22329d3d990150b11a0c48e0012bd3a618aa32642c368", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.machine_acceptState_ne_rejectState": "50c018d3f15c2a164829b16b0fe2ca32e64c805692c8f13fcf596e90ceebcce9", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedAppenderOutput_timeout": "9e5f625915248b16b8dd0f1cf7d49dc2b677042e124cdf516d93760627a756a3", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedAppenderTally_timeout": "2e175fcc8fdb75ae3d4205ce7755b99135d507b7cc88c4cfbfc9f1414986be6e", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedCursorScratch_timeout": "72d38f305b2f9b9bf1c27c04f8347c29d04c1f13242d31ef04402f9495e4e9fd", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.nextTokenSlot_direct_eq_padding": "54b9312ad8a9b18c67cac645d001998a643421b34d0fb2b58d6d61ede5314a8e", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefixEndpoint_before_launch_timeout": "ef2ff5e0ee17fb34efdf831948eb0fbebf896133be96eef41e7db93ed7d67396", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefixFinish_launch_workStep": "9989fbd32dbd87acdfbfa3ed268b161ed72551c4dd4834b068e92ecaff977d29", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefix_workRunExact": "3738025f114ce30215b351257c711f28a49792cfc515824de43838177446afff", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rawTimeBound_eval": "6f1e9b871dddc4d8c6c3186d01a3973a181a2470e0c465d5bb2f43dfdbb1847c", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rawTimeBound_le": "377993cf0fb47ad28cca0773dcf44e6350af5f592cac3a157905a5d06b22f4e9", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rule_source_ne_acceptState": "2a8881dcb8a68b1f67019b2ee4290da37c40a30fb33525c3ff914eab076d88fa", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rules_length": "9f6e18040cf51d9a1a8611c0793901dd40fee32c85c87be0b070199922efbbd0", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rules_pairwise_query_distinct": "d803f70ac45ab90010de99fc0be91e1f2c11a78b49573d7da71b5cb8053c127c", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_exact": "f284e7b47d28b13c0ea8beec07a334d690392c2107aa65c6c75b7f842110d6e5", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_rawTimeBound": "81cba5ccbd644d54378976069fa5ddfe229733142f1709d01449d4e08b720c27", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_rawTimeBound_blankEquivalent": "7c60d776e0e68ec7c83dc4fe0057b541260fd663b2334bc27aab049ab1869008", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.specification_next_step": "70ea9284c37f6089f5fb7a8b4552a4c7d5d580f528b2dc6970c2dde5bc611cf6", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.specification_terminator_step": "402361d5149d7098ed666f369ec34c454f4d8a4f3c4225916cd606defa3952c0", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.suffix_workRunExact": "8e5f0929129901d10c47ac9124056295fb85d5e7c5e936cc9e1b3377dc784843", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.workBoundedDecide_accept": "1d0e1d25d634b9f6b70cfba55e959bed21497bb688634c3135a7d631097b3ebf", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.workRunExact": "91a6316e03b7ba0e5ee147efe438769e57e3abcda8f7f0c8f01c61ad763ac392", "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.work_one_step_short_timeout": "ad9a7c851ddec845e6556e79cc7c6b8b0d80a63a853585e9d47c8f3299f61118" }, "cookLevinBuilderFourthClausePrefixExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.workRunExact", "cookLevinBuilderFourthClausePrefixTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.specification_terminator_step", "cookLevinBuilderFourthClausePrefixNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.specification_next_step", "cookLevinBuilderFourthClausePrefixCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.fourthClauseTokens_eq_canonical_formula_prefix", "cookLevinBuilderFourthClausePrefixFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTokenBits_eq_encodedFormula_fourthClause", "cookLevinBuilderFourthClausePrefixAdvancedCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.finalTokenSlot_eq_fourthClauseStart_add_nine", "cookLevinBuilderFourthClausePrefixClauseTerminatorTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.clauseTerminatorSlot_direct_eq_finish", "cookLevinBuilderFourthClausePrefixNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.nextTokenSlot_direct_eq_padding", "cookLevinBuilderFourthClausePrefixRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rules_length", "cookLevinBuilderFourthClausePrefixRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.rules_pairwise_query_distinct", "cookLevinBuilderFourthClausePrefixFinishTokenCursorRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.FinishTokenCursor.rules_length", "cookLevinBuilderFourthClausePrefixCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_exact", "cookLevinBuilderFourthClausePrefixCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.run_compile_rawTimeBound", "cookLevinBuilderFourthClausePrefixAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.boundedDecide_compile_accept", "cookLevinBuilderFourthClausePrefixNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.boundedDecide_compile_ne_timeout", "cookLevinBuilderFourthClausePrefixPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.prefixEndpoint_before_launch_timeout", "cookLevinBuilderFourthClausePrefixAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderFourthClausePrefixMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedAppenderTally_timeout", "cookLevinBuilderFourthClausePrefixMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedAppenderOutput_timeout", "cookLevinBuilderFourthClausePrefixMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.malformedCursorScratch_timeout", "cookLevinBuilderFourthClausePrefixOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePrefix.work_one_step_short_timeout", "cookLevinBuilderFourthClausePrefixPredecessorDeadStepTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep", "cookLevinBuilderFourthClausePrefixPredecessorMalformedDispatchTheorem": "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead", "cookLevinBuilderFourthClausePrefixAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFourthClausePrefixProjectAxiomClosure": [], "cookLevinBuilderFourthClausePaddingRunFormalized": true, "cookLevinBuilderFourthClausePaddingRunAxiomAuditPassed": true, "cookLevinBuilderFourthClausePaddingRunAuditedDeclarationCount": 68, "cookLevinBuilderFourthClausePaddingRunCompiledRawMachineFormalized": true, "cookLevinBuilderFourthClausePaddingRunExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFourthClausePaddingRunExactFormulaBitsFormalized": true, "cookLevinBuilderFourthClausePaddingRunRemainingPaddingCountFormalized": true, "cookLevinBuilderFourthClausePaddingRunDirectPaddingBlockFormalized": true, "cookLevinBuilderFourthClausePaddingRunFifthClauseSlotStartFormalized": true, "cookLevinBuilderFourthClausePaddingRunRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFourthClausePaddingRunNoEmissionSpecificationFormalized": true, "cookLevinBuilderFourthClausePaddingRunInputPrefixAppenderComposed": true, "cookLevinBuilderFourthClausePaddingRunFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFourthClausePaddingRunWorkTime": "BuilderFourthClausePrefix.workSteps(problem) + 1 + BuilderUnaryPolynomial.workSteps(remainingPaddingPolynomial verifier, input) + 1 + PaddingCountdown.loopSteps(countControllerPrefixLength, remainingPaddingCount) + 1 + BuilderUnaryPolynomial.workSteps(fifthClauseSlotStartPolynomial verifier, input)", "cookLevinBuilderFourthClausePaddingRunRawTimePolynomial": "BuilderFourthClausePrefix.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps", "cookLevinBuilderFourthClausePaddingRunRuleCount": "4328 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier)", "cookLevinBuilderFourthClausePaddingRunTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le": "972da09f44b6d35d56ce775bd4a46687be45609dacd0670bc983d603715bf278", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact": "ff60669772a7f137755431c1300c4368e8004a05b1d36972a768b50d1846cf5a", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.boundedDecide_compile_accept": "9acee05fa4512869a18bae9a297d313d80d88528f621af9651f8e1dfc3172b5b", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.boundedDecide_compile_ne_timeout": "5520b9bc98fece7a257cd6f2ccd345bc15c722be0df4801f3b49815f63eafa10", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.countEvaluator_workRunExact": "b28730bda8a54aaee384efc5b2015235b28007931a5c54d0927f943d46cd036f", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.countdownBoundPolynomial_eval": "e1ede27183b7814ca216cf36cdbaee89deec439dc1dea6890ba559e431adfc9c", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.countdown_workRunExact": "1c93ba1a46248fc7e8199286eee95d1279ae632ce9d6c0f7d1ee0e45514b9038", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.fifthClauseSlotStart_direct_eq_padding": "fb8f5c3fbe2559381f2a28424083c52062217f134af5a1db352f33ab4b54c0af", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.fifthClauseSlotStart_eq": "fcc08bc84a107f2c54bb874c7261c06f03ecaf32b7e98870c29900990c0302f8", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalConfiguration_state": "982e9fbbdf71f09c3ce0e7ae2610943e3cf5e78ffec8f8914baca2ef550d85d8", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalOutside_contains_finalTokenSlot": "3c68cf911868f3f582169dd08d44d2afb04eed85770d442d9ad7511a8a216ba4", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTape_represents": "fa458f6cd22392e25aa831091c82a051dcc6980b6a0cbb5a1b1c605b2459d32b", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTokenBits_eq_encodedFormula_fourthClause": "14885a1b3a2cf43dc131d9bff4901137060f894263f6f51a53338cbdfc97a8e4", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTokenSlot_eq_fifthClauseSlotStart": "95595ed49e8a7fc08f4dc3c58b500d4e3b00aaedbde112c7e3937d5b27ac4983", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.launch_workStep": "e61f94120eb9e1759c67e9626470939a3ea20eff209a13ac68bf237f85491bb2", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.machine_acceptState_ne_rejectState": "fbc2ce90b22affcffa45e39f23a1c74ed4c928db57ea96bee0aabbdc1625376a", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.malformedCountdownRoot_timeout": "0271388ca1bf65acc9ff1391417abc6b5eb6ff9d189c5eb2f9658d7db75a5207", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.malformedCountdownScratch_timeout": "3c88f67d8aad5bbd508e5271bcffc84a05dc1c0e8f1ffcfb2b2884aa009f22ba", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.paddingSlot_direct_eq_padding": "0e208441e0c7d12a256dc8c7e89ac267ff776eb20d8aa2ccfa5e48b2c2927a71", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.predecessorSlot_add_remainingPaddingCount": "b018da2019da895cb3796c4c24fccb61d085ba830b75df16d9f1a6146f0946b5", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.prefixEndpoint_before_launch_timeout": "6f2dc10eb099ef9d51fda2c7b792a74f0d49e2deeb5a268b7098877cfa31f339", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.prefix_workRunExact": "e8f779b71c5012a9db625675e1fa129686a7893d044caedd6e60a83d8fd3d70c", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rawTimeBound_eval": "2c8d74b5ed3eb7b40831fe61bb4319c5c7d3bce51586171a38a7c9280859bc89", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rawTimeBound_le": "94c39cfae3d42fa0cc79afeab45dcfb307c9f2148c2cc57a11a3dc50edac49c2", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_eq": "5062223b78e762517bce485533b24a381dff7000b22fcd60b4c1d093bf72b4c9", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_nine": "01f10c080a3ed147b813835e76af337e41a2c42cf3c6cb697336e7a304f60363", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_positive": "fec5d1fc00efa399b168d3aae0db54a1f6c43405cb318fa086adc8707483acfe", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rule_source_ne_acceptState": "7341d7b321fb64c876dda543b67deeee3d9d2129e4bf2da1f57a8bb0777e07e4", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rules_length": "c5b954268d25cbeade7b274324386962570873682ee17a2475ab201de0cec9fd", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rules_pairwise_query_distinct": "11d1d5abbd72b763455f68f42c06e4327f70c416491c5195121189289245bd6e", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_exact": "fad4b552da1f6712455bde735026b4c42f601c9b0c80b3c0cc3c21a2297e6daa", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_rawTimeBound": "453a63125881996562ae744bb166f0d21c87128c9862a8f611a2ce72448b4e76", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_rawTimeBound_blankEquivalent": "a869d1d3e1104db35e1ec1f82a0e23c8abb5b3525ed3f5e7e9291795581cc6cb", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.specification_padding_run": "f57b82447f23a30652fe23e690f295bbe4fdbd55a1aed88cd90c53cabb71aede", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.specification_target_step": "5e99b1dbdd5b8130ab454ca4a8757eecab585145bf58e04e26594dbe42b8f969", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.targetEvaluator_workRunExact": "1d4621d21a41eed9361c0a83c5926975327e8b2e918b29f94745022a26aed419", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.workBoundedDecide_accept": "4118131aa2a4b9013e6cc2e6e3ab3bb656837cff5e351ffd2ea57539bbf95e03", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.workRunExact": "0f15cc26c89f1acb106b3c9cbef205bc3620d47ff5cf213baadf3576d0bce9d9", "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.work_one_step_short_timeout": "fcbadd548f98f16fc4c24fe7c7a11c7ddabfda7a8af048fc9916b2fc4ec14073" }, "cookLevinBuilderFourthClausePaddingRunExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.workRunExact", "cookLevinBuilderFourthClausePaddingRunPaddingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.specification_padding_run", "cookLevinBuilderFourthClausePaddingRunTargetSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.specification_target_step", "cookLevinBuilderFourthClausePaddingRunFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTokenBits_eq_encodedFormula_fourthClause", "cookLevinBuilderFourthClausePaddingRunRemainingCountTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.remainingPaddingCount_eq_formulaTokensPerClause_sub_nine", "cookLevinBuilderFourthClausePaddingRunFifthClauseCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.finalTokenSlot_eq_fifthClauseSlotStart", "cookLevinBuilderFourthClausePaddingRunDirectPaddingTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.paddingSlot_direct_eq_padding", "cookLevinBuilderFourthClausePaddingRunDirectFifthClausePaddingTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.fifthClauseSlotStart_direct_eq_padding", "cookLevinBuilderFourthClausePaddingRunRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rules_length", "cookLevinBuilderFourthClausePaddingRunRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.rules_pairwise_query_distinct", "cookLevinBuilderFourthClausePaddingRunCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_exact", "cookLevinBuilderFourthClausePaddingRunCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.run_compile_rawTimeBound", "cookLevinBuilderFourthClausePaddingRunAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.boundedDecide_compile_accept", "cookLevinBuilderFourthClausePaddingRunNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.boundedDecide_compile_ne_timeout", "cookLevinBuilderFourthClausePaddingRunMalformedRootTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.malformedCountdownRoot_timeout", "cookLevinBuilderFourthClausePaddingRunMalformedScratchTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.malformedCountdownScratch_timeout", "cookLevinBuilderFourthClausePaddingRunOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFourthClausePaddingRun.work_one_step_short_timeout", "cookLevinBuilderFourthClausePaddingRunAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFourthClausePaddingRunProjectAxiomClosure": [], "cookLevinBuilderFifthClausePaddingRunFormalized": true, "cookLevinBuilderFifthClausePaddingRunAxiomAuditPassed": true, "cookLevinBuilderFifthClausePaddingRunAuditedDeclarationCount": 68, "cookLevinBuilderFifthClausePaddingRunCompiledRawMachineFormalized": true, "cookLevinBuilderFifthClausePaddingRunExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFifthClausePaddingRunExactFormulaBitsFormalized": true, "cookLevinBuilderFifthClausePaddingRunPaddingCountFormalized": true, "cookLevinBuilderFifthClausePaddingRunDirectPaddingBlockFormalized": true, "cookLevinBuilderFifthClausePaddingRunSixthClauseSlotStartFormalized": true, "cookLevinBuilderFifthClausePaddingRunRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFifthClausePaddingRunNoEmissionSpecificationFormalized": true, "cookLevinBuilderFifthClausePaddingRunInputPrefixAppenderComposed": true, "cookLevinBuilderFifthClausePaddingRunFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFifthClausePaddingRunWorkTime": "BuilderFourthClausePaddingRun.workSteps(problem) + 1 + BuilderUnaryPolynomial.workSteps(paddingPolynomial verifier, input) + 1 + PaddingCountdown.loopSteps(countControllerPrefixLength, paddingCount) + 1 + BuilderUnaryPolynomial.workSteps(sixthClauseSlotStartPolynomial verifier, input)", "cookLevinBuilderFifthClausePaddingRunRawTimePolynomial": "BuilderFourthClausePaddingRun.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps", "cookLevinBuilderFifthClausePaddingRunRuleCount": "4380 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier)", "cookLevinBuilderFifthClausePaddingRunTheoremKernelTypeSha256": { 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"904e936b34ecfdc60f5fd33f7e63c4564d98224882c8db5ba2357c6142a33160", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.sixthClauseSlotStart_direct_eq_padding": "9a29793b21f2fe3186c5f09bb753fb55c9d839bdd2a9e2155edbfcb9d085b534", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.sixthClauseSlotStart_eq": "e21d4d531aa55cf88bcbded5c850f385fa4896a833f4b01d682364d2c57c7b38", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalConfiguration_state": "f3b35d12ccc6554be17db79e6bca93bdb32872289fc9a14ae547423fc1f05f4c", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalOutside_contains_finalTokenSlot": "3a6294636ac88405dc1752be425834bb78fd2494a9f795891d1503bd4c41b1e0", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTape_represents": "bc3ff104ab65256f2dd125d85428bccbb6c31dc9b309e31907b95915e00593b6", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTokenBits_eq_encodedFormula_fourthClause": "4784634e836036979fedf7fc4eee139412095862749635acbf9bb1db29b491a2", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTokenSlot_eq_sixthClauseSlotStart": "54267c1b3e5ab05679838db25f0297e8e7becdc32487806717471fcdfad02c8c", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.launch_workStep": "54b6aa4fec94c1f2a2927505b9f1c105ed00b58b4a41d4309b36160bc14231a4", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.machine_acceptState_ne_rejectState": "815a1fd2428c0133a66f49e0dd48da7cdb062babaf4ae9d3ad36d84cd92eb4b0", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.malformedCountdownRoot_timeout": "7448d3b305c16b2d861c08f7bfcd511edfc9876bf5001aeed3629b7bb80815d6", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.malformedCountdownScratch_timeout": "3339d5d7581d20e80a8b6c848ca3a8edb6b631dd17d37a2319fa6fcdcb76c0ae", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingSlot_direct_eq_padding": "72b67c01032ce5c773b4a4efddac7e1e13d06918a41ed46e0772bb53083800ff", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.predecessorSlot_add_paddingCount": "b7cc1e9f1554188b3f1c1a3f38e1ad0a7e94b176a03c96577a742a8a392102d5", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.prefixEndpoint_before_launch_timeout": "1b357b4a92c9dced281e1322c47d6abf2b9f8838fdd3bdac825325d7a7031aa7", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.prefix_workRunExact": "f389f5f08cddc0ebbd699c304837a5c5bc1da390885c04b617e5d7d8bc2a5f86", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rawTimeBound_eval": "bda404cb6532658eff69761a9c871f45522e4fc1368683997b766f6ddd8a9858", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rawTimeBound_le": "58743e4f6475545ba3d032850a62c38b3cd91b6b77649d025f9896903d1e8087", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_eq": "083f595938257e7336b6150604c7edc76c99e9006c166d843596042b920a41da", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_eq_formulaTokensPerClause": "807ba4584b561134dd773e3581d15671f0ad3d95cd727dfbbbdcf49a002c1b07", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_positive": "7755d65ee5ccbce18d9c6624b634b53ecff7f3f1d8cda10c523146d5bb0919a8", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rule_source_ne_acceptState": "74529525b90db36979f07534e39de4831d7c566caca3318c2639342029f62553", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rules_length": "09373a631451d72e19bf403e5cd2aef671bcf67ddd7a987b6854cc9ba03c0714", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rules_pairwise_query_distinct": "23c36363073ec68fab1e5190b427837a532d281620c701500f8cc520422b5f9f", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_exact": "0b4668aa455e593b187d7ccc88aa15e638fc3a6d9a5e83aa324ab8e8a72bed00", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_rawTimeBound": "bd564f5a85729d0e55dc2eff6c89bdb3cf7818b78c7a071f755affcb98e6b6e3", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_rawTimeBound_blankEquivalent": "073f969cc8a9e0d27162149df59343e269e3610711ec9e8f868e1fb04be6ca49", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.specification_padding_run": "6bd891f67e08c3d9180bbd70d0a17f55728a1e681eca1abe904414638d5d8b2f", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.specification_target_step": "1c04822e047dcb82a5c6d5eb25a5871b6ca1e895a2badaedec29964895bc4016", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.targetEvaluator_workRunExact": "02e2d1d498c4a1c24909fa54715762eeab4524846a797626096625d2a8bc29f1", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.workBoundedDecide_accept": "711bb71aaf3be7b7f26b4075ed0d2f36c36a54d4f1832fa1fcedbd6928db5de4", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.workRunExact": "7363ad1bf9d11b6a8967d58d5df02b3970ff2df0028d3c8e8562b35e9a6461ec", "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.work_one_step_short_timeout": "6526f3f4553449188d0c0086860c6c69b7ed66f258b0bcfc328759f1261237fe" }, "cookLevinBuilderFifthClausePaddingRunExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.workRunExact", "cookLevinBuilderFifthClausePaddingRunPaddingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.specification_padding_run", "cookLevinBuilderFifthClausePaddingRunTargetSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.specification_target_step", "cookLevinBuilderFifthClausePaddingRunFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTokenBits_eq_encodedFormula_fourthClause", "cookLevinBuilderFifthClausePaddingRunPaddingCountTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingCount_eq_formulaTokensPerClause", "cookLevinBuilderFifthClausePaddingRunSixthClauseCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.finalTokenSlot_eq_sixthClauseSlotStart", "cookLevinBuilderFifthClausePaddingRunDirectPaddingTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.paddingSlot_direct_eq_padding", "cookLevinBuilderFifthClausePaddingRunDirectSixthClausePaddingTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.sixthClauseSlotStart_direct_eq_padding", "cookLevinBuilderFifthClausePaddingRunRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rules_length", "cookLevinBuilderFifthClausePaddingRunRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.rules_pairwise_query_distinct", "cookLevinBuilderFifthClausePaddingRunCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_exact", "cookLevinBuilderFifthClausePaddingRunCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.run_compile_rawTimeBound", "cookLevinBuilderFifthClausePaddingRunAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.boundedDecide_compile_accept", "cookLevinBuilderFifthClausePaddingRunNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.boundedDecide_compile_ne_timeout", "cookLevinBuilderFifthClausePaddingRunMalformedRootTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.malformedCountdownRoot_timeout", "cookLevinBuilderFifthClausePaddingRunMalformedScratchTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.malformedCountdownScratch_timeout", "cookLevinBuilderFifthClausePaddingRunOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFifthClausePaddingRun.work_one_step_short_timeout", "cookLevinBuilderFifthClausePaddingRunAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFifthClausePaddingRunProjectAxiomClosure": [], "cookLevinBuilderFirstConstraintPaddingRunFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunAxiomAuditPassed": true, "cookLevinBuilderFirstConstraintPaddingRunAuditedDeclarationCount": 68, "cookLevinBuilderFirstConstraintPaddingRunCompiledRawMachineFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunExactFormulaBitsFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunPaddingCountFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunDirectPaddingBlockFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunSecondConstraintSeparatorFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunNoEmissionSpecificationFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunInputPrefixAppenderComposed": true, "cookLevinBuilderFirstConstraintPaddingRunFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFirstConstraintPaddingRunWorkTime": "BuilderFifthClausePaddingRun.workSteps(problem) + 1 + BuilderUnaryPolynomial.workSteps(paddingPolynomial verifier, input) + 1 + PaddingCountdown.loopSteps(countControllerPrefixLength, paddingCount) + 1 + BuilderUnaryPolynomial.workSteps(secondConstraintStartPolynomial verifier, input)", "cookLevinBuilderFirstConstraintPaddingRunRawTimePolynomial": "BuilderFifthClausePaddingRun.rawTimeBound + 18 + 6 * countEvaluator.workSteps + 6 * (D * (2 * countRootPrefixLength + 8) + D * D) + 6 * targetEvaluator.workSteps", "cookLevinBuilderFirstConstraintPaddingRunRuleCount": "4432 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", "cookLevinBuilderFirstConstraintPaddingRunTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loopSteps_le": "972da09f44b6d35d56ce775bd4a46687be45609dacd0670bc983d603715bf278", "PNP.Concrete.CookLevin.BuilderFirstClausePaddingRun.PaddingCountdown.loop_workRunExact": "ff60669772a7f137755431c1300c4368e8004a05b1d36972a768b50d1846cf5a", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.boundedDecide_compile_accept": "d063ed370c52932399e35def06cbc186de1756b587c5270dca02a0f2e11bf360", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.boundedDecide_compile_ne_timeout": "178fa91774e3fc39425cb93f7fb473b3301a97e993e0c603796dbfdd233d1bb4", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.countEvaluator_workRunExact": "0f297436297f2fd9a36ccf253d79642ee1031d251297a62976e5bdb3edbf23c1", 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"PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTape_represents": "a171dd033b905d08ddc08e75ffbb92180d4a8bb47b5528dd687cdcbb9831c412", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTokenBits_eq_encodedFormula_fourthClause": "7e6edbccbf9e8fe5e539428ae89ff334a3892de8f18b76d597932d5833910809", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTokenSlot_eq_secondConstraintStart": "8aa76319b194c84fb73af74a16274429586f2bba4a197783f53e39b80b01f146", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.launch_workStep": "2fb294a3699331c66d333449a4fef8af1ed89833cad800ca74dd30aad913ee55", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.machine_acceptState_ne_rejectState": "45b351017a6288ba05e7f9d121e34a3bad213093e6b1299ca4a6b1a3d713a6d3", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.malformedCountdownRoot_timeout": "410b9f0882c178812dc70ce76738f4ca7346c84734f54942c59d52a9e1d8f7e9", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.malformedCountdownScratch_timeout": "9c2f753cb7dfd97cbc67bb1986b32014baec978c118947dcd9120e4fd6591469", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingSlot_direct_eq_padding": "639e1b345151140fba344cdbcb572c245547bba74552f9622da731df2a317557", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.predecessorSlot_add_paddingCount": "e301a77095d89e8cc0f4a46db4f25731a30897cf64f0034ef3390cca5144fa85", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.prefixEndpoint_before_launch_timeout": "1def2c783b872b5052e9dbfda047cdf01f65d9e9afa19215b7551c81afad4f68", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.prefix_workRunExact": "c3985b4979d0a63981b75a62b4647326a5ce49c5ffce58c23affdde8773ebba8", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rawTimeBound_eval": "8580c21203e487bbc1d057e91891f5b190fc7a7326bf4fb80ca5accfdd7aa51f", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rawTimeBound_le": "0f144eea3e680c782b39a91429641d0ece71b58bd6ea6250f0d67c848fb76650", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_eq": "b772f9a8361196d8ffa8b1c6d26664a0f6a18dc1a4b1f9032ad110b060489298", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_eq_remaining_first_constraint": "990b2dcfbc447ca94d9830aafe34b5c5ac7f2fcda0954d0a66558589eb4a77d6", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_positive": "284bfabe0b56124a352725af2ebd29e4174c3bb11fd8678d8265c96af147ee45", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rule_source_ne_acceptState": "7b458aa116c23f5177bbc424b47fac306c8b5ef120217c4eac3ba416da13a50a", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rules_length": "a752d658b4c304c5f6f52db023cd9a797a79c82407c78e53e694b5d36b278db3", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rules_pairwise_query_distinct": "18ce17ad370172549bfa684d6b7a30175b0d60649b4ab1f30123516615de63bb", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_exact": "5d9a76acde81b9ca312c46b78d282dda4e6b5b4fb558733e903482853ee39400", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_rawTimeBound": "fadc94fc47c31ee2fe4d673ae603346898be223687e6c70c727f4041e1ee1839", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_rawTimeBound_blankEquivalent": "93f7aae93c34b7b13781504f1d25d609f3aef90ec5cd05acfff98c0d41c59f3c", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.specification_padding_run": "b7117f6639941d7ab1ae3240668e29ee167ed53445a10ac260e7914e56a86eef", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.specification_target_step": "d7ff00c63f3316dd7bbc5cd2bae74be76a5602bc69c3ed32f9d8dc003c9ba29a", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.targetEvaluator_workRunExact": "1bf4f7612bdc1de4c994bade577fe823d34c2c1da6fa81e566e4b902a86be7b7", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.workBoundedDecide_accept": "544186abf6db45bf1dadec3253fa9e214c80d88b4dcc016d7124acdec4a0e6f2", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.workRunExact": "9182f0d678ba27d6b7bdb64886b6ae78ae4f06bb71eaea327a95e71abb76d17b", "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.work_one_step_short_timeout": "94a37c7fbbae6b29faea9739d6845249a43a32b2285459539a6d70e55794906e" }, "cookLevinBuilderFirstConstraintPaddingRunExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.workRunExact", "cookLevinBuilderFirstConstraintPaddingRunPaddingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.specification_padding_run", "cookLevinBuilderFirstConstraintPaddingRunTargetSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.specification_target_step", "cookLevinBuilderFirstConstraintPaddingRunFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTokenBits_eq_encodedFormula_fourthClause", "cookLevinBuilderFirstConstraintPaddingRunPaddingCountTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingCount_eq_remaining_first_constraint", "cookLevinBuilderFirstConstraintPaddingRunSecondConstraintCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.finalTokenSlot_eq_secondConstraintStart", "cookLevinBuilderFirstConstraintPaddingRunDirectPaddingTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.paddingSlot_direct_eq_padding", "cookLevinBuilderFirstConstraintPaddingRunDirectSecondConstraintSeparatorTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.secondConstraintStart_direct_eq_sep", "cookLevinBuilderFirstConstraintPaddingRunRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rules_length", "cookLevinBuilderFirstConstraintPaddingRunRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.rules_pairwise_query_distinct", "cookLevinBuilderFirstConstraintPaddingRunCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_exact", "cookLevinBuilderFirstConstraintPaddingRunCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.run_compile_rawTimeBound", "cookLevinBuilderFirstConstraintPaddingRunAcceptTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.boundedDecide_compile_accept", "cookLevinBuilderFirstConstraintPaddingRunNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.boundedDecide_compile_ne_timeout", "cookLevinBuilderFirstConstraintPaddingRunMalformedRootTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.malformedCountdownRoot_timeout", "cookLevinBuilderFirstConstraintPaddingRunMalformedScratchTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.malformedCountdownScratch_timeout", "cookLevinBuilderFirstConstraintPaddingRunOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderFirstConstraintPaddingRun.work_one_step_short_timeout", "cookLevinBuilderFirstConstraintPaddingRunAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFirstConstraintPaddingRunProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintSeparatorStepFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintSeparatorStepAuditedDeclarationCount": 56, "cookLevinBuilderSecondConstraintSeparatorStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepSecondConstraintSeparatorFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepInputPrefixAppenderComposed": true, "cookLevinBuilderSecondConstraintSeparatorStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintSeparatorStepWorkTime": "BuilderFirstConstraintPaddingRun.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, fourthClauseTokens) + 1 + CursorAdvance.advanceWorkSteps(cursorWord)", "cookLevinBuilderSecondConstraintSeparatorStepRawTimePolynomial": "BuilderFirstConstraintPaddingRun.rawTimeBound + 534 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderSecondConstraintSeparatorStepRuleCount": "4554 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", "cookLevinBuilderSecondConstraintSeparatorStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.machine_acceptState_ne_rejectState": "eee6920f72c0fa3566bb3cc5fec3951b18a9b2aa1b50b5cf34436d0183ab750b", "PNP.Concrete.CookLevin.BuilderSecondClauseSeparatorStep.SeparatorCursor.rule_source_ne_acceptState": 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"1b5bdfd0f093d0c78c95288af36231728482ad26d0f6db20d936619fc2b014af", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefixSeparator_launch_workStep": "c1f23a6262d2733031c887688442778c762db0a0c86e60d4dd766897071a0b75", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefix_workRunExact": "05ce5495de963ecd03c458aab04d41c32e9220a6d67443b4ac4e250e1b866517", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rawTimeBound_eval": "53f6d484c653a0d090e63ab549397c784e393f82b057178b3fd72d2758c6b6d6", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rawTimeBound_le": "d28fdf29615ee46887946545bba7ce4b93471d900560cc11678fc93208208620", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rule_source_ne_acceptState": "e3ea0599e5f6615ca654fb887723ee54de28fcf1df81045b661f671cbc283859", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rules_length": "75dea177eae80332ab0207f6cbe927c433429f57effde980ab01fad922b76952", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rules_pairwise_query_distinct": "bdb4622f308892c9da6cfd33546c5b05f14462f2aa47f38412f57effd452fdd8", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_exact": "0f9916e728eef9ffd6cb3eb45d89d607433a98766f2c2849ea337c57a5bc4298", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_rawTimeBound": "fb9e16b13cfb4cb7724a9c0c7880d12ede01d6df9c274dee61044ea4422d7215", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_rawTimeBound_blankEquivalent": "cb72725167fcb6dd2f23d56d177893e72bce964513c911d7289001e2d728fe01", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.secondConstraintStartTokens_eq_canonical_formula_prefix": "665280230db3da72c2b7e041a511bf86d070834c933a3d23de8fda4ade98b56e", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.separatorCursor_launch_workStep": "819ac4109b39752296f303fff7410b8b31306fa3f271e05c1013bf724ec3c7d4", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.specification_next_step": "3700f98a292c88a39a199d8304bc8882a4b6cf97dbb0415306fbc3c3aeacfffb", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.specification_separator_step": "a9d7ec294af9cfe8b84a4c8c8d987c1fc4a02514c682a6030518af82beef7ee7", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.suffix_workRunExact": "d87d0c0c1ff63cab97fee0167b026a41b1db66d01b4cc1f26c5835f8205049c1", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.workBoundedDecide_accept": "0d805271278807d6b15306e8545d9b3882cbecf2d6ae628630a544a482ff2197", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.workRunExact": "d3052938ed779208f1213415d0764d3e534089f0d5875524d1d624023b7d5355", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.work_one_step_short_timeout": "381732429388f6b4fbed79b0ea327645859d3fdcb84651ccfcbd30adf91b0a30" }, "cookLevinBuilderSecondConstraintSeparatorStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.workRunExact", "cookLevinBuilderSecondConstraintSeparatorStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintSeparatorStepAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.appender_workRunExact", "cookLevinBuilderSecondConstraintSeparatorStepCursorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.cursor_workRunExact", "cookLevinBuilderSecondConstraintSeparatorStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintSeparatorStepSeparatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.specification_separator_step", "cookLevinBuilderSecondConstraintSeparatorStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.specification_next_step", "cookLevinBuilderSecondConstraintSeparatorStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalTokenBits_eq_encodedFormula_secondConstraintStart", "cookLevinBuilderSecondConstraintSeparatorStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.secondConstraintStartTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintSeparatorStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.finalTokenSlot_eq_secondConstraintStart_add_one", "cookLevinBuilderSecondConstraintSeparatorStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.nextTokenSlot_direct_eq_t", "cookLevinBuilderSecondConstraintSeparatorStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rules_length", "cookLevinBuilderSecondConstraintSeparatorStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintSeparatorStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_exact", "cookLevinBuilderSecondConstraintSeparatorStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintSeparatorStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintSeparatorStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintSeparatorStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintSeparatorStepAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderSecondConstraintSeparatorStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.malformedAppenderOutput_timeout", "cookLevinBuilderSecondConstraintSeparatorStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.malformedAppenderTally_timeout", "cookLevinBuilderSecondConstraintSeparatorStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.malformedCursorScratch_timeout", "cookLevinBuilderSecondConstraintSeparatorStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeparatorStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintSeparatorStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintSeparatorStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFirstLiteralSignStepFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepAuditedDeclarationCount": 56, "cookLevinBuilderSecondConstraintFirstLiteralSignStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepSecondConstraintFirstLiteralSignFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepInputPrefixAppenderComposed": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSignStepWorkTime": "BuilderSecondConstraintSeparatorStep.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, secondConstraintStartTokens) + 1 + CursorAdvance.advanceWorkSteps(cursorWord)", "cookLevinBuilderSecondConstraintFirstLiteralSignStepRawTimePolynomial": "BuilderSecondConstraintSeparatorStep.rawTimeBound + 546 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderSecondConstraintFirstLiteralSignStepRuleCount": "4676 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", "cookLevinBuilderSecondConstraintFirstLiteralSignStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.machine_acceptState_ne_rejectState": "8751719f745f8345308450a6fa63c4555415c822188cbbcac76ae752890895e8", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rule_source_ne_acceptState": "11ea0df62f1691605a85227e5f0b315f3232a811aac074053c18d465743d560b", "PNP.Concrete.CookLevin.BuilderSecondClauseSecondLiteralPrefix.TrueTokenCursor.rules_length": 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"9e12ff647421e89b1342a93b37303f9447c1e941729e3e0f399709ab6b1ebcbe", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.machine_acceptState_ne_rejectState": "86ec64893892fd9f47df33ad37d14d2f95c1516222ad66efd42d9ba1e04e4d6e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedAppenderOutput_timeout": "b5ef06bc1a51bd99df58c87049798fdeba804a3515cafbbad92713f39048aba7", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedAppenderTally_timeout": "6d1e6258d424ef1dac8e4d0a174dd51b9af61ab63ba66c304ef6d029cb612f7a", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedCursorScratch_timeout": "119be3566e9bd0aca34b768bbc1c027366c435b391be5b5331e13814ad402331", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.nextTokenSlot_direct_eq_t": "69cacf7771ad233ddbb0efe53d58c5559b1f03458da0c3d322ce68d9df99cd0f", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefixEndpoint_before_launch_timeout": "2fc534c2299ec8125cf37a98999011f0c39fde6f030dadf6f80fd2d8c9fcad94", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefixSign_launch_workStep": "775c8e9d305c053a954a3daf12724d23bc3171b7783d9a031bdc6ddfc16a66ce", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefix_workRunExact": "a5fe74a6d0b9d32cf0b1e813dabdf82b9e5440139f126ce9e697957aad0e95f2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rawTimeBound_eval": "7a20de2dd6cb163a3bb71a0ed727a371d4332a96c0db15fa7a56cd2b8caff93e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rawTimeBound_le": "e08747bf26b7f9dd044766df4de78774caf278646b1afa216e6e28d0d61849f2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rule_source_ne_acceptState": "0db76d877297d4bf1e4d0babf385ead3d15d9e7d096ae26250b25f326d4fd32f", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rules_length": "907c682a758a4a6972cd13eafb74e8ce6cbcbe9b1d2c80b85cc738b46129049f", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rules_pairwise_query_distinct": "04180d0b62373446042a935b35b37beed0e7731fc5811c3e807a6a827bb23050", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_exact": "7a4614abe536a9dc7525904cf338dd6eb5cdbeff29cd564931aa29676aa7e3d4", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_rawTimeBound": "9556f35a72f5ea52c7817e6a746a937df52b61b2480385d3004dccd69c3dc989", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_rawTimeBound_blankEquivalent": "7d74301d25bde976647a6f96e2ec009d7ca7d38739f33077b13add9c5478cdf5", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.secondConstraintFirstLiteralSignTokens_eq_canonical_formula_prefix": "e2568ec28e32c518641b4bf6eb08662ee342c688d69b731645973504c4ee6a44", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.specification_next_step": "bd11d588a52d3c18ff3312f9f95644f2a36a0c5ed957380fdde72838037284b5", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.specification_sign_step": "b23e109d626394572ca8f7b4d53a5ce2a6b49c11dc96f9d4e5b14300f07b1da2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.suffix_workRunExact": "07beecf536541e8aa55075fff55c456c91108ec6d2b0d5d99c5710c33b8f7794", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.trueTokenCursor_launch_workStep": "884b421a4819a446a7ef374a0e3f2200c714feeacd2f8cafdb71a2b388ede903", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.workBoundedDecide_accept": "80fc7a505b6be74ad42102121d3b8e3783b60e9a4c33ef7de48b4a088e932752", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.workRunExact": "014629e4eda6ce0023acf35a14258b5b15d1b05060eb526f64acbbcd3a7c16e2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.work_one_step_short_timeout": "8ccc8f114cc27a53afc423f5cae8088a0c8283666e04bc21fa788613830da960" }, "cookLevinBuilderSecondConstraintFirstLiteralSignStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSignStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSignStepAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.appender_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSignStepCursorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.cursor_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSignStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSignStepSignSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.specification_sign_step", "cookLevinBuilderSecondConstraintFirstLiteralSignStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.specification_next_step", "cookLevinBuilderSecondConstraintFirstLiteralSignStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSign", "cookLevinBuilderSecondConstraintFirstLiteralSignStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.secondConstraintFirstLiteralSignTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFirstLiteralSignStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.finalTokenSlot_eq_secondConstraintStart_add_two", "cookLevinBuilderSecondConstraintFirstLiteralSignStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.nextTokenSlot_direct_eq_t", "cookLevinBuilderSecondConstraintFirstLiteralSignStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rules_length", "cookLevinBuilderSecondConstraintFirstLiteralSignStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFirstLiteralSignStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_exact", "cookLevinBuilderSecondConstraintFirstLiteralSignStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFirstLiteralSignStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFirstLiteralSignStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedAppenderOutput_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedAppenderTally_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.malformedCursorScratch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSignStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSignStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFirstLiteralSignStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAuditedDeclarationCount": 56, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepSecondConstraintFirstLiteralFirstUnaryUnitFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepInputPrefixAppenderComposed": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepWorkTime": "BuilderSecondConstraintFirstLiteralSignStep.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, secondConstraintFirstLiteralSignTokens) + 1 + CursorAdvance.advanceWorkSteps(cursorWord)", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepRawTimePolynomial": "BuilderSecondConstraintFirstLiteralSignStep.rawTimeBound + 558 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepRuleCount": "4798 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", 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"2680d200f12429c24181bbd3ceebffc458ce87bcf5576736cbbd14682148f650", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rules_length": "90c9ee2b4c8f6c59cd7a874247eb17cab7b13f027144d6ff2740b858f08df212", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rules_pairwise_query_distinct": "d0a539543395dd1c61d6d1e3e4237dca39a506b16cd5f0fad05046ed5adfbe18", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_exact": "7a20d408c5d1624c1fbbafefd13edb341cc12a7acd664b95d6f41ad3dd2b35b2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_rawTimeBound": "398617fbb0c7bc751ccc113c71eb75472be57529af22ba9bf28016b71b17cfac", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_rawTimeBound_blankEquivalent": "52a226cd176235f1ccca2d1dae1a6d63305c0733729a31589e1d66119aa2dbe4", 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"PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.workBoundedDecide_accept": "a6345a7531ffdd7faf4fdd9658c70c5d3811970a33649d1cd4d50603f725fd3e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.workRunExact": "7c5d577bd40c86ab833dd83f890f2abf9a831bd46a599cf2a40ebb3f6c8aa573", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.work_one_step_short_timeout": "31ead161b9a3da5ea25282d27e2469230e3a46d3321932df3ad1454e84451f28" }, "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.appender_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepCursorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.cursor_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFirstUnaryUnitSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.specification_firstUnaryUnit_step", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.specification_next_step", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralFirstUnary", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.secondConstraintFirstLiteralFirstUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.finalTokenSlot_eq_secondConstraintStart_add_three", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.nextTokenSlot_direct_eq_t", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rules_length", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_exact", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.malformedAppenderOutput_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.malformedAppenderTally_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.malformedCursorScratch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFirstLiteralFirstUnaryUnitStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepAuditedDeclarationCount": 56, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepSecondConstraintFirstLiteralSecondUnaryUnitFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepInputPrefixAppenderComposed": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepWorkTime": "BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, secondConstraintFirstLiteralFirstUnaryTokens) + 1 + CursorAdvance.advanceWorkSteps(cursorWord)", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepRawTimePolynomial": "BuilderSecondConstraintFirstLiteralFirstUnaryUnitStep.rawTimeBound + 570 + 24 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BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", 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"1e53c32294940518e2fd94d6e425875f14f217508cf99d6ff98d810ef14debae", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rules_pairwise_query_distinct": "9d48fa37e146750f01c0b3e44af25871c9a1c64d610bf19f195cdfa2a0c481fa", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_exact": "3e597828167ea8c553894ca1058b06b053050c8b7b8ed42e3f9bc0e5b0a161db", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_rawTimeBound": "5641619775501350b6dcf7a7f8eafbf55519983b57109c00e8ae6cd4465225e9", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_rawTimeBound_blankEquivalent": "bf53444d3af1dface5402e4e353fc66d6b1b1fb6d95bac97777e71125a1f9ef9", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.secondConstraintFirstLiteralSecondUnaryTokens_eq_canonical_formula_prefix": "532a808fb1343c01516b82ca4fe05e6f751279cefac1db4c5210b79a35846bfc", 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"cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepSecondUnaryUnitSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.specification_secondUnaryUnit_step", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.specification_next_step", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSecondUnary", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.secondConstraintFirstLiteralSecondUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.finalTokenSlot_eq_secondConstraintStart_add_four", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.nextTokenSlot_direct_eq_t", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rules_length", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_exact", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.malformedAppenderOutput_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.malformedAppenderTally_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.malformedCursorScratch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFirstLiteralSecondUnaryUnitStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAuditedDeclarationCount": 56, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepSecondConstraintFirstLiteralThirdUnaryUnitFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepInputPrefixAppenderComposed": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepWorkTime": "BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.workSteps(problem) + 1 + BuilderTokenAppender.workSteps(input, secondConstraintFirstLiteralSecondUnaryTokens) + 1 + CursorAdvance.advanceWorkSteps(cursorWord)", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepRawTimePolynomial": "BuilderSecondConstraintFirstLiteralSecondUnaryUnitStep.rawTimeBound + 582 + 24 * inputLength + 12 * FormulaWidth + 12 * cursorWord.length", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepRuleCount": "5042 + BuilderUnaryPolynomial.ruleCount(widthPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", 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"c54485a8c270d9595f072f51005387f8b7fb9167f57d1957aca6af78f256a10d" }, "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.appender_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepCursorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.cursor_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepThirdUnaryUnitSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.specification_thirdUnaryUnit_step", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.specification_next_step", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralThirdUnary", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.secondConstraintFirstLiteralThirdUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.finalTokenSlot_eq_secondConstraintStart_add_five", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.nextTokenSlot_direct_eq_f", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rules_length", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.run_compile_exact", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.malformedAppenderOutput_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.malformedAppenderTally_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.malformedCursorScratch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralThirdUnaryUnitStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFirstLiteralThirdUnaryUnitStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAuditedDeclarationCount": 56, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepSecondConstraintFirstLiteralTerminatorFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepInputPrefixAppenderComposed": true, 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BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier)", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.deadState_workStep": "681cac71bc2a0b9c3c42250a3b3e4ef28bb743f8b409b0b440a64230655eabaf", "PNP.Concrete.CookLevin.BuilderDynamicTokenCursorStep.CursorAdvance.malformedScratch_enters_dead": "bfde87bc9e3bc501eb3ca0f3edb197ab2b120fef845b632574bdf14209c72292", "PNP.Concrete.CookLevin.BuilderSecondClauseFirstLiteralPrefix.FalseTokenCursor.machine_acceptState_ne_rejectState": "100d797c35b0c6669b7073cdb854d4081c9d53d8688205e876159170ec7db7ec", 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"0eceb1b509a506de60c8cb593e8cf8af4675471dbf8a3c99e215735780a51519", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rawTimeBound_eval": "1bcb13beb72593384346105f0bd4d8f80388bf3e01d7835675b4da7bb476824c", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rawTimeBound_le": "dfd231c96c2f3b20e77e0d4c6df38c18db17fdb7e5064111f522f9eff00391fd", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rule_source_ne_acceptState": "ac0762731742e936ed8ad0e912df197919ce92c0f17096af939a3f99d8cbf1d1", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rules_length": "370897369780dd8063317ea14aee9f26de1b37393fc57ee009e13c04c09ba7ba", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rules_pairwise_query_distinct": "ea58bf0e9afa02ade1bb34891ee3e2e68c335edba9b34ba88b4202e8b13ba2db", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_exact": "806d20ffe678e704325b717000f04be866bd31459b6b96c9236026082462892b", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_rawTimeBound": "4ccef47a0ab7d30b1b5f92cf2bfe1ff113008a948f1170ff933a261cc76ff361", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_rawTimeBound_blankEquivalent": "57bc22257f9c3f2e6a411b3f9cc06568f16df1ef1db2eb12e9814634d6671b7a", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.secondConstraintFirstLiteralTerminatorTokens_eq_canonical_formula_prefix": "0fd2b27d7c81368f41785ec4371a181606360ee5ce9053cd0f2bfc679eb8a13b", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.specification_next_step": "a972180655ecc1bc4d98b7611048c69f9e16fc206ad9c9b4e7987b972fee14f2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.specification_terminator_step": "1cbe4b31a33414491557330eb9d0abb229e417df577516581008c0c9c0fe2359", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.suffix_workRunExact": "8fb3d03c91a0e5dc966a1a30426e5f98e1f5f846c8e07191ae503875696bffe5", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.workBoundedDecide_accept": "73dddea6607e880d28653459b713c0e755d68fdea468e2a20ece9a36ee0366e6", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.workRunExact": "89605b8520de400b16a22ea8a7cf32725300f838027701d81ed56b132aa8ba2f", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.work_one_step_short_timeout": "d3193050fdf656bc13c8644e227785ea195ab4c727b83f7a66e17e8cc84f603f" }, "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.appender_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepCursorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.cursor_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepTerminatorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.specification_terminator_step", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepNextSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.specification_next_step", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralTerminator", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.secondConstraintFirstLiteralTerminatorTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.finalTokenSlot_eq_secondConstraintStart_add_six", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepNextTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.nextTokenSlot_direct_eq_finish_or_t", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rules_length", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_exact", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAppenderEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.appenderEndpoint_before_cursor_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepMalformedAppenderOutputTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.malformedAppenderOutput_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepMalformedAppenderTallyTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.malformedAppenderTally_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepMalformedCursorScratchTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.malformedCursorScratch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFirstLiteralTerminatorStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepSecondConstraintFirstLiteralSuccessorTokenFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepInputPrefixAppenderComposed": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepWorkTime": "BuilderSecondConstraintFirstLiteralTerminatorStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepRawTimePolynomial": "BuilderSecondConstraintFirstLiteralTerminatorStep.rawTimeBound + 600 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepRuleCount": "5284 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(successorTokenSlotPolynomial verifier)", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.machine_acceptState_ne_rejectState": "26f035f528660d27a4ab29f6fa83ff0be3bf211d51b877c5d8f55a6bca4bf0bd", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.rule_source_ne_acceptState": "73519e5b76b191f565920df973d2d15e71fed0196fbcb0d24e6a9c35d88d8619", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.rules_length": "9f2da68043f6366c6dc3232fe40291881ce18415221f2cd836bd0c44a4fcc79f", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.rules_pairwise_query_distinct": "abb4eaea26d7ef9e3d86e895302515bb6126a413934fb530e091ac629112fbae", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.WidthBranchAppender.workRunExact": "d9966e99eeb445d386480c291e24cdfc83b44822171ff235ab807916ff9300ae", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.boundedDecide_compile_accept": "2974881bf936a601402f136504c634064de6eee6b74db2e14f3b6bf30785bded", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.boundedDecide_compile_ne_timeout": "7950b2c6aa50794f82a8a93b31299a253258e13a71dc81558f8be99dbbb35831", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.branchAppender_workRunExact": "656fa450d88c3ac059883996f42e1f72825dd27f43d684683933bb6ac102ace3", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalConfiguration_state": "ba5d159555c56a0e35d3563237cb5be8aae3485a85c5cadcb3379a1f3ba4ab77", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalOutside_contains_finalTokenSlot": "b35506c903ed7d464411f4a767363ac4ac4ac7671cb6511f717879f0329886a6", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTape_represents": "0b42408e8c8e7146209703ac220390ed26b598145a35a162590d50f1f1fe84a9", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSuccessor": "8b93c44b2207985d9c12028af92bf9b3c3bb0e0b9842a0fa4eda03299da78537", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTokenSlot_eq_secondConstraintStart_add_seven": "5294a729ef9400eaad75dc3dda2c15f5e488e1f2ed715ab987d7011bb1edd664", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.followingTokenSlot_direct_eq_padding_or_t": "0ea8ed7ccc01327214a58db8a5b970061116746222776ee67419c2fb8dafa178", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.machine_acceptState_ne_rejectState": "f07594967b19ac7cc87f9fbadb1084974da855b08a2a551f2c9bdd5497590fd4", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefixEndpoint_before_launch_timeout": "ceabb85637bcf7de23e27f893cb40352588d37f527cf98daf19b6573a4b73d05", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefixSuffix_launch_workStep": "db2aed768f194c38b036d8a28446e1c580d4590156280f224c89a13d1d5d1247", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefix_workRunExact": "651e9288a2fcafb42e7ab115eeb26604873c60f9341e46227a3eb5253a2ce50d", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rawTimeBound_eval": "b67e4865ef8177ca7e9cbde86adca94501f4da0406c2bef7b050c98757d261f5", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rawTimeBound_le": "46dd4fca4157ebfa876da2d8a63dd409f738e0f22fda34d1a4cc8200179f2a02", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rule_source_ne_acceptState": "5e32a44cb162c8564264c6faf299d4a8f53caf67c645a4815c88dbede77e2af4", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rules_length": "e7687df58435c4b9c0e18364af16624c1625a2e8ea5fbf2e904ddfae6e78e3ae", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rules_pairwise_query_distinct": "ae1a1df4b8bfa7fb4766663d5066889191276a340092ea44282d8e2b7e278347", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_exact": "d857094fdef46584af5ca826ce4f57c9685ec217ad4c2c3b85842c258101ce00", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_rawTimeBound": "bf447a94be3c95c7caea9b5bb4b986d3cc31b2375ac0261b4832851043116838", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_rawTimeBound_blankEquivalent": "1f1f7b5518ff8f9d2cb611321b1b6b16affd9fdf532f4f704eb42ad40a57a655", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.secondConstraintFirstLiteralSuccessorTokens_eq_canonical_formula_prefix": "59ed9184c4374498a2cab6a218d612c0baca45e4d7d197e87dbb450658866302", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.specification_following_step": "30d3e7f5a9b63989ec3b2ec75e0b9527dc0deb36758cb2d0d27e3a323b36a63d", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.specification_successor_step": "584f684a75aaa1fd01ee7e0ef48b309c3b7df8aac4d4e423c190e9c14b873d8e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlot_eq_secondConstraintStart_add_seven": "7ab8fc10b44cd42c91102163ee9da7a8f8366226baeb9785f2247ceebd7cdd20", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.suffix_workRunExact": "55bb37e533b70c61671fd56218f23511ebef5f49268ae2dc9fba5e8911ede68b", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.targetEvaluator_workRunExact": "9787f58bb283b63678991cbb88c781bf82f0478e81f9f2232e38f0d2c8e2b34c", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthEvaluator_workRunExact": "22adad662ac7e27a7af87604fc469b9f53307e3a49898e1467a7417e7511cd41", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.width_eq_tapeWidth": "985b0ff6bb5300a1f11d312f9a6414fa48a574d5439d3ff54f465396f07fcff7", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.width_positive": "a4aaf365dc5b74581cdf70d2e2984942c945de26c61868716e4e5f6b59d40001", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.workBoundedDecide_accept": "50a8dc2e2912b9e2478cc239af5c2087b44bd340c024d6ff58e2deb70b83b760", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.workRunExact": "0a9fd2bbd873c4e3a221e5fbb1b474d3b9669dfa881a0f2c5938b2e28d6ba044", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.work_one_step_short_timeout": "ace2256a9c787009b4a4f28b5fb8b81c74039054d4150997c0bc0ed6a7e161f5", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor": "f8c64b3fc103e6fbff2cba888ecb8cebf0fd99eb0e23cada70cbabd9da8b26de", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.followingTokenSlot_direct_eq_padding_or_t": "71d49f89174b2c0264812e788a2b5c72ec3f3107244c6e653aa017515046ed34" }, "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepWidthEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthEvaluator_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepBranchAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.branchAppender_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepSuccessorSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.specification_successor_step", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.specification_following_step", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTokenBits_eq_encodedFormula_secondConstraintFirstLiteralSuccessor", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.secondConstraintFirstLiteralSuccessorTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.finalTokenSlot_eq_secondConstraintStart_add_seven", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rules_length", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_exact", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralSuccessorTokenStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFirstLiteralSuccessorTokenStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepPaddingOrUnaryOpportunityFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepWorkTime": "BuilderSecondConstraintFirstLiteralSuccessorTokenStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepRawTimePolynomial": "BuilderSecondConstraintFirstLiteralSuccessorTokenStep.rawTimeBound + 612 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepRuleCount": "5404 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_optional_unary": "e2430440ee1e6c9a103e78f021f0c91e7b6903385ee8cc9ca053c3303a743b2e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.secondFollowingTokenSlot_direct_eq_padding_or_t": "d97c0e58efba2b1a8b8da8d85f6c1fec57624d4957588a9625dac1fc8d40b134", 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"PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepOpportunitySpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.specification_opportunity_step", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.specification_following_step", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintPaddingOrUnary", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.secondConstraintPaddingOrUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_eight", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintPaddingOrUnaryOpportunityStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepSecondPaddingOrUnaryOpportunityFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepWorkTime": "BuilderSecondConstraintPaddingOrUnaryOpportunityStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepRawTimePolynomial": "BuilderSecondConstraintPaddingOrUnaryOpportunityStep.rawTimeBound + 624 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepRuleCount": "5524 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_two_optional_unary": 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"c4f2ed8dd7a01b0052a2bb30ba3f5e9e32efd829ff14669002aae261e8d8cdf2", "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.suffix_workRunExact": "930694db17ec2841b3129bf5184be1f10057959a595961eb8eab86b1268aef8f", "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact": "33c98d8e4f3174ac3be6acf00e6dd4c75e12fc99e699e43a5fdcb8ccab13c05c", "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact": "cc014a6b37d87b836753d6cb8bd2f7d6a7ee17b22774ea2b1e7b1bf3e8dcffb5", "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.width_eq_tapeWidth": "0b7350be6f623b47381e0bc758061bca1543e0d68d9c7feb6524a74c112617bc", "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.width_positive": "aaadfe185e75dfd6fa9103bed1258a39b9755b4f3f38b302b0ee311ab99576e0", 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"cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepWidthEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepOptionalAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepOpportunitySpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.specification_opportunity_step", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.specification_following_step", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintSecondPaddingOrUnary", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.secondConstraintSecondPaddingOrUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_nine", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintSecondPaddingOrUnaryOpportunityStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepThirdPaddingOrUnaryOpportunityFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepWorkTime": "BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepRawTimePolynomial": "BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.rawTimeBound + 636 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepRuleCount": "5644 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_three_optional_unary": "92700cf1a70adfb254512d9ac5492a634ba0e083e939b218f99361e52762da75", 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"67e20eb90086c37044bc00bb444bee5a909ba457d1299282c4ca4dba1c63b259", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.suffix_workRunExact": "addf9cf399e43f0f50c1e529aa071babad135b659c35cc353e7bb137ff1efdb6", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact": "842671f5aeed70c06bfbf4d33aff81c8b82331c97eaf63b8894f660de942f174", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact": "e92e844f2cf758eb5b6d108b62e9b42e1714f9f8f9f811d389e0ab24cb34b86a", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.width_eq_tapeWidth": "52a2898f0b2217d3c4a8f22a9a752addcf190d578e57c03bf93d94b0be28644d", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.width_positive": "f52ea3dc2e2a29f29c9c9942622bfc6af86e200cc07ee1820363004ad4ae70cd", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.workBoundedDecide_accept": "3936815ec1a00008023b687778730cee36de996aeb618e770b10cd3f4acf23db", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.workRunExact": "2d7c5f90a792bc76c6ecf14490977c09787aacde1c5b29d4bb41496129a8516b", "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.work_one_step_short_timeout": "c1196241b0ad006950c8d41a0907ae14fee0d65054ea4ee546ed55eb2cc44b2e" }, "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.workRunExact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepWidthEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepOptionalAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepOpportunitySpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.specification_opportunity_step", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.specification_following_step", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintThirdPaddingOrUnary", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.secondConstraintThirdPaddingOrUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_ten", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintThirdPaddingOrUnaryOpportunityStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFourthPaddingOrUnaryOpportunityFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepWorkTime": "BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepRawTimePolynomial": "BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.rawTimeBound + 648 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepRuleCount": "5764 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary": "90d6dbf3d5226e04b2e37831bcefa905586c90db15377024a3e218d7edb1de05", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.fifthFollowingTokenSlot_direct_eq_padding_or_f": "d5c4dea0c8f489deb0da66ca7e1d0d09f6f30ded7df49fc380a1be878e220b0a", "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState": "00646e05af7bfd520e71f745bb259cb69485558c6549bf815ef6fcd133d94a6d", "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rule_source_ne_acceptState": "8f8b05a91e211208c224875a9178377c3e52b724cca70c9a59ef9c65e610d6cb", "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.rules_length": "e4e38f2778e12014f5fccec5f35db63144b3892d78798da71c1bf240a6e30f06", 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"PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalOutside_contains_finalTokenSlot": "fddb36cde2010c476a4f66021510e205ee0333ad192e2dd1637fed4e56da0ac3", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTape_represents": "5c8ccf623a9b834bac3f8d013007014bbe091a48f0a38021d4fe92759ca2674a", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintFourthPaddingOrUnary": "43066344ed25a035a6a22f9e4d2ab36c28b656a4338c5f09d28486922764c213", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_eleven": "ad0db6e5dbd40c68b1f56afc4040fb88ede225060c5d8381662f4914d81a2ef7", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_f": "e2cd51f4208940aec96615c5e5f16b20f89fcb306fbd9b5422253598e8c5143a", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState": "15d5c31cab53e35f47ac062ee731930c03dad6c7e4768c0cea4b1e80f7a3539d", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_eleven": "dc117f1a2490c6182a67983add5f11ef0d4093a3019d2de9ad5846e3fed25c6b", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact": "4a363e3c66e5fe2475c9df01bb937e4a2a8b295413eaefa4ff25186832d69559", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout": "5fddca85a6402e015060f78577040e03c72751129bcd14942469ab45c5ea6b5b", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep": "e428412f739d1c095e8f4c7a93df53f05427c3a304ac6e82a1f884dcbe04e4dd", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefix_workRunExact": "3919d0564293ec6dcb3660b39ee2c5700f2273e74d8cba76d74d7bf4dc5ae178", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rawTimeBound_eval": "e3aa65b20799546d1e628733a6357064a5b5a60e90b23bd278e3d27e76f6de4c", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rawTimeBound_le": "7feadd89268d196a812213657d5a46086bb85098bf881cf8ff7843db55c6da66", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState": "bef60f4a2bdb466fa9dbc158fe8fffc260d79a929aa5a96c8ee4d1ce244b972e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rules_length": "ffccf1de760643adfd4e5a06679299a0ad65fb923517d9859f5be557d99351e2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct": "82bc4222f1864a7c0a611871a562f2f20b8be3a68e52e7991259dbb6714ffab9", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_exact": "b5e7aec473cd1c0eb82efb16daca3303add74c40aa3b3a410aab92653c86768a", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound": "effacd0544f83b90fb047c1c9a21d30235cf8b2cd9e5acc40953bf957324ac76", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent": "5ad826de8ca0a5008da760de91b29352f44221b4f0738c7b0f74f11730eaf470", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.secondConstraintFourthPaddingOrUnaryTokens_eq_canonical_formula_prefix": "1cb0ccbc9c579555533e243e2f41e14531ffbb49408794da6d21fbceb24d6dec", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.specification_following_step": "988dd77067aa184ce87a74508ae2f099402cc0f96db08288b8261e274a66069e", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.specification_opportunity_step": "95cd4875866fad291d36ed16ee94585334af76476303807b72434d2fdd457598", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.suffix_workRunExact": "bcd496884f3dc5cc5aa228c2b507e13ff0f5fd5ae4ca87321f6914e7db99bac0", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact": "6e436653aea35005ce464eb5bd50feee5b3611a9f6c34cb492cfca2818365dd9", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact": "d7cd7a597d9989ad7427814657b53811d5afc3a98cbd5b670c2fc18c5d67ca4d", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.width_eq_tapeWidth": "9e9e10d87ae65032af9a5e69a42597eb4d858c0c69a3ee6ab99ba2263b59141d", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.width_positive": "c35259f5638056d2ab1ecf37d6f6efdfa2a2427e2362114a18f1eb11eb6a429a", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.workBoundedDecide_accept": "72777d6206cf8690a21534891823738710a870334d25d2e1b10937fdec08de88", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.workRunExact": "1e62bbccbf1734f9bf53bbb1bf5c93d7dd92c8a8bd062531926b946a91d8ff42", "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.work_one_step_short_timeout": "64df07760fb22ef741d75374614390f08a65a7d213e34b6cb1a6b5064b91d4ef" }, "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.workRunExact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepWidthEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepOptionalAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepOpportunitySpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.specification_opportunity_step", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.specification_following_step", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintFourthPaddingOrUnary", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.secondConstraintFourthPaddingOrUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_eleven", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_f", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintFourthPaddingOrUnaryOpportunityStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFifthPaddingOrTerminatorOpportunityFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepInputPrefixOptionalTerminatorAppenderComposed": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepWorkTime": "BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepRawTimePolynomial": "BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.rawTimeBound + 660 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepRuleCount": "5884 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary_and_optional_terminator": "8f4243419d3a6b2b4811b8c456180b78c134b58f4c29cfb79c616d317ed7eeff", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.sixthFollowingTokenSlot_direct_eq_padding_or_t": "eba2c8e54be0a480a24bfea4e0f8864b39928a4ab986a5fd3b899111decf4af3", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.machine_acceptState_ne_rejectState": "f5139a98a479839d5ba2af0abb4d0c98bc994238640511badbfe3ab416e33dcb", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.rule_source_ne_acceptState": "b09ffd0fe566949217bccc9c1964fd4d681a8ed96ab882a63fe5210a9dac49c4", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.rules_length": "278b3d89df728d9474693f6dd417e73349b200985976368618e46c29191c23d5", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.rules_pairwise_query_distinct": "3893921014db022d3b2fad1bf7997193bf678fb4a6b74ffc9434379fb4e4b7da", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.WidthOptionalTerminatorAppender.workRunExact": 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"PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintFifthPaddingOrTerminator": "331f73e7ee6ef4448f1e3118e8f8fc93c8d3079c443cc669c834ba180263d161", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_twelve": "db43aa276d409fc40977ee79755a285a0d405e1d5bab489d0d141f1845e2e4fe", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.followingTokenSlot_direct_eq_padding_or_t": "a166bc07f39d568cf09b959cddaefe6b5396932e27083183a0db7ca37f98acf2", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.machine_acceptState_ne_rejectState": "aea0677d0b9ed2dc6d8353a56aea5c25732db249f9c5f52ff9fe38219a895694", "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_twelve": 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"PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.secondConstraintFifthPaddingOrTerminatorTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_twelve", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepSixthPaddingOrOpeningUnaryOpportunityFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepInputPrefixOptionalAppenderComposed": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepWorkTime": "BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepRawTimePolynomial": 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BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary_and_optional_terminator_and_optional_opening_unary": 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"Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.workRunExact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepWidthEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.widthEvaluator_workRunExact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepOptionalAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.optionalAppender_workRunExact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepOpportunitySpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.specification_opportunity_step", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.specification_following_step", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintSixthPaddingOrOpeningUnary", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.secondConstraintSixthPaddingOrOpeningUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_thirteen", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepCompiledBoundTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.run_compile_rawTimeBound", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepAcceptTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.boundedDecide_compile_accept", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepNoTimeoutTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.boundedDecide_compile_ne_timeout", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepPrefixEndpointTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.prefixEndpoint_before_launch_timeout", "cookLevinBuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStepOneStepShortTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.work_one_step_short_timeout", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepAxiomAuditPassed": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepAuditedDeclarationCount": 82, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepCompiledRawMachineFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepExternalInputSizePolynomialFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepExactFormulaBitsFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepSeventhPaddingOrUnaryOpportunityFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepRetainedAdvancedTokenCoordinateFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepInputPrefixOptionalAppenderComposed": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepWorkTime": "BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.workSteps(problem) + 1 + widthWorkSteps(problem) + 1 + branchWorkSteps(problem) + 1 + targetWorkSteps(problem)", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepRawTimePolynomial": "BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.rawTimeBound + 684 + 24 * inputLength + 12 * FormulaWidth + 12 * width + 12 * widthRootPrefixLength + 6 * widthWorkSteps + 6 * targetWorkSteps", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepRuleCount": "6124 + BuilderUnaryPolynomial.ruleCount(BuilderCompleteHeader.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderBodyStartPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstLiteralPrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePrefix.nextTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstClausePaddingRun.secondClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondClausePaddingRun.thirdClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderThirdClausePaddingRun.fourthClauseStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.remainingPaddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFourthClausePaddingRun.fifthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFifthClausePaddingRun.sixthClauseSlotStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.paddingPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderFirstConstraintPaddingRun.secondConstraintStartPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFirstLiteralSuccessorTokenStep.successorTokenSlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSecondPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintThirdPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFourthPaddingOrUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintFifthPaddingOrTerminatorOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(BuilderSecondConstraintSixthPaddingOrOpeningUnaryOpportunityStep.opportunitySlotPolynomial verifier) + BuilderUnaryPolynomial.ruleCount(widthPolynomial problem) + BuilderUnaryPolynomial.ruleCount(opportunitySlotPolynomial verifier)", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.encodeCNFTokens_eq_terminator_then_successor_and_four_optional_unary_and_optional_terminator_and_optional_opening_unary_and_optional_first_unary": "d84e664bc9f9a319f4be056013df50f32cae94aad1c237f79058397d97884cb8", "PNP.Concrete.CookLevin.BuilderSecondConstraintFirstLiteralTerminatorStep.eighthFollowingTokenSlot_direct_eq_padding_or_t": "ac60ed66d4c80a480d8ce3ed84681e09f702fdfc7382d3be78fc14725b3626a9", "PNP.Concrete.CookLevin.BuilderSecondConstraintPaddingOrUnaryOpportunityStep.WidthOptionalAppender.machine_acceptState_ne_rejectState": 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"a82ae82e73f007f07c804ea43b6ccb81a9fb98d637a56a8fced746eb904e3c7a", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_fourteen": "f8512ba52edb2ee69fb8f0862f6457db826ae96e8fd85f67b07bd6e5579b3450", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t": "42e26b7513ddffec40b8803395464fe904a0e8d40219b7d0fa24be4c5c722f79", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.machine_acceptState_ne_rejectState": "e40ad9fc4ec89fd72752a0a91b3203c37375927ed0f8aa76e17d16090c599fae", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.opportunitySlot_eq_secondConstraintStart_add_fourteen": "9389e98d5d4b372061529782f5b800501d0def9d7c1e12259a988830f20f08c6", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact": "3c73c594d0623b9fa7b11b98642a99e8901f94e30a40359d4b2f55c16268118f", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefixEndpoint_before_launch_timeout": "1e34cd891cbe8990725f3e857b113d7bcc0e320211fbf948b19563c4f6f45fbc", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefixSuffix_launch_workStep": "f2dc6ee983da03ef50e43c2f20d462e109c119008a6e69a467edbeb33d076fc7", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefix_workRunExact": "32449fb0e24e7f70080824617e02edd301b274791a8fe4bad2a1be58dc83efdc", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rawTimeBound_eval": "e738f2168c15bcd4f3f771f94d2b4e7aaba3c3003c4b8fde486fa692b78d38c9", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rawTimeBound_le": "9e572244b7cf88aa8242ccfdb2719982e03ab8f500d7c0ed264ab5c92590a3a5", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rule_source_ne_acceptState": "97c936f37b9ad1290a320108607ae83ec18495544b99031c976fea50e3000d8b", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rules_length": "8b722b00eb78f6e64119dd8bfe68a60c424056b2a39a0fe41093056b5d311fc7", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct": "ef58636c12e7f22e3a08388071a99e700712c684c9acd90239753583e52ebd38", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_exact": "5f4ee2dd911f8ae3631b224fafef465e28ebf1a3e054a673efc3227f154f5ce1", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound": "00c54f67988cc31726bb0fe9ed3e3507120f25510470215d218169d2e909fe43", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_rawTimeBound_blankEquivalent": "9b0bd28b74e4c481096d6a060b511f82ffd6e8ef788bc633e0b7144d63a39c2b", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.secondConstraintSeventhPaddingOrUnaryTokens_eq_canonical_formula_prefix": "af53d4cb36534cfcde9fe6e55fc7bd6f34b20b54bcdb7936ea988a8405144faf", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.specification_following_step": "d4ef2eb421f67daadd2c1c1b8e4a36944b4455ab18d0472e9b92c54c6364283a", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.specification_opportunity_step": "d7119a828edb5a63a6fa7463ad3868c9d342530c3e8fbe234c3a345dd186b00d", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.suffix_workRunExact": "900d05b8a05cab64fc16fa9a5e7318de256b77893f1e299f7ede3fc168c681a6", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact": "084e0fb64ea20a5048ff5da48b7c85599b00d0648faca7e3db0bebf5b37520ac", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact": "0abcc3e827852463bb66d90d13787b53a1f6cb59bee28f4d2e04979a5a89a856", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.width_eq_tapeWidth": "7d8d3b9c13fe607186569ff1e5d44f3a2a57520c1493c28a743fb2fd9c0e4771", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.width_positive": "34cea853d68409e80595403fd83292ed3c4f88c03a2d017b8c75b4a9eb1e5623", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.workBoundedDecide_accept": "db7ddb05770943d64831d27c4cbab212d8bcdddd1a8c820f63fa5975474d1617", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.workRunExact": "4792556f69ee248807ac629d5065faa36959c90b785ef10632c294c6b0ae18e9", "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.work_one_step_short_timeout": "5c19810a5913a26a89e4bb14592dced7de7b2834a8eef5d0e20597fd1f084c76" }, "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepProjectAxiomClosure": [], "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepExactWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.workRunExact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepPrefixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.prefix_workRunExact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepWidthEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.widthEvaluator_workRunExact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepOptionalAppenderWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.optionalAppender_workRunExact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepTargetEvaluatorWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.targetEvaluator_workRunExact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepSuffixWorkRunTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.suffix_workRunExact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepOpportunitySpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.specification_opportunity_step", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFollowingSpecificationTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.specification_following_step", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFormulaBitsTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalTokenBits_eq_encodedFormula_secondConstraintSeventhPaddingOrUnary", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepCanonicalPrefixTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.secondConstraintSeventhPaddingOrUnaryTokens_eq_canonical_formula_prefix", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFinalCoordinateTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.finalTokenSlot_eq_secondConstraintStart_add_fourteen", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepFollowingTokenTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.followingTokenSlot_direct_eq_padding_or_t", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepRulesLengthTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rules_length", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepRulesDistinctTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.rules_pairwise_query_distinct", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepCompiledExactTheorem": "PNP.Concrete.CookLevin.BuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStep.run_compile_exact", "cookLevinBuilderSecondConstraintSeventhPaddingOrUnaryOpportunityStepCompiledBoundTheorem": 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"PNP.DirectWire.terminalBN6_packet_selector_handles": "e8a07c5f17493ec6d905cf7dd28ad46f4a4e24ad24fc3ab75f918a7a279576c8" }, "residualTerminalPacketSelectorHandlesAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPacketSelectorHandlesProjectAxiomClosure": [], "residualTerminalPacketSelectorHandlesUniverseMembershipTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_mem_universe", "residualTerminalPacketSelectorHandlesInjectiveTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_injective", "residualTerminalPacketSelectorHandlesCarrierTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_sublist_carrier", "residualTerminalPacketSelectorHandlesSizeTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_large", "residualTerminalPacketSelectorHandlesPayloadTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_hasPayloadAt", "residualTerminalPacketSelectorHandlesSelectorTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorFootprint_hasPacketPayloadSelectorAt", "residualTerminalPacketSelectorHandlesExistenceTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.hasFinitePacketSelectorHandleAt_iff_payloadSelector", "residualTerminalPacketSelectorHandlesUniqueTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.existsUnique_packetSelectorHandle_iff_payloadSelector", "residualTerminalPacketSelectorHandlesPayloadConclusionTheorem": "PNP.DirectWire.TerminalPacketPayloadSelectorConclusion.selectorHandles", "residualTerminalPacketSelectorHandlesPacketConclusionTheorem": "PNP.DirectWire.TerminalBN6PacketConclusion.selectorHandles", "residualTerminalPacketSelectorHandlesTheorem": "PNP.DirectWire.terminalBN6_packet_selector_handles", "residualTerminalPacketSelectorCodecFormalized": true, "residualTerminalPacketSelectorCodecAxiomAuditPassed": true, "residualTerminalPacketSelectorCodecAuditedDeclarationCount": 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"PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_length_le_universe": "7f5caf0819a8e1696463e99993399a78d3bc6a786a64b13604e69f08c7c40485", "PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_canonical": "0a85db798dea4e5fc887c33e7db492fa102a081123cf1adfccd4cf30561f6165", "PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_payloadEvidence": "df145b8b2bac1ea58116085bc04500a96c44248cd6aac404e0d9b769565d608b", "PNP.DirectWire.TerminalBN6GroupedFamily.hasEncodedPacketSelectorAt_iff_payloadSelector": "accf0d6418551d74babe5b1ce76b0f490d217b463e57b7b725b9c9b01b84dd1b", "PNP.DirectWire.TerminalBN6GroupedFamily.existsUnique_encodedPacketSelector_iff_payloadSelector": "f8f44b0800ee90410e97ae05705549c3bb5f11cd7c5e63a7d6161f605ed40108", "PNP.DirectWire.TerminalPacketPayloadSelectorConclusion.selectorCodes": "f518eec40806af1a781cddec358e0970e4bca8a5341865477865ad794d5c6ccc", "PNP.DirectWire.TerminalBN6PacketConclusion.selectorCodes": "a52bf419363cbe01c1101984c07ee9cf551796860db78d53faeeafa00ee1d2aa", "PNP.DirectWire.terminalBN6_packet_selector_codes": "031617e6b11b9c96848cfb9597d2afff584fc5e8dba4ad0d12b6a329a1b26ffe" }, "residualTerminalPacketSelectorCodecAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPacketSelectorCodecProjectAxiomClosure": [], "residualTerminalPacketSelectorCodecRoundTripTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_encode", "residualTerminalPacketSelectorCodecInjectiveTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_injective", "residualTerminalPacketSelectorCodecExactLengthTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_length", "residualTerminalPacketSelectorCodecUniverseBoundTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.encodePacketSelectorHandle_length_le_universe", "residualTerminalPacketSelectorCodecCanonicalTheorem": 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"residualTerminalPacketSelectorPayloadRealizationAxiomAuditPassed": true, "residualTerminalPacketSelectorPayloadRealizationAuditedDeclarationCount": 21, "residualTerminalPacketSelectorPayloadRealizationEmptyAxiomDeclarationCount": 0, "residualTerminalPacketSelectorPayloadRealizationPropextOnlyDeclarationCount": 12, "residualTerminalPacketSelectorPayloadRealizationPropextQuotSoundDeclarationCount": 9, "residualTerminalPacketSelectorPayloadRealizationScope": "all-finite-explicit-bn6-grouped-families-total-fail-closed-source-payload-realization-exact-original-cell-footprint-positive-atom-and-packet-branch-preservation", "residualTerminalPacketSelectorPayloadRealizationTheoremKernelTypeSha256": { "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorCell_footprint": "585917f43db54d9d5be3852605dcfcc01256d09d34bde1ed3e7ff0b0e2500e0f", "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadAtom_mem": "bc42f6f75392b9ce43345b06aba862a758d32d9a8670945f111f33960abdbe3d", "PNP.DirectWire.TerminalBN6GroupedFamily.realizePacketSelectorPayload_eq_none_iff": "cbc666a2d051af090a607a177509340486e60215434e7ed7b15692e6ffe0557b", "PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_eq_some_of_realize": "d09a9d1b541eed299f676de5b47dfd84fe9b54228b6b2c2789db4a989c033e0e", "PNP.DirectWire.TerminalBN6GroupedFamily.exists_realizePacketSelectorPayload_encode": "5b52d770dcba2dac6f9314dbf3620d01445d2a71b1b47f0fd52d65719a5312bd", "PNP.DirectWire.TerminalBN6GroupedFamily.realizePacketSelectorPayload_sound": "5a40df6a1b6f66efa77c827ff11ce46698aa0960a4891cd70d6196d8bfc156cf", "PNP.DirectWire.TerminalBN6GroupedFamily.isRealizedPacketSelectorAt_iff_encoded": "2d0a3ccb47c7b326c8fb44ce651fe5da452d986adc8435c71385fef772bc8870", "PNP.DirectWire.TerminalBN6GroupedFamily.hasRealizedPacketSelectorAt_iff_payloadSelector": "65968a464059a6b3d4805f2e451306e0fd37d46bf5a7cb30b720b632d376a444", "PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.selectorPayloadRealizations": "d369c4f09b76a34298569a24eb7a7586e5e538fa03c5c80061ce057319e7d977", "PNP.DirectWire.TerminalBN6PacketConclusion.selectorPayloadRealizations": "c9ee54cb1fc4b623af2e96a88481a62ccf66e14f5aed608d8975ee4690c0b6c4", "PNP.DirectWire.terminalBN6_packet_selector_payload_realizations": "87e78d7623809a2026145930b4df7438605f484d17f11e99f700abf99cd5338d" }, "residualTerminalPacketSelectorPayloadRealizationAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPacketSelectorPayloadRealizationProjectAxiomClosure": [], "residualTerminalPacketSelectorPayloadRealizationCellFootprintTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorCell_footprint", "residualTerminalPacketSelectorPayloadRealizationAtomMemberTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorPayloadAtom_mem", "residualTerminalPacketSelectorPayloadRealizationFailClosedTheorem": 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"PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_eq_some_of_gainScan": "6eb7f2b430542b24beeb43e87a5f4f89fb924a60165e6d1a6962b7a252406d10", "PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorGains_sound": "aa97c40ce86ffa1fcde24c71191dd97ac4a4bd8bd842d05ff112ff65e02a9af2", "PNP.DirectWire.TerminalBN6GroupedFamily.exists_scanPacketSelectorGains_encode": "5a8e39e629c17ddff71b06f625a74ec1143ff3e59ed85f3ff0eaa297da66e46f", "PNP.DirectWire.TerminalBN6GroupedFamily.hasPacketSelectorGainScanAt_iff_encoded": "22461d4ebcecae3bad666da8313baaf99ee302d0ea0e6dea80643dc280e66bed", "PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.gainScans": "d281b4b953c16f80afa51d606669bbb64e41c12cb24decc77ba379b4b1299a58", "PNP.DirectWire.TerminalBN6PacketConclusion.gainScans": "c32f91d5404c84e2c5453226b2c4b5ee606c4d2cbc5fb2596f8818e8cefc6bdb", "PNP.DirectWire.terminalBN6_packet_selector_gain_scans": "54570f3b2c287367fd79ed45fe365049ee662b7c2af25faaa0a7f3fef02f4325" }, "residualTerminalPacketSelectorGainScanAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPacketSelectorGainScanProjectAxiomClosure": [], "residualTerminalPacketSelectorGainScanCandidateMembershipTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.mem_packetSelectorCandidateImplementations_iff", "residualTerminalPacketSelectorGainScanOutcomeSoundnessTheorem": "PNP.DirectWire.TerminalPacketCandidateGainOutcome.sound", "residualTerminalPacketSelectorGainScanResidualDescentTheorem": "PNP.DirectWire.TerminalPacketCandidateGainOutcome.gain_strictResidualDescent", "residualTerminalPacketSelectorGainScanFailClosedTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorGains_eq_none_iff", "residualTerminalPacketSelectorGainScanExistenceIffTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.exists_scanPacketSelectorGains_iff", "residualTerminalPacketSelectorGainScanDecodedHandleTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.decodePacketSelectorHandle_eq_some_of_gainScan", "residualTerminalPacketSelectorGainScanSoundnessTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorGains_sound", "residualTerminalPacketSelectorGainScanEncodedExistenceTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.exists_scanPacketSelectorGains_encode", "residualTerminalPacketSelectorGainScanEncodedIffTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.hasPacketSelectorGainScanAt_iff_encoded", "residualTerminalPacketSelectorGainScanEncodedConclusionTheorem": "PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.gainScans", "residualTerminalPacketSelectorGainScanPacketConclusionTheorem": "PNP.DirectWire.TerminalBN6PacketConclusion.gainScans", "residualTerminalPacketSelectorGainScanTheorem": "PNP.DirectWire.terminalBN6_packet_selector_gain_scans", "residualTerminalPacketSelectorUniverseGainScanFormalized": true, "residualTerminalPacketSelectorUniverseGainScanAxiomAuditPassed": true, "residualTerminalPacketSelectorUniverseGainScanAuditedDeclarationCount": 19, "residualTerminalPacketSelectorUniverseGainScanEmptyAxiomDeclarationCount": 0, "residualTerminalPacketSelectorUniverseGainScanPropextOnlyDeclarationCount": 9, "residualTerminalPacketSelectorUniverseGainScanPropextQuotSoundDeclarationCount": 10, "residualTerminalPacketSelectorUniverseGainScanScope": "all-finite-explicit-bn6-grouped-families-exhaustive-canonical-selector-scan-with-checked-strict-gain-or-family-local-no-gain-and-packet-branch-preservation", "residualTerminalPacketSelectorUniverseGainScanTheoremKernelTypeSha256": { "PNP.DirectWire.TerminalBN6GroupedFamily.mem_packetSelectorHandles": "22cb55480f5bbe81fb8540e5e44baae06fe2a37d1f569a315d1ea6e613d77a1d", "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorHandles_length": "3d685cc640a9b0eebec7e777ba4eb0ba97e849864b1a49f983701f713c0f72db", "PNP.DirectWire.TerminalPacketSelectorHandleListGainOutcome.sound": "ad8a3c4868e04bac82feacae9f4da4240351fbaea9de3366a0bab4243495af76", "PNP.DirectWire.TerminalPacketSelectorUniverseGainOutcome.sound": "6f1bab3555fe49689a663406f474357fa987a15a5978be77aa0c592d2942b624", "PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorUniverseGains_sound": "c52533b196e485c0bf91c0dff1f6ae39289c30946c7e8f792786953ca68c76a8", "PNP.DirectWire.TerminalPacketSelectorUniverseGainOutcome.gain_strictResidualDescent": "211b3c22fb1a6c4c6bf9803a38a7d04902d79dd054ebda9e3d3ea492e00a4549", "PNP.DirectWire.TerminalBN6GroupedFamily.universeGain_source_and_code": "908bfb961e16547356af3e1dacda10db97114f3f3658dcbc404fa57527ca38cc", "PNP.DirectWire.TerminalBN6GroupedFamily.universeNoGain_of_gainScan": "b31b67e308423d933c862df8872bd70b331ac6fd86be0e1c658849a569e1f133", "PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.universeGainScan_packet": "373902d79d328259df3d62d93d2ab45f63191d236f52a3cc03eb2e50aeb1c418", "PNP.DirectWire.terminalBN6_packet_selector_universe_gain_scan_sound": "a9a9e9ccf505501b0576f0462c43d3d9283177b2079cae2c2a8d432a43153b8f" }, "residualTerminalPacketSelectorUniverseGainScanAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPacketSelectorUniverseGainScanProjectAxiomClosure": [], "residualTerminalPacketSelectorUniverseGainScanHandleMembershipTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.mem_packetSelectorHandles", "residualTerminalPacketSelectorUniverseGainScanHandleCountTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.packetSelectorHandles_length", "residualTerminalPacketSelectorUniverseGainScanHandleListOutcomeSoundnessTheorem": "PNP.DirectWire.TerminalPacketSelectorHandleListGainOutcome.sound", "residualTerminalPacketSelectorUniverseGainScanOutcomeSoundnessTheorem": "PNP.DirectWire.TerminalPacketSelectorUniverseGainOutcome.sound", "residualTerminalPacketSelectorUniverseGainScanScanSoundnessTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.scanPacketSelectorUniverseGains_sound", "residualTerminalPacketSelectorUniverseGainScanResidualDescentTheorem": "PNP.DirectWire.TerminalPacketSelectorUniverseGainOutcome.gain_strictResidualDescent", "residualTerminalPacketSelectorUniverseGainScanSourceAndCodeTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.universeGain_source_and_code", "residualTerminalPacketSelectorUniverseGainScanNoGainCoverageTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.universeNoGain_of_gainScan", "residualTerminalPacketSelectorUniverseGainScanPacketConclusionTheorem": "PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.universeGainScan_packet", "residualTerminalPacketSelectorUniverseGainScanTheorem": "PNP.DirectWire.terminalBN6_packet_selector_universe_gain_scan_sound", "residualTerminalPacketSelectorGainCoverageFormalized": true, "residualTerminalPacketSelectorGainCoverageAxiomAuditPassed": true, "residualTerminalPacketSelectorGainCoverageAuditedDeclarationCount": 14, "residualTerminalPacketSelectorGainCoverageEmptyAxiomDeclarationCount": 0, "residualTerminalPacketSelectorGainCoveragePropextOnlyDeclarationCount": 7, "residualTerminalPacketSelectorGainCoveragePropextQuotSoundDeclarationCount": 7, "residualTerminalPacketSelectorGainCoverageScope": "all-finite-explicit-bn6-grouped-families-explicit-global-gain-coverage-certificate-conditional-source-gain-or-proof-bearing-zero-slack-with-packet-branch-preservation", "residualTerminalPacketSelectorGainCoverageTheoremKernelTypeSha256": { "PNP.DirectWire.TerminalPacketSelectorGainCoverage.noStrictEquivalentGain": "7b1ef90c27c9aceb97b855c14a94d198ef82637d27434fd2de966841a42dee32", "PNP.DirectWire.TerminalPacketSelectorGainCoverage.residualSlack_eq_zero_of_noGain": "543a2c30236108717a975f337b6fe9e6419d61bf39adb4c0f55735df8b8473c2", "PNP.DirectWire.TerminalPacketSelectorCoveredGainOutcome.sound": "def8db61dd5030d4c8c04c4dec62898c81955561bbdffcee39493ed2dc326380", "PNP.DirectWire.TerminalPacketSelectorCoveredGainOutcome.residualSlack_spec": "59e59cd46feb3e8d7ccd20649d876a17ee8e240acf01b01d7d151cf4017f547c", "PNP.DirectWire.TerminalBN6GroupedFamily.scanCoveredPacketSelectorGains_sound": "7474e55f1b655cfc544b8edd7dbcee3afc58e8f6542eae2c327782eafead28b2", "PNP.DirectWire.TerminalPacketEncodedSelectorConclusion.coveredGainScan_packet": "6e718e5038e7b09be9f0fba0772c7861094c45929f950fe9e859678ed2e1fffd", "PNP.DirectWire.terminalBN6_packet_selector_covered_gain_scan_sound": "bcc35fc1024c340c7eac8bb0d3359b66b3363df819002c8eea8bf4cd64272031" }, "residualTerminalPacketSelectorGainCoverageAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPacketSelectorGainCoverageProjectAxiomClosure": [], "residualTerminalPacketSelectorGainCoverageNoGainTheorem": "PNP.DirectWire.TerminalPacketSelectorGainCoverage.noStrictEquivalentGain", 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"residualTerminalPacketBudgetRouteReflectionRankDescentTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.rankDescent_of_packetSelectorPayloadFaithfulWithComputedBN5FrontierObligationActivationDirectionBudgetRoutes", "residualTerminalPacketBudgetRouteReflectionTablePreservationTheorem": "PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationDirectionBudgetFaithfulness_preserves", "residualTerminalPacketBudgetRouteReflectionTableFaithfulnessTheorem": "PNP.DirectWire.TerminalPacketTypedRealizerTable.withComputedPacketSelectorBN5FrontierObligationActivationDirectionBudgetFaithfulness_faithful", "residualTerminalPacketBudgetRouteReflectionSelectorSilenceFailureTheorem": "PNP.DirectWire.TerminalBN6PacketConclusion.existsBudgetReflectedFirstRouteFailure_of_selectorSilence", "residualTerminalPacketBudgetRouteReflectionHBFirstRouteFailureTheorem": "PNP.DirectWire.terminalBN6_packet_budget_reflected_hb_first_route_failure", 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"residualTerminalPacketSemanticHNActivityBindingEmptyAxiomDeclarationCount": 0, "residualTerminalPacketSemanticHNActivityBindingPropextOnlyDeclarationCount": 4, "residualTerminalPacketSemanticHNActivityBindingQuotSoundOnlyDeclarationCount": 0, "residualTerminalPacketSemanticHNActivityBindingPropextQuotSoundDeclarationCount": 5, "residualTerminalPacketSemanticHNActivityBindingScope": "all-arbitrary-finite-frontier-obligation-activation-direction-mismatch-to-HN-activity-checked-sole-descent-route-under-checked-semantic-HN-budget-HB-and-well-founded-HB-closure", "residualTerminalPacketSemanticHNActivityBindingCheckIffTheorem": "PNP.DirectWire.TerminalPacketTypedRealizerTable.checkPacketSemanticHNActivityBinding_eq_true_iff", "residualTerminalPacketSemanticHNActivityBindingSemanticFieldsAgreementTheorem": "PNP.DirectWire.TerminalPacketTypedRealizerTable.packetSemanticFieldsAgree_of_checkedHNActivityBinding", "residualTerminalPacketSemanticHNActivityBindingSemanticRoutesExcludedTheorem": 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"residualTerminalPacketDescentNoLowerBindingPropextQuotSoundDeclarationCount": 4, "residualTerminalPacketDescentNoLowerBindingScope": "all-arbitrary-finite-canonical-packet-handles-exhaustive-local-descent-no-lower-row-rejected-under-checked-positive-packet-semantic-HN-budget-HB-selector-silence-and-HB-closure", "residualTerminalPacketDescentNoLowerBindingCheckIffTheorem": "PNP.DirectWire.TerminalBN6GroupedFamily.checkPacketDescentNoLower_eq_true_iff", "residualTerminalPacketDescentNoLowerBindingRejectionTheorem": "PNP.DirectWire.TerminalBN6PacketConclusion.checkPacketDescentNoLower_eq_false_of_selectorSilence", "residualTerminalPacketDescentNoLowerBindingContradictionTheorem": "PNP.DirectWire.TerminalBN6PacketConclusion.false_of_checkedPacketDescentNoLower_and_selectorSilence", "residualTerminalPacketDescentNoLowerBindingNamedEndpointTheorem": "PNP.DirectWire.terminalBN6_packet_descent_no_lower_rejected", "residualTerminalPacketDescentNoLowerBindingTheoremKernelTypeSha256": { 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"residualTerminalHResolveCoverageLedgerAxiomAuditPassed": true, "residualTerminalHResolveCoverageLedgerAuditedDeclarationCount": 10, "residualTerminalHResolveCoverageLedgerEmptyAxiomDeclarationCount": 0, "residualTerminalHResolveCoverageLedgerPropextOnlyDeclarationCount": 4, "residualTerminalHResolveCoverageLedgerQuotSoundOnlyDeclarationCount": 0, "residualTerminalHResolveCoverageLedgerPropextQuotSoundDeclarationCount": 6, "residualTerminalHResolveCoverageLedgerScope": "all-arbitrary-finite-supplied-HResolve-candidates-unique-route-ledger-and-NoHereditary-sidecar-excludes-exact-and-gain-under-decidable-supplied-predicates", "residualTerminalHResolveCoverageLedgerExactIffTheorem": "PNP.DirectWire.terminalHResolveClassify_eq_exact_iff", "residualTerminalHResolveCoverageLedgerGainIffTheorem": "PNP.DirectWire.terminalHResolveClassify_eq_gain_iff", "residualTerminalHResolveCoverageLedgerBlockedIffTheorem": "PNP.DirectWire.terminalHResolveClassify_eq_blocked_iff", "residualTerminalHResolveCoverageLedgerUnresolvedIffTheorem": "PNP.DirectWire.terminalHResolveClassify_eq_unresolved_iff", "residualTerminalHResolveCoverageLedgerLedgerSoundnessTheorem": "PNP.DirectWire.TerminalHResolveFamily.routeLedger_sound", "residualTerminalHResolveCoverageLedgerLedgerCompletenessTheorem": "PNP.DirectWire.TerminalHResolveFamily.routeLedger_complete", "residualTerminalHResolveCoverageLedgerCheckIffTheorem": "PNP.DirectWire.TerminalHResolveFamily.checkNoHereditarySidecar_eq_true_iff", "residualTerminalHResolveCoverageLedgerNotExactTheorem": "PNP.DirectWire.TerminalHResolveFamily.not_exact_of_checkedNoHereditarySidecar", "residualTerminalHResolveCoverageLedgerNotGainTheorem": "PNP.DirectWire.TerminalHResolveFamily.not_gain_of_checkedNoHereditarySidecar", "residualTerminalHResolveCoverageLedgerNamedEndpointTheorem": "PNP.DirectWire.terminal_hresolve_checked_sidecar_excludes_constructive_routes", "residualTerminalHResolveCoverageLedgerTheoremKernelTypeSha256": { 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"residualTerminalHResolveSupportResolverPropextQuotSoundDeclarationCount": 14, "residualTerminalHResolveSupportResolverScope": "all-finite-direct-wire-candidates-terminal-derived-duplicate-free-support-universe-computed-exact-or-gain-with-semantic-minimum-or-strict-equivalent-gain-evidence", "residualTerminalHResolveSupportResolverSubsetsNodupTheorem": "PNP.DirectWire.terminalListSubsets_nodup", "residualTerminalHResolveSupportResolverFamilyNodupTheorem": "PNP.DirectWire.terminalHResolveSupportFamily_nodup", "residualTerminalHResolveSupportResolverCanonicalSeedMemberTheorem": "PNP.DirectWire.canonicalTerminalSupportSeed_mem_terminalHResolveSupportFamily", "residualTerminalHResolveSupportResolverExactIffTheorem": "PNP.DirectWire.terminalHResolveSupportExact_iff_semanticallyMinimum", "residualTerminalHResolveSupportResolverGainIffTheorem": "PNP.DirectWire.terminalHResolveSupportGain_iff_exists_strictEquivalentGain", "residualTerminalHResolveSupportResolverExactOrGainTheorem": 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"2a9dbe37bb6f13d6cb78be8d374fbcc826079845b2c9c724ac4f6d58ad2c51e3" }, "residualTerminalSelectorHBZeroSlackSidecarAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalSelectorHBZeroSlackSidecarProjectAxiomClosure": [], "residualTerminalPacketBudgetNoLowerZeroSlackSidecarFormalized": true, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarAxiomAuditPassed": true, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarAuditedDeclarationCount": 6, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarEmptyAxiomDeclarationCount": 1, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarPropextOnlyDeclarationCount": 0, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarQuotSoundOnlyDeclarationCount": 0, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarPropextQuotSoundDeclarationCount": 5, "residualTerminalPacketBudgetNoLowerZeroSlackSidecarScope": 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"residualTerminalBCELPacketNoLowerZeroSlackSidecarAxiomAuditPassed": true, "residualTerminalBCELPacketNoLowerZeroSlackSidecarAuditedDeclarationCount": 5, "residualTerminalBCELPacketNoLowerZeroSlackSidecarEmptyAxiomDeclarationCount": 1, "residualTerminalBCELPacketNoLowerZeroSlackSidecarPropextOnlyDeclarationCount": 1, "residualTerminalBCELPacketNoLowerZeroSlackSidecarQuotSoundOnlyDeclarationCount": 0, "residualTerminalBCELPacketNoLowerZeroSlackSidecarPropextQuotSoundDeclarationCount": 3, "residualTerminalBCELPacketNoLowerZeroSlackSidecarScope": "all-arbitrary-finite-proof-bearing-BCEL-constant-activation-to-positive-Packet-contradiction-against-the-same-checked-no-lower-family", "residualTerminalBCELPacketNoLowerZeroSlackSidecarCarrierAtLeastTwoTheorem": "PNP.BCELContradictionCertificate.carrier_at_least_two", "residualTerminalBCELPacketNoLowerZeroSlackSidecarNoPositivePacketTheorem": "PNP.BCELContradictionCertificate.no_positive_packet", 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"119db0567f3e4b314f5e9347e700aa53c749813938a5cf3b1e26a6cbf3c0a48d" }, "residualTerminalZeroSlackPacketSelectorHBCoherenceAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalZeroSlackPacketSelectorHBCoherenceProjectAxiomClosure": [], "residualTerminalFiniteBCELReadyCompositionFormalized": true, "residualTerminalFiniteBCELReadyCompositionAxiomAuditPassed": true, "residualTerminalFiniteBCELReadyCompositionAuditedDeclarationCount": 6, "residualTerminalFiniteBCELReadyCompositionEmptyAxiomDeclarationCount": 0, "residualTerminalFiniteBCELReadyCompositionPropextOnlyDeclarationCount": 0, "residualTerminalFiniteBCELReadyCompositionQuotSoundOnlyDeclarationCount": 0, "residualTerminalFiniteBCELReadyCompositionPropextQuotSoundDeclarationCount": 6, "residualTerminalFiniteBCELReadyCompositionScope": "all-finite-direct-wire-candidates-executable-models-proof-bearing-positive-full-slack-anchor-problems-recomputed-finite-saturate-positive-to-computed-bcel-ready-branch", 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"concreteLegacyLockedNANDCompatibilityProjectAxiomClosure": [], "concreteResidualBandCompatibilityFormalized": true, "concreteResidualBandCompatibilityAxiomAuditPassed": true, "concreteResidualBandCompatibilityAuditedDeclarationCount": 10, "concreteResidualBandCompatibilityEndpointProjectAssumptionFree": true, "concreteResidualBandCompatibilityCallerReductionRemoved": true, "concreteResidualBandCompatibilityScope": "all-bitstring-and-arbitrary-typed-candidate-exact-reference-minimum-threshold-semantics-with-fail-closed-decoding-and-identity-locked-to-residual-transport", "concreteResidualBandCompatibilityCandidateSemanticsTheorem": "PNP.Concrete.LockedNAND.encodedDirectWireMinimumThreshold_ofCandidate_iff", "concreteResidualBandCompatibilityEncodedSemanticsTheorem": "PNP.residual_band_encoded_candidate_iff_reference_minimum", "concreteResidualBandCompatibilityReductionTheorem": "PNP.locked_nand_reduces_to_residual_band_checked", "concreteResidualBandCompatibilityTransportTheorem": "PNP.locked_nand_in_p_from_residual_band_in_p", "concreteResidualBandCompatibilityReportIdentityTheorem": "PNP.report_residual_band_eq_concrete_minimum_threshold", "concreteResidualBandCompatibilityLockedIdentityTheorem": "PNP.report_locked_nand_eq_residual_band", "concreteResidualBandCompatibilityCheckedCompleteTheorem": "PNP.concrete_residual_band_compatibility_checked_complete", "concreteResidualBandCompatibilityTheoremKernelTypeSha256": { "PNP.Concrete.LockedNAND.encodedDirectWireMinimumThreshold_ofCandidate_iff": "a3389cacce2ed9318204b1f683565d78a15690d860eec12a7bb6ac57970f6d62", "PNP.residual_band_encoded_candidate_iff_reference_minimum": "b8492328752d6674474909daf183d0097d28d794c65a0156cbd90494eae7882f", "PNP.locked_nand_reduces_to_residual_band_checked": "403079c3a44b17388b0c199e82adeac566f6125dc245f04a85dfa18e53c3c497", "PNP.locked_nand_in_p_from_residual_band_in_p": "687aee8e08c38b6be49dca31a051d7fd019adc9866c456712657fa5ee7606286", "PNP.report_residual_band_eq_concrete_minimum_threshold": "07dc72c6a93d72ab65435705ba99ea6b84f69c2d06930af90c07f6bd09b5fc8a", "PNP.report_locked_nand_eq_residual_band": "14140f257b5e6ddf140cc9957a86248b1ed7defb691daf40c6080a859ce6e128", "PNP.concrete_residual_band_compatibility_checked_complete": "c4d3ccd4bc92297fd50b22d1be51b80d3930a10ecebce2d3e6c3ee25d95d03db" }, "concreteResidualBandCompatibilityAxiomClosure": [ "propext" ], "concreteResidualBandCompatibilityProjectAxiomClosure": [], "typedPCCPackReflectionFormalized": true, "typedPCCPackReflectionAxiomAuditPassed": true, "typedPCCPackReflectionAuditedDeclarationCount": 15, "typedPCCPackReflectionEndpointProjectAssumptionFree": true, "typedPCCPackReflectionOpaqueDeclarationsRemoved": true, "typedPCCPackReflectionScope": "all-explicit-proof-bearing-pccmin-loop-certificates-with-transparent-canonical-packaging-structural-identifier-checking-exact-projection-and-mismatch-rejection", "typedPCCPackReflectionCheckedCompleteTheorem": "PNP.typed_pccpack_reflection_checked_complete", "typedPCCPackReflectionTheoremKernelTypeSha256": { "PNP.typed_pccpack_reflection_checked_complete": "ac6c0a5045437ffb1df36a971ad4924f5e2cc785c97132e720c91f9461b16659" }, "typedPCCPackReflectionAxiomClosure": [ "Quot.sound", "propext" ], "typedPCCPackReflectionProjectAxiomClosure": [], "pccMinTotalOracleLoopFormalized": true, "pccMinTotalOracleLoopAxiomAuditPassed": true, "pccMinTotalOracleLoopAuditedDeclarationCount": 8, "pccMinTotalOracleLoopEndpointProjectAssumptionFree": true, "pccMinTotalOracleLoopHasUnresolvedOutcome": false, "pccMinTotalOracleLoopConstructsOracle": false, "pccMinTotalOracleLoopExactnessUnderOracleFormalized": true, "pccMinTotalOracleLoopGainIterationBoundFormalized": true, "pccMinTotalOracleLoopPolynomialRuntimeProved": false, "pccMinTotalOracleLoopScope": "all-finite-direct-wire-implementations-under-an-explicit-proof-bearing-total-oracle-with-strict-slack-descent-exact-terminal-evidence-and-gain-iteration-bound", "pccMinTotalOracleLoopCheckedCompleteTheorem": "PNP.DirectWire.pccmin_total_oracle_loop_checked_complete", "pccMinTotalOracleLoopTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_total_oracle_loop_checked_complete": "c4ef37cd1b66ccbc8cd49384abcc8f93610aa02fdb5aa78fc951c60960371c75" }, "pccMinTotalOracleLoopAxiomClosure": [], "pccMinTotalOracleLoopProjectAxiomClosure": [], "pccMinNormalizeOracleCompositionFormalized": true, "pccMinNormalizeOracleCompositionAxiomAuditPassed": true, "pccMinNormalizeOracleCompositionAuditedDeclarationCount": 10, "pccMinNormalizeOracleCompositionEndpointProjectAssumptionFree": true, "pccMinNormalizeOracleCompositionHasUnresolvedOutcome": false, "pccMinNormalizeOracleCompositionConstructsNormalizer": false, "pccMinNormalizeOracleCompositionConstructsOracle": false, "pccMinNormalizeOracleCompositionLiftedGainFormalized": true, "pccMinNormalizeOracleCompositionExactEndpointTransportFormalized": true, "pccMinNormalizeOracleCompositionPolynomialRuntimeProved": false, "pccMinNormalizeOracleCompositionScope": "all-finite-direct-wire-implementations-under-explicit-proof-bearing-normalizer-and-oracle-stages-with-nonincreasing-semantic-normalization-lifted-strict-gains-exact-endpoint-transport-and-the-checked-well-founded-loop", "pccMinNormalizeOracleCompositionCheckedCompleteTheorem": "PNP.DirectWire.pccmin_normalize_oracle_loop_checked_complete", "pccMinNormalizeOracleCompositionTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_normalize_oracle_loop_checked_complete": "aab40681d92f9e3bdf97f667660943103c90886a3fec08d9d7063ae5a72f6fb9" }, "pccMinNormalizeOracleCompositionAxiomClosure": [], "pccMinNormalizeOracleCompositionProjectAxiomClosure": [], "pccMinRankOrderedOracleFormalized": true, "pccMinRankOrderedOracleAxiomAuditPassed": true, "pccMinRankOrderedOracleAuditedDeclarationCount": 15, "pccMinRankOrderedOracleEndpointProjectAssumptionFree": true, "pccMinRankOrderedOracleHasUnresolvedOutcome": false, "pccMinRankOrderedOracleCanonicalAllRanksFormalized": true, "pccMinRankOrderedOracleCompleteSilenceRequired": true, "pccMinRankOrderedOracleConstructsResolvers": false, "pccMinRankOrderedOracleConstructsSelectorRows": false, "pccMinRankOrderedOracleProvesZeroSlackClosure": false, "pccMinRankOrderedOraclePolynomialRuntimeProved": false, "pccMinRankOrderedOracleScope": "all-finite-direct-wire-implementations-under-explicit-proof-bearing-normalizer-hresolve-budgetresolve-arbitrary-finite-rank-selector-rows-typed-blocker-silence-and-zeroslack-closure-with-canonical-all-rank-scanning-and-the-checked-well-founded-loop", "pccMinRankOrderedOracleCheckedCompleteTheorem": "PNP.DirectWire.pccmin_normalize_rank_ordered_oracle_loop_checked_complete", "pccMinRankOrderedOracleTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_normalize_rank_ordered_oracle_loop_checked_complete": "943d3c75e57843ac72b3760b6292c96c27f045a714cb7a1225bddf2e8866dc81" }, "pccMinRankOrderedOracleAxiomClosure": [ "Quot.sound", "propext" ], "pccMinRankOrderedOracleProjectAxiomClosure": [], "pccMinCheckedPacketRankedSelectorFormalized": true, "pccMinCheckedPacketRankedSelectorAxiomAuditPassed": true, "pccMinCheckedPacketRankedSelectorAuditedDeclarationCount": 15, "pccMinCheckedPacketRankedSelectorEndpointProjectAssumptionFree": true, "pccMinCheckedPacketRankedSelectorChecksEveryCanonicalHandle": true, "pccMinCheckedPacketRankedSelectorDerivesExactRankRows": true, "pccMinCheckedPacketRankedSelectorConstructsTerminalFamily": false, "pccMinCheckedPacketRankedSelectorConstructsResolvers": false, "pccMinCheckedPacketRankedSelectorProvesZeroSlackClosure": false, "pccMinCheckedPacketRankedSelectorPolynomialRuntimeProved": false, "pccMinCheckedPacketRankedSelectorScope": "all-finite-direct-wire-implementations-under-explicit-normalizer-hresolve-budgetresolve-supplied-grouped-packet-family-rank-map-data-only-claim-table-complete-checker-acceptance-and-zeroslack-silence-closure-with-canonical-exact-rank-row-derivation-and-the-checked-well-founded-loop", "pccMinCheckedPacketRankedSelectorCheckedCompleteTheorem": "PNP.DirectWire.pccmin_normalize_checked_packet_rank_ordered_oracle_loop_checked_complete", "pccMinCheckedPacketRankedSelectorTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_normalize_checked_packet_rank_ordered_oracle_loop_checked_complete": "5cc809cf616f667af21b848b8dd894d0e27483c96adab0369936e663d7856d64" }, "pccMinCheckedPacketRankedSelectorAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketRankedSelectorProjectAxiomClosure": [], "pccMinCheckedPacketHBZeroSlackBridgeFormalized": true, "pccMinCheckedPacketHBZeroSlackBridgeAxiomAuditPassed": true, "pccMinCheckedPacketHBZeroSlackBridgeAuditedDeclarationCount": 15, "pccMinCheckedPacketHBZeroSlackBridgeEndpointProjectAssumptionFree": true, "pccMinCheckedPacketHBZeroSlackBridgeDerivesSelectorSilence": true, "pccMinCheckedPacketHBZeroSlackBridgeChecksHBClosure": true, "pccMinCheckedPacketHBZeroSlackBridgeDerivesConditionalZeroSlack": true, "pccMinCheckedPacketHBZeroSlackBridgeConstructsPositiveSlackBridge": false, "pccMinCheckedPacketHBZeroSlackBridgeUnconditionalZeroSlack": false, "pccMinCheckedPacketHBZeroSlackBridgePolynomialRuntimeProved": false, "pccMinCheckedPacketHBZeroSlackBridgeScope": "all-finite-direct-wire-implementations-under-explicit-normalizer-hresolve-budgetresolve-supplied-grouped-packet-family-rank-map-data-only-claim-table-positive-slack-to-faithful-selector-bridge-and-checked-hb-no-outcome-closure-with-derived-selector-silence-conditional-zeroslack-and-the-checked-well-founded-loop", "pccMinCheckedPacketHBZeroSlackBridgeCheckedCompleteTheorem": "PNP.DirectWire.pccmin_normalize_checked_packet_hb_zeroslack_loop_checked_complete", "pccMinCheckedPacketHBZeroSlackBridgeTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_normalize_checked_packet_hb_zeroslack_loop_checked_complete": "7ba2f69a353b7c3a7b3aca107791c07f906c326b679c0a8580e59dbce5b4b29c" }, "pccMinCheckedPacketHBZeroSlackBridgeAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketHBZeroSlackBridgeProjectAxiomClosure": [], "pccMinCheckedPacketBN6HBZeroSlackBridgeFormalized": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeAxiomAuditPassed": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeAuditedDeclarationCount": 12, "pccMinCheckedPacketBN6HBZeroSlackBridgeEndpointProjectAssumptionFree": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeDerivesGeneralBN6Packet": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeComputesSelectorFaithfulness": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeIndependentBindingRemoved": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeDerivesConditionalZeroSlack": true, "pccMinCheckedPacketBN6HBZeroSlackBridgeConstructsConstantActivation": false, "pccMinCheckedPacketBN6HBZeroSlackBridgeUnconditionalZeroSlack": false, "pccMinCheckedPacketBN6HBZeroSlackBridgePolynomialRuntimeProved": false, "pccMinCheckedPacketBN6HBZeroSlackBridgeScope": "all-finite-direct-wire-implementations-under-explicit-normalizer-hresolve-budgetresolve-supplied-grouped-bn6-family-carrier-lower-bound-rank-map-route-clear-computed-payload-faithfulness-data-only-claim-table-positive-slack-to-constant-activation-bridge-and-checked-hb-no-outcome-closure-with-derived-conditional-zeroslack-and-the-checked-well-founded-loop", "pccMinCheckedPacketBN6HBZeroSlackBridgeCheckedCompleteTheorem": "PNP.DirectWire.pccmin_normalize_checked_packet_bn6_hb_zeroslack_loop_checked_complete", "pccMinCheckedPacketBN6HBZeroSlackBridgeTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_normalize_checked_packet_bn6_hb_zeroslack_loop_checked_complete": "6c0c7f23d66a1bb4560c99d84c7d21c846052d544669da051047db429e9a2c62" }, "pccMinCheckedPacketBN6HBZeroSlackBridgeAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6HBZeroSlackBridgeProjectAxiomClosure": [], "pccMinCheckedPacketBN6BCELActivationRouteFormalized": true, "pccMinCheckedPacketBN6BCELActivationRouteAxiomAuditPassed": true, "pccMinCheckedPacketBN6BCELActivationRouteAuditedDeclarationCount": 15, "pccMinCheckedPacketBN6BCELActivationRouteEndpointProjectAssumptionFree": true, "pccMinCheckedPacketBN6BCELActivationRouteTotalClassifier": true, "pccMinCheckedPacketBN6BCELActivationRouteDerivesConstantActivation": true, "pccMinCheckedPacketBN6BCELActivationRouteRetainsMismatchRoutes": true, "pccMinCheckedPacketBN6BCELActivationRouteDerivesConditionalZeroSlack": true, "pccMinCheckedPacketBN6BCELActivationRouteUnconditionalZeroSlack": false, "pccMinCheckedPacketBN6BCELActivationRoutePolynomialRuntimeProved": false, "pccMinCheckedPacketBN6BCELActivationRouteScope": "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-grouped-bn6-packet-family-with-total-carrier-cut-value-and-all-proper-cut-activation-classification-proof-bearing-mismatch-routes-derived-coherent-constant-activation-and-conditional-zeroslack", "pccMinCheckedPacketBN6BCELActivationRouteCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_activation_route_or_zeroslack_checked_complete", "pccMinCheckedPacketBN6BCELActivationRouteTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_activation_route_or_zeroslack_checked_complete": "d8f06c12a7a22514231020f3b257ba78372c532dfc39f019f66701d1b58af24f" }, "pccMinCheckedPacketBN6BCELActivationRouteAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6BCELActivationRouteProjectAxiomClosure": [], "pccMinCheckedPacketBN6BCELDerivedFamilyFormalized": true, "pccMinCheckedPacketBN6BCELDerivedFamilyAxiomAuditPassed": true, "pccMinCheckedPacketBN6BCELDerivedFamilyAuditedDeclarationCount": 14, "pccMinCheckedPacketBN6BCELDerivedFamilyEndpointProjectAssumptionFree": true, "pccMinCheckedPacketBN6BCELDerivedFamilyConstructsFamilyFromBCEL": true, "pccMinCheckedPacketBN6BCELDerivedFamilyDerivesCarrier": true, "pccMinCheckedPacketBN6BCELDerivedFamilyDerivesCutValue": true, "pccMinCheckedPacketBN6BCELDerivedFamilyEliminatesDuplicateMismatchRoutes": true, "pccMinCheckedPacketBN6BCELDerivedFamilyRetainsActivationMismatchRoute": true, "pccMinCheckedPacketBN6BCELDerivedFamilyDerivesConditionalZeroSlack": true, "pccMinCheckedPacketBN6BCELDerivedFamilyUnconditionalZeroSlack": false, "pccMinCheckedPacketBN6BCELDerivedFamilyPolynomialRuntimeProved": false, "pccMinCheckedPacketBN6BCELDerivedFamilyScope": "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-grouped-cell-ledger-with-bcel-derived-family-carrier-cut-value-positivity-impossible-duplicate-data-routes-exact-proper-cut-activation-mismatch-or-conditional-zeroslack", "pccMinCheckedPacketBN6BCELDerivedFamilyCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_derived_family_route_or_zeroslack_checked_complete", "pccMinCheckedPacketBN6BCELDerivedFamilyTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_derived_family_route_or_zeroslack_checked_complete": "2d50a967736e342be58071bd6c39783abf0cc18d67ef398fdf22803e6d4bd76a" }, "pccMinCheckedPacketBN6BCELDerivedFamilyAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6BCELDerivedFamilyProjectAxiomClosure": [], "pccMinCheckedPacketBN6BCELCanonicalGroupingFormalized": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingAxiomAuditPassed": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingAuditedDeclarationCount": 34, "pccMinCheckedPacketBN6BCELCanonicalGroupingEndpointProjectAssumptionFree": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingNormalizesSupportsInCarrier": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingConstructsSingletonConsumerSystems": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingCoalescesDuplicateFootprints": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingPreservesPayloadAtoms": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingDerivesConditionalZeroSlack": true, "pccMinCheckedPacketBN6BCELCanonicalGroupingDerivesCellsFromTerminalInput": false, "pccMinCheckedPacketBN6BCELCanonicalGroupingUnconditionalZeroSlack": false, "pccMinCheckedPacketBN6BCELCanonicalGroupingPolynomialRuntimeProved": false, "pccMinCheckedPacketBN6BCELCanonicalGroupingScope": "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-raw-positive-support-payload-ledger-with-carrier-normalized-supports-canonical-singleton-consumer-systems-duplicate-footprint-coalescing-payload-preservation-and-exact-activation-mismatch-or-conditional-zeroslack", "pccMinCheckedPacketBN6BCELCanonicalGroupingCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_grouping_route_or_zeroslack_checked_complete", "pccMinCheckedPacketBN6BCELCanonicalGroupingTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_grouping_route_or_zeroslack_checked_complete": "2627394268f34bc51ed578bcc12fac9dd82223592387848816cd3af507a9137f" }, "pccMinCheckedPacketBN6BCELCanonicalGroupingAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6BCELCanonicalGroupingProjectAxiomClosure": [], "pccMinCheckedPacketBN6BCELCanonicalCutLedgerFormalized": true, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerAxiomAuditPassed": true, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerAuditedDeclarationCount": 9, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerEndpointProjectAssumptionFree": true, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerRawMassConserved": true, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerUsesDirectRawCutLedger": true, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerDerivesConditionalZeroSlack": true, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerDerivesCellsFromTerminalInput": false, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerDerivesConstantActivation": false, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerMismatchIsGain": false, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerUnconditionalZeroSlack": false, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerPolynomialRuntimeProved": false, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerScope": "arbitrary-finite-same-candidate-checked-bcel-nucleus-and-supplied-raw-positive-cell-ledger-with-exact-canonical-grouped-to-raw-cut-mass-conservation-and-direct-raw-proper-cut-mismatch-or-conditional-zeroslack", "pccMinCheckedPacketBN6BCELCanonicalCutLedgerCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_cut_ledger_route_or_zeroslack_checked_complete", "pccMinCheckedPacketBN6BCELCanonicalCutLedgerTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_cut_ledger_route_or_zeroslack_checked_complete": "95f8a4d49ae159d8d3df6fd868ec11d03dfc1179df65d54c8c1f7745cad20891" }, "pccMinCheckedPacketBN6BCELCanonicalCutLedgerAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6BCELCanonicalCutLedgerProjectAxiomClosure": [], "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisFormalized": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisAxiomAuditPassed": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisAuditedDeclarationCount": 22, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisEndpointProjectAssumptionFree": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisEquivalentToAllProperCuts": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisClassifierTotal": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisAvoidsProperCutPowerset": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisUsesDirectRawCutLedger": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisDerivesConstantActivation": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisDerivesConditionalZeroSlack": true, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisDerivesCellsFromTerminalInput": false, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisRejectedRouteIsGain": false, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisUnconditionalZeroSlack": false, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisPolynomialRuntimeProved": false, "pCCMinCheckedPacketBN6BCELCanonicalConstantCutBasisScope": "arbitrary-finite-sparse-v53-shape-specific-constant-cut-basis-equivalent-to-all-proper-cuts-with-total-typed-classifier-and-direct-checked-bn6-bcel-hb-conditional-zeroslack-adapter-over-supplied-terminal-data", "pccMinCheckedPacketBN6BCELCanonicalConstantCutBasisCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_cut_basis_route_or_zeroslack_checked_complete", "pccMinCheckedPacketBN6BCELCanonicalConstantCutBasisTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_canonical_cut_basis_route_or_zeroslack_checked_complete": "0d72ea90cc0f14ce2dbd5baa16a2f0fd925dbef2d471236cfeff12cb7fbcdea9" }, "pccMinCheckedPacketBN6BCELCanonicalConstantCutBasisAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6BCELCanonicalConstantCutBasisProjectAxiomClosure": [], "pCCMinCheckedPacketBN6BCELSparseActivationRouteFormalized": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteAxiomAuditPassed": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteAuditedDeclarationCount": 30, "pCCMinCheckedPacketBN6BCELSparseActivationRouteEndpointProjectAssumptionFree": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteSingletonPairFamilyComplete": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteSingletonPairFamilyNodup": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteQuadraticListBound": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteEquivalentToAllProperCuts": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteClassifierTotal": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteReturnsExactRawMismatch": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteAvoidsProperCutPowerset": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteDerivesConditionalZeroSlack": true, "pCCMinCheckedPacketBN6BCELSparseActivationRouteDerivesCellsFromTerminalInput": false, "pCCMinCheckedPacketBN6BCELSparseActivationRouteMismatchIsGain": false, "pCCMinCheckedPacketBN6BCELSparseActivationRouteGlobalRankDecreaseProved": false, "pCCMinCheckedPacketBN6BCELSparseActivationRouteCompleteEncodedPolynomialRuntimeProved": false, "pCCMinCheckedPacketBN6BCELSparseActivationRouteUnconditionalZeroSlack": false, "pCCMinCheckedPacketBN6BCELSparseActivationRouteScope": "arbitrary-finite-sparse-positive-v53-singleton-pair-proper-cut-equation-equivalent-to-all-proper-cuts-with-quadratic-list-bound-total-first-mismatch-classifier-and-direct-checked-raw-activation-mismatch-or-conditional-zeroslack-over-supplied-terminal-data", "pccMinCheckedPacketBN6BCELSparseActivationRouteCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_sparse_activation_route_or_zeroslack_checked_complete", "pccMinCheckedPacketBN6BCELSparseActivationRouteTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_bn6_bcel_sparse_activation_route_or_zeroslack_checked_complete": "ec85750acf0658c02ee2c8bcfc0b48c71e483796ddae699fd5fc62114168e2a0" }, "pccMinCheckedPacketBN6BCELSparseActivationRouteAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketBN6BCELSparseActivationRouteProjectAxiomClosure": [], "residualTerminalPkgCBN6PositiveCellizationFormalized": true, "residualTerminalPkgCBN6PositiveCellizationAxiomAuditPassed": true, "residualTerminalPkgCBN6PositiveCellizationAuditedDeclarationCount": 19, "residualTerminalPkgCBN6PositiveCellizationEndpointProjectAssumptionFree": true, "residualTerminalPkgCBN6PositiveCellizationSourceCellsArbitraryFinite": true, "residualTerminalPkgCBN6PositiveCellizationRawSupportsDerived": true, "residualTerminalPkgCBN6PositiveCellizationFootprintSizeDerivedFromActiveCut": true, "residualTerminalPkgCBN6PositiveCellizationPkgCCancellationProofBearing": true, "residualTerminalPkgCBN6PositiveCellizationActivationWeightConservedAllCuts": true, "residualTerminalPkgCBN6PositiveCellizationPayloadOrderPreserved": true, "residualTerminalPkgCBN6PositiveCellizationDerivesCellsFromTerminalInput": false, "residualTerminalPkgCBN6PositiveCellizationRestorerConstructedFromTerminalInput": false, "residualTerminalPkgCBN6PositiveCellizationCancellationIsGlobalGain": false, "residualTerminalPkgCBN6PositiveCellizationCompletePkgCBN6Integration": false, "residualTerminalPkgCBN6PositiveCellizationCompleteEncodedPolynomialRuntimeProved": false, "residualTerminalPkgCBN6PositiveCellizationUnconditionalZeroSlack": false, "residualTerminalPkgCBN6PositiveCellizationScope": "arbitrary-finite-supplied-active-v54-consumer-systems-over-one-carrier-classified-by-exact-pkgc-same-key-cancellation-or-derived-raw-bn6-positive-cells-with-payload-order-and-all-cut-activation-conservation-over-a-supplied-restorer", "residualTerminalPkgCBN6PositiveCellizationCheckedCompleteTheorem": "PNP.DirectWire.terminalPkgC_bn6_positive_cellization_checked_complete", "residualTerminalPkgCBN6PositiveCellizationTheoremKernelTypeSha256": { "PNP.DirectWire.terminalPkgC_bn6_positive_cellization_checked_complete": "0715d92380dace6d7dd5f04311a9c7dc2e5172ae1464a09e2524246ac0897f86" }, "residualTerminalPkgCBN6PositiveCellizationAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPkgCBN6PositiveCellizationProjectAxiomClosure": [], "pccMinCheckedPacketPkgCBN6BCELSourceRouteFormalized": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteAxiomAuditPassed": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteAuditedDeclarationCount": 7, "pccMinCheckedPacketPkgCBN6BCELSourceRouteEndpointProjectAssumptionFree": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteSourceCellsArbitraryFinite": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteRawCellsDerivedFromPkgCSource": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteActivationWeightConservedAllCuts": true, "pccMinCheckedPacketPkgCBN6BCELSourceRoutePkgCCancellationProofBearing": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteSparseCutLengthAtMostTwo": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteActivationMismatchReflectedToSourceLedger": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteConditionalZeroSlackOnly": true, "pccMinCheckedPacketPkgCBN6BCELSourceRouteDerivesSourcesFromTerminalInput": false, "pccMinCheckedPacketPkgCBN6BCELSourceRouteConstructsDownstreamTables": false, "pccMinCheckedPacketPkgCBN6BCELSourceRouteCancellationOrMismatchIsGlobalGain": false, "pccMinCheckedPacketPkgCBN6BCELSourceRouteCompletePkgCBN6Integration": false, "pccMinCheckedPacketPkgCBN6BCELSourceRouteCompleteEncodedPolynomialRuntimeProved": false, "pccMinCheckedPacketPkgCBN6BCELSourceRouteUnconditionalZeroSlack": false, "pccMinCheckedPacketPkgCBN6BCELSourceRouteScope": "arbitrary-finite-supplied-active-pkgc-source-ledger-over-the-exact-checked-bcel-nucleus-with-source-derived-raw-bn6-cells-exact-pkgc-cancellation-or-source-ledger-singleton-pair-activation-mismatch-and-conditional-zeroslack-under-supplied-checked-downstream-data", "pccMinCheckedPacketPkgCBN6BCELSourceRouteCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_pkgc_bn6_bcel_source_route_or_zeroslack_checked_complete", "pccMinCheckedPacketPkgCBN6BCELSourceRouteTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_pkgc_bn6_bcel_source_route_or_zeroslack_checked_complete": "93e5eba6868b241e355f7ce76248ee5da358e64424c7138ee0b4b231051f12ea" }, "pccMinCheckedPacketPkgCBN6BCELSourceRouteAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketPkgCBN6BCELSourceRouteProjectAxiomClosure": [], "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteFormalized": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteAxiomAuditPassed": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteAuditedDeclarationCount": 10, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteEndpointProjectAssumptionFree": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteAmbientLedgerArbitraryFinite": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteAmbientOrderIndependent": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteMultiplicityPreserved": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteRemainderComputed": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteNoEmbeddingProofBearing": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteCandidateBN4KernelConstructed": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteResidualReductionExact": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteConditionalZeroSlackOnly": true, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteDerivesAmbientLedgerFromTerminalInput": false, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteDerivesSourcesFromTerminalInput": false, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteCancellationReductionIsGlobalGain": false, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteCompletePkgCBN6Integration": false, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteCompleteEncodedPolynomialRuntimeProved": false, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteUnconditionalZeroSlack": false, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteScope": "arbitrary-finite-multiplicity-preserving-order-independent-extraction-of-generated-pkgc-cancellation-cells-from-a-supplied-candidate-bound-ambient-bn4-ledger-with-computed-remainder-exact-residual-reduction-or-proof-of-no-exact-embedding-composed-with-m202-conditional-zeroslack-and-source-activation-routing", "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_pkgc_ambient_bn4_extraction_route_or_zeroslack_checked_complete", "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_pkgc_ambient_bn4_extraction_route_or_zeroslack_checked_complete": "54025d7d0c4eb695f282dab133e4de9c51639783ebb5cbb1ab62d7c7e4cef276" }, "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketPkgCAmbientBN4ExtractionRouteProjectAxiomClosure": [], "residualTerminalPkgCRestorationCoverageAmbientRouteFormalized": true, "residualTerminalPkgCRestorationCoverageAmbientRouteAxiomAuditPassed": true, "residualTerminalPkgCRestorationCoverageAmbientRouteAuditedDeclarationCount": 17, "residualTerminalPkgCRestorationCoverageAmbientRouteEndpointProjectAssumptionFree": true, "residualTerminalPkgCRestorationCoverageAmbientRouteConsumerSystemArbitraryFinite": true, "residualTerminalPkgCRestorationCoverageAmbientRouteRestorationUniverseArbitraryFinite": true, "residualTerminalPkgCRestorationCoverageAmbientRouteAmbientLedgerArbitraryFinite": true, "residualTerminalPkgCRestorationCoverageAmbientRouteTypedRestorerRequired": false, "residualTerminalPkgCRestorationCoverageAmbientRouteHallDeficitProofBearing": true, "residualTerminalPkgCRestorationCoverageAmbientRouteCoverageCancellationConstructed": true, "residualTerminalPkgCRestorationCoverageAmbientRouteRemainderComputed": true, "residualTerminalPkgCRestorationCoverageAmbientRouteNoEmbeddingProofBearing": true, "residualTerminalPkgCRestorationCoverageAmbientRouteResidualReductionExact": true, "residualTerminalPkgCRestorationCoverageAmbientRouteMaterializesSemanticFullCandidates": false, "residualTerminalPkgCRestorationCoverageAmbientRouteDerivesRestorationUniverseFromTerminalInput": false, "residualTerminalPkgCRestorationCoverageAmbientRouteDerivesAmbientLedgerFromTerminalInput": false, "residualTerminalPkgCRestorationCoverageAmbientRouteHallRouteIsGlobalGain": false, "residualTerminalPkgCRestorationCoverageAmbientRouteCompletePkgCBN6Integration": false, "residualTerminalPkgCRestorationCoverageAmbientRouteCompleteEncodedPolynomialRuntimeProved": false, "residualTerminalPkgCRestorationCoverageAmbientRouteUnconditionalZeroSlack": false, "residualTerminalPkgCRestorationCoverageAmbientRouteScope": "arbitrary-finite-restoration-coordinate-coverage-classified-as-an-exact-q-restoration-hall-deficit-or-a-constructed-balanced-bn4-unit-cancellation-subledger-with-computed-arbitrary-order-ambient-remainder-exact-residual-reduction-or-proof-of-no-exact-embedding", "residualTerminalPkgCRestorationCoverageAmbientRouteCheckedCompleteTheorem": "PNP.DirectWire.terminalPkgC_restorationCoverage_ambientBN4_route_checked_complete", "residualTerminalPkgCRestorationCoverageAmbientRouteTheoremKernelTypeSha256": { "PNP.DirectWire.terminalPkgC_restorationCoverage_ambientBN4_route_checked_complete": "ae5f113cf4640de616197206f04fbcb6db1fd6b37c0f3e5007a5d83cb81d977c" }, "residualTerminalPkgCRestorationCoverageAmbientRouteAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPkgCRestorationCoverageAmbientRouteProjectAxiomClosure": [], "residualTerminalPkgCRestorationCoverageBN6LedgerFormalized": true, "residualTerminalPkgCRestorationCoverageBN6LedgerAxiomAuditPassed": true, "residualTerminalPkgCRestorationCoverageBN6LedgerAuditedDeclarationCount": 11, "residualTerminalPkgCRestorationCoverageBN6LedgerEndpointProjectAssumptionFree": true, "residualTerminalPkgCRestorationCoverageBN6LedgerSourceLedgerArbitraryFinite": true, "residualTerminalPkgCRestorationCoverageBN6LedgerTypedRestorerRequired": false, "residualTerminalPkgCRestorationCoverageBN6LedgerAllSourceSingletonizationRequiredForCellization": true, "residualTerminalPkgCRestorationCoverageBN6LedgerFirstObstructionPreserved": true, "residualTerminalPkgCRestorationCoverageBN6LedgerBN6CellsConstructed": true, "residualTerminalPkgCRestorationCoverageBN6LedgerPayloadOrderPreserved": true, "residualTerminalPkgCRestorationCoverageBN6LedgerAllCutActivationConserved": true, "residualTerminalPkgCRestorationCoverageBN6LedgerDerivesRestorationUniverseFromTerminalInput": false, "residualTerminalPkgCRestorationCoverageBN6LedgerDerivesAmbientLedgerFromTerminalInput": false, "residualTerminalPkgCRestorationCoverageBN6LedgerHallRouteIsGlobalGain": false, "residualTerminalPkgCRestorationCoverageBN6LedgerComputedRemainderProvedEmpty": false, "residualTerminalPkgCRestorationCoverageBN6LedgerCompletePkgCBN6Integration": false, "residualTerminalPkgCRestorationCoverageBN6LedgerCompleteEncodedPolynomialRuntimeProved": false, "residualTerminalPkgCRestorationCoverageBN6LedgerUnconditionalZeroSlack": false, "residualTerminalPkgCRestorationCoverageBN6LedgerScope": "arbitrary-finite-supplied-active-pkgc-source-ledger-scanned-in-list-order-for-the-first-exact-restoration-hall-ambient-reduction-or-no-embedding-outcome-or-complete-derived-bn6-cellization-with-payload-order-and-all-cut-activation-conservation", "residualTerminalPkgCRestorationCoverageBN6LedgerCheckedCompleteTheorem": "PNP.DirectWire.terminalPkgC_restorationCoverage_bn6_cellization_checked_complete", "residualTerminalPkgCRestorationCoverageBN6LedgerTheoremKernelTypeSha256": { "PNP.DirectWire.terminalPkgC_restorationCoverage_bn6_cellization_checked_complete": "17d75201994721d64f24d4ee95a20a13dfd3b3b25eef4e5b8093481c81055737" }, "residualTerminalPkgCRestorationCoverageBN6LedgerAxiomClosure": [ "Quot.sound", "propext" ], "residualTerminalPkgCRestorationCoverageBN6LedgerProjectAxiomClosure": [], "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteFormalized": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteAxiomAuditPassed": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteAuditedDeclarationCount": 4, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteEndpointProjectAssumptionFree": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteSourceLedgerArbitraryFinite": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCandidateBoundAmbientLedgers": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteTypedRestorerRequired": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteRawBN6CellsDerived": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteFirstObstructionPreserved": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteConditionalZeroSlackOnly": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteActivationMismatchReflectedToSourceLedger": true, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteDerivesSourcesFromTerminalInput": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteConstructsDownstreamTables": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteHallRouteIsGlobalGain": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteComputedRemainderProvedEmpty": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCompletePkgCBN6Integration": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCompleteEncodedPolynomialRuntimeProved": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteUnconditionalZeroSlack": false, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteScope": "arbitrary-finite-candidate-bound-restoration-coverage-pkgc-source-ledger-with-first-exact-hall-ambient-reduction-or-no-embedding-outcome-or-derived-bn6-cellization-entering-the-checked-sparse-bcel-route-with-source-reflected-activation-mismatch-and-conditional-zeroslack", "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_pkgc_restoration_coverage_bn6_bcel_route_or_zeroslack_checked_complete", "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_pkgc_restoration_coverage_bn6_bcel_route_or_zeroslack_checked_complete": "122d0276d734cc4012cf8ab58127d9a60a7d146f9ff4f7018bd9b40d96123ce4" }, "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketPkgCRestorationCoverageBN6BCELRouteProjectAxiomClosure": [], "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentCheckedCompleteTheorem": "PNP.DirectWire.pccmin_checked_packet_pkgc_restoration_coverage_charge_route_or_zeroslack_checked_complete", "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentTheoremKernelTypeSha256": { "PNP.DirectWire.pccmin_checked_packet_pkgc_restoration_coverage_charge_route_or_zeroslack_checked_complete": "2205a2a1ef56e31519ab2320d6ed83004a252026e1d92731de4fba539c4a9d7e" }, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentAxiomClosure": [ "Quot.sound", "propext" ], "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentProjectAxiomClosure": [], "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentFormalized": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentAxiomAuditPassed": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentAuditedDeclarationCount": 16, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentEndpointProjectAssumptionFree": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentArbitraryFinite": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentUnsignedChargeMassDerived": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentExactPermutationRequired": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentRemovedChargeStrictlyPositive": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentResidualLedgerPreserved": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentChargeSizeStrictlyDecreases": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentResidualRankChargeCoordinateDecreases": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentRankContextParametric": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentCallerSuppliedRankProofRequired": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentM206BranchesPreserved": true, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentHallRouteIsGlobalGain": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentAmbientMismatchIsGlobalRoute": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentActivationMismatchIsGlobalRoute": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentComputedRemainderProvedEmpty": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentCompleteGlobalRouteCoverage": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentCompletePkgCBN6Integration": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentCompleteEncodedPolynomialRuntimeProved": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentUnconditionalZeroSlack": false, "pccMinCheckedPacketPkgCRestorationCoverageChargeDescentScope": "arbitrary-finite-m206-restoration-coverage-ambient-embedding-with-mass-sensitive-unsigned-charge-decomposition-strict-remainder-charge-decrease-and-context-parametric-exact-terminal-residual-rank-charge-coordinate-descent-while-all-other-m206-outcomes-remain-explicit", "cookLevinBuilderFullScheduleCursorControllerCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderFullScheduleCursorController.cook_levin_full_schedule_cursor_controller_checked_complete", "cookLevinBuilderFullScheduleCursorControllerTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderFullScheduleCursorController.cook_levin_full_schedule_cursor_controller_checked_complete": "43e0a8a651dea0dba61e661579405cd081a7ec33df48be4575cc4b3729bdbc95" }, "cookLevinBuilderFullScheduleCursorControllerAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderFullScheduleCursorControllerProjectAxiomClosure": [], "cookLevinBuilderFullScheduleCursorControllerFormalized": true, "cookLevinBuilderFullScheduleCursorControllerAxiomAuditPassed": true, "cookLevinBuilderFullScheduleCursorControllerAuditedDeclarationCount": 70, "cookLevinBuilderFullScheduleCursorControllerExactRawTraceFormalized": true, "cookLevinBuilderFullScheduleCursorControllerExternalInputSizePolynomialFormalized": true, "cookLevinBuilderFullScheduleCursorControllerFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderFullScheduleCursorControllerEmitsBodyTokens": false, "cookLevinBuilderArbitrarySlotHeaderRouterCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderArbitrarySlotHeaderRouter.cook_levin_arbitrary_slot_header_router_checked_complete", "cookLevinBuilderArbitrarySlotHeaderRouterTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderArbitrarySlotHeaderRouter.cook_levin_arbitrary_slot_header_router_checked_complete": "6794a8f27d2587b3c7960116aa3fdd0ac582ab71f9b90f39644c3a676d2cf2bf" }, "cookLevinBuilderArbitrarySlotHeaderRouterAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderArbitrarySlotHeaderRouterProjectAxiomClosure": [], "cookLevinBuilderArbitrarySlotHeaderRouterFormalized": true, "cookLevinBuilderArbitrarySlotHeaderRouterAxiomAuditPassed": true, "cookLevinBuilderArbitrarySlotHeaderRouterAuditedDeclarationCount": 51, "cookLevinBuilderArbitrarySlotHeaderRouterLiteralRawMachineFormalized": true, "cookLevinBuilderArbitrarySlotHeaderRouterExactRawTraceFormalized": true, "cookLevinBuilderArbitrarySlotHeaderRouterExternalInputSizePolynomialFormalized": true, "cookLevinBuilderArbitrarySlotHeaderRouterFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderArbitrarySlotHeaderRouterDecodesPostHeaderCoordinate": false, "cookLevinBuilderArbitrarySlotHeaderRouterEmitsBodyTokens": false, "cookLevinBuilderArbitrarySlotPostHeaderDecoderCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderArbitrarySlotPostHeaderDecoder.cook_levin_arbitrary_slot_post_header_decoder_checked_complete", "cookLevinBuilderArbitrarySlotPostHeaderDecoderTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderArbitrarySlotPostHeaderDecoder.cook_levin_arbitrary_slot_post_header_decoder_checked_complete": "56ce613c7f034579229b382e1eb985564fd443a612579191daea72381d709d9c" }, "cookLevinBuilderArbitrarySlotPostHeaderDecoderAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderArbitrarySlotPostHeaderDecoderProjectAxiomClosure": [], "cookLevinBuilderArbitrarySlotPostHeaderDecoderFormalized": true, "cookLevinBuilderArbitrarySlotPostHeaderDecoderAxiomAuditPassed": true, "cookLevinBuilderArbitrarySlotPostHeaderDecoderAuditedDeclarationCount": 22, "cookLevinBuilderArbitrarySlotPostHeaderDecoderAllCoordinateSemanticDecoderFormalized": true, "cookLevinBuilderArbitrarySlotPostHeaderDecoderExactClauseWithinClauseReconstructionFormalized": true, "cookLevinBuilderArbitrarySlotPostHeaderDecoderDirectBodyTokenRouteFormalized": true, "cookLevinBuilderArbitrarySlotPostHeaderDecoderRawPostHeaderRemainderExtractionFormalized": true, "cookLevinBuilderArbitrarySlotPostHeaderDecoderRawDivisionFormalized": false, "cookLevinBuilderArbitrarySlotPostHeaderDecoderRawBodyTokenEmissionFormalized": false, "cookLevinBuilderPostHeaderRawDividerCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPostHeaderRawDivider.cook_levin_builder_post_header_raw_divider_checked_complete", "cookLevinBuilderPostHeaderRawDividerTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPostHeaderRawDivider.cook_levin_builder_post_header_raw_divider_checked_complete": "49eafb1e2702755c9a011c7dfcb37897242ab96021b03f64ea75fa621160ea75" }, "cookLevinBuilderPostHeaderRawDividerAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderPostHeaderRawDividerProjectAxiomClosure": [], "cookLevinBuilderPostHeaderRawDividerFormalized": true, "cookLevinBuilderPostHeaderRawDividerAxiomAuditPassed": true, "cookLevinBuilderPostHeaderRawDividerAuditedDeclarationCount": 57, "cookLevinBuilderPostHeaderRawDividerLiteralRawMachineFormalized": true, "cookLevinBuilderPostHeaderRawDividerExactRawTraceFormalized": true, "cookLevinBuilderPostHeaderRawDividerCompiledRawSimulationFormalized": true, "cookLevinBuilderPostHeaderRawDividerExactQuotientRemainderDecodeFormalized": true, "cookLevinBuilderPostHeaderRawDividerExternalUnaryEncodedSizeQuadraticBoundFormalized": true, "cookLevinBuilderPostHeaderRawDividerFailClosedBoundaryTimeoutFormalized": true, "cookLevinBuilderPostHeaderRawDividerRawBodyTokenEmissionFormalized": false, "cookLevinBuilderPostHeaderRawLaunchCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPostHeaderRawLaunch.cook_levin_builder_post_header_raw_launch_checked_complete", "cookLevinBuilderPostHeaderRawLaunchTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPostHeaderRawLaunch.cook_levin_builder_post_header_raw_launch_checked_complete": "0361f9b8c05cea70ce199c78a74e55473765ae3e49d39565a46696915558fda1" }, "cookLevinBuilderPostHeaderRawLaunchAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderPostHeaderRawLaunchProjectAxiomClosure": [], "cookLevinBuilderPostHeaderRawLaunchFormalized": true, "cookLevinBuilderPostHeaderRawLaunchAxiomAuditPassed": true, "cookLevinBuilderPostHeaderRawLaunchAuditedDeclarationCount": 24, "cookLevinBuilderPostHeaderRawLaunchExactHandoffFormalized": true, "cookLevinBuilderPostHeaderRawLaunchAllRoutesFormalized": true, "cookLevinBuilderPostHeaderRawLaunchSourceSizePolynomialBoundFormalized": true, "cookLevinBuilderPostHeaderRawLaunchLiteralTapeBridgeFormalized": false, "cookLevinBuilderPostHeaderRawLaunchRawBodyTokenEmissionFormalized": false, "cookLevinBuilderPostHeaderRawTapeBridgeCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPostHeaderRawTapeBridge.cook_levin_builder_post_header_raw_tape_bridge_checked_complete", "cookLevinBuilderPostHeaderRawTapeBridgeTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPostHeaderRawTapeBridge.cook_levin_builder_post_header_raw_tape_bridge_checked_complete": "4471f7d515cd8fc13191d7228a74e226adb6ee9fcfa4277d13f38fef26880753" }, "cookLevinBuilderPostHeaderRawTapeBridgeAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderPostHeaderRawTapeBridgeProjectAxiomClosure": [], "cookLevinBuilderPostHeaderRawTapeBridgeFormalized": true, "cookLevinBuilderPostHeaderRawTapeBridgeAxiomAuditPassed": true, "cookLevinBuilderPostHeaderRawTapeBridgeAuditedDeclarationCount": 78, "cookLevinBuilderPostHeaderRawTapeBridgeExactRouterTapeInputsFormalized": true, "cookLevinBuilderPostHeaderRawTapeBridgeLiteralTapeBridgeFormalized": true, "cookLevinBuilderPostHeaderRawTapeBridgeArbitraryWorkspacePreservedFormalized": true, "cookLevinBuilderPostHeaderRawTapeBridgeShieldedDividerTraceFormalized": true, "cookLevinBuilderPostHeaderRawTapeBridgeAllRoutesFormalized": true, 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"cookLevinBuilderPostDividerRawRouteClassifierCompiledSimulationFormalized": true, "cookLevinBuilderPostDividerRawRouteClassifierOneStepShortNonhaltingFormalized": true, "cookLevinBuilderPostDividerRawRouteClassifierSourceSizePolynomialBoundFormalized": true, "cookLevinBuilderPostDividerRawRouteClassifierRawBodyTokenEmissionFormalized": false, "cookLevinBuilderPostDividerRawRouteClassifierCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPostDividerRawRouteClassifier.cook_levin_builder_post_divider_raw_route_classifier_checked_complete", "cookLevinBuilderPostDividerRawRouteClassifierTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPostDividerRawRouteClassifier.cook_levin_builder_post_divider_raw_route_classifier_checked_complete": "59409490565859dd69d80adf3261d0942f5cd81d05d0703a160f7e82388dede6" }, "cookLevinBuilderPostDividerRawRouteClassifierAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderPostDividerRawRouteClassifierProjectAxiomClosure": [], 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"cookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchExternalInputSizePolynomialFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatch.cook_levin_builder_physical_classifier_all_route_staged_request_mirrored_dispatch_checked_complete", "cookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatch.cook_levin_builder_physical_classifier_all_route_staged_request_mirrored_dispatch_checked_complete": "f8323850eefda8fb9f731c4be6af9f85f797744e9b90c79539316bab48c11871" }, "cookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderPhysicalClassifierAllRouteStagedRequestMirroredDispatchProjectAxiomClosure": [], 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"cookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitExactWorkTraceFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitCompiledRawMachineFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitOneStepShortNonhaltingFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitExternalInputSizePolynomialFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteDerivedFinishSplit.cook_levin_builder_physical_classifier_all_route_derived_finish_split_checked_complete", "cookLevinBuilderPhysicalClassifierAllRouteDerivedFinishSplitTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteDerivedFinishSplit.cook_levin_builder_physical_classifier_all_route_derived_finish_split_checked_complete": "20e0743e1b3e03452e458c24f0ef41584b837cbc6534186d9c42c7906e63f8c1" }, 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"cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitFinishEndpointPreservedFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitClauseOccupancyFormalized": false, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitBodyRequestSynthesisFormalized": false, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitPaddingRequestSynthesisFormalized": false, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitSuccessiveConfigurationsFormalized": false, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitRepeatedBuilderLoopFormalized": false, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitExactWorkTraceFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitCompiledRawMachineFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitOneStepShortNonhaltingFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitExternalInputSizePolynomialFormalized": true, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitCheckedCompleteTheorem": "PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteBodyRemainderSplit.cook_levin_builder_physical_classifier_all_route_body_remainder_split_checked_complete", "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.BuilderPhysicalClassifierAllRouteBodyRemainderSplit.cook_levin_builder_physical_classifier_all_route_body_remainder_split_checked_complete": "5cb01b3ff8e154613151d8d131f576ce86bdc33e2d24d355793a3ca55ce7208f" }, "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinBuilderPhysicalClassifierAllRouteBodyRemainderSplitProjectAxiomClosure": [], "cookLevinCompleteBuilderFormalized": true, "cookLevinCompleteBuilderAxiomAuditPassed": true, "cookLevinCompleteBuilderTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.formulaBuilderMachine_accept": "f78cfac94de5b6d1c2e461b4542527ddb8490796f83741389238daf13c48f048", "PNP.Concrete.CookLevin.formulaBuilderMachine_output": "51f7ea88d2b8333cb5bfefd5d7c6b122c895e90b13508d7b48a5b00952d440f3", "PNP.Concrete.CookLevin.formulaBuilder_output": "9517c55b7e470350cfec99950cd933ddc6455e7d158c94f8b85eece418e28293", "PNP.Concrete.CookLevin.formulaBuilder_rawRefinement_output": "5afca0de879c1ff185aab5093c5622d7bc606404c2f05361c7bfa1231aa1b06e", "PNP.Concrete.CookLevin.polynomialReduction_output": "5957ea8d28eb75362bba1cfb0dba94d3840d139b2904899c2c8a61b2423698ed", "PNP.Concrete.CookLevin.cook_levin_formula_builder_checked_complete": "7c319be45d775041419206e62eec233cda9c000839b697d43f7e2bc25423b35c" }, "cookLevinCompleteBuilderCheckedCompleteTheorem": "PNP.Concrete.CookLevin.cook_levin_formula_builder_checked_complete", "cookLevinCompleteBuilderExecutionAxiomClosure": [ "Quot.sound", "propext" ], "cookLevinCompleteBuilderAxiomClosure": [ "Classical.choice", "Quot.sound", "propext" ], "cookLevinCompleteBuilderProjectAxiomClosure": [], "cnfSATNPCompletenessAxiomAuditPassed": true, "cnfSATNPCompletenessAuditedDeclarationCount": 2, "cnfSATNPCompletenessTheoremKernelTypeSha256": { "PNP.Concrete.CookLevin.cnfSAT_np_hard": "c2cae5f7ad14a81b32888e8405210b57552dea928200cc77e9ebb34099ec9909", "PNP.Concrete.CookLevin.cnfSAT_np_complete": "7b1c0556dde7066ebe7abc9706b400857b9dd41dc1d704930a1f1d6c423bbe35" }, "cnfSATNPCompletenessTheorem": "PNP.Concrete.CookLevin.cnfSAT_np_complete", "cnfSATNPCompletenessHardnessTheorem": "PNP.Concrete.CookLevin.cnfSAT_np_hard", "cnfSATNPCompletenessAxiomClosure": [ "Classical.choice", "Quot.sound", "propext" ], "cnfSATNPCompletenessProjectAxiomClosure": [], "milestoneBatchM232M258": { "kind": "PNPLabsCompiledMilestoneBatch0", "batchId": "m232-m258", "reviewedSource": { "commit": "6296c6e1130fbae674548ccbf949f6e608b996c7", "tree": "78648f5978d16ff5055c5b493e5bb97ff4cd7cac", "statusCoordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-258" }, "milestones": [ { "number": 232, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-232", "id": "residual-terminal-profile-dependency-semantics", "title": "Candidate-derived terminal profile dependency reflection and noninterference", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalProfileDependencySemanticsFormalized": true, "leanResidualTerminalProfileDependencySemanticsAxiomAuditPassed": true, "leanResidualTerminalProfileDependencySemanticsAuditedDeclarationCount": 4, "leanResidualTerminalProfileDependencyNoninterferenceTheorem": "PNP.DirectWire.terminalCandidateSaturate_profile_noninterference", "leanResidualTerminalProfileDependencySemanticsScope": "all-finite-candidates-executable-models-computed-profile-influence-role-labelled-edges-and-computed-saturation-noninterference-in-canonical-contexts-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalGateInfluencesProfile_eq_true_iff": "6b889ca06140498835da44305ac96f7ab8820e0640b2b8175e36566910082ab3", "PNP.DirectWire.terminalCandidateProfileRequires_eq_influence": "1f58c87385f0dbbe2932a1f1cbdc6a156dc0218a15171539d1c78daae7dec92a", "PNP.DirectWire.terminalCandidateSaturate_profile_noninterference": "3f9d0b7f8bd9fd56cdf1b1b2883913ddf6516d64680c6850870a6129ba89fb5d" }, "theoremAxioms": { "PNP.DirectWire.terminalGateInfluencesProfile_eq_true_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateProfileRequires_eq_influence": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturate_profile_noninterference": [ "Quot.sound", "propext" ] } }, { "number": 233, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-233", "id": "residual-terminal-profile-locality", "title": "Retained ambient-profile locality and whole-support preservation", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalProfileLocalityFormalized": true, "leanResidualTerminalProfileLocalityAxiomAuditPassed": true, "leanResidualTerminalProfileLocalityAuditedDeclarationCount": 5, "leanResidualTerminalProfileLocalityTheorem": "PNP.DirectWire.terminalCandidateSaturate_profile_locality", "leanResidualTerminalProfilePreservationTheorem": "PNP.DirectWire.terminalCandidateSaturate_profile_preserved", "leanResidualTerminalProfileLocalityScope": "all-finite-candidates-executable-models-arbitrary-primitive-record-supports-computed-saturation-retained-ambient-profile-locality-and-preservation-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.extractTerminalSupport_eq_of_gateSelected_eq": "36de3a72b162389f2f8f5a3411a8fc000007cf55da00a39898b4b59d76957f05", "PNP.DirectWire.terminalAmbientSupportImplementation_eq_of_gateSelected_eq": "991e7712503e87f358b0d5a8fa89978d4a0552e28ce55fda31b3768fdf9e05a1", "PNP.DirectWire.terminalCandidateProfileObservation_eq_of_gateMembership_iff": "520e4c036df985fe6f97aa3c59fe3f7b14253fb85fec508464f077031da09d12", "PNP.DirectWire.terminalCandidateSaturate_profile_locality": "90f27df9e3ef24ce34a8ca9ebbe4658cd2c400652701b50f6847f6fbb44aa683", "PNP.DirectWire.terminalCandidateSaturate_profile_preserved": "059c535361ddcce72aae10142584704865fd604cdedc853c71b30e6a213f61da" }, "theoremAxioms": { "PNP.DirectWire.extractTerminalSupport_eq_of_gateSelected_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalAmbientSupportImplementation_eq_of_gateSelected_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateProfileObservation_eq_of_gateMembership_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturate_profile_locality": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturate_profile_preserved": [ "Quot.sound", "propext" ] } }, { "number": 234, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-234", "id": "residual-terminal-saturation-trace-fidelity", "title": "Computed saturation trace fidelity and metadata cost balance", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalSaturationTraceFidelityFormalized": true, "leanResidualTerminalSaturationTraceFidelityAxiomAuditPassed": true, "leanResidualTerminalSaturationTraceFidelityAuditedDeclarationCount": 5, "leanResidualTerminalSaturationReplayTheorem": "PNP.DirectWire.terminalSaturateTrace_replayRecords_iff", "leanResidualTerminalSaturationEventValidityTheorem": "PNP.DirectWire.terminalSaturateTrace_event_valid", "leanResidualTerminalSaturationMetadataTransparencyTheorem": "PNP.DirectWire.terminalCandidateSaturateTrace_metadata_transparent", "leanResidualTerminalSaturationTraceFidelityScope": "all-finite-systems-candidates-executable-models-seeds-generated-events-actual-replay-ambient-endpoint-cost-snapshot-and-metadata-transparency-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalSaturateTrace_replayRecords_iff": "7f80f837010adcb3f2fae342d28dd62abc409952246ae543f7b42d45e5ad4fa4", "PNP.DirectWire.terminalSaturateTrace_event_valid": "c1b87935414b4d1f64511851d7a2f16950aabf4a941ecc67f2d377f8c9435733", "PNP.DirectWire.terminalCandidateSaturateTrace_ambient_eq": "9c95df1a18426898db16b49a2181726decbb73bd693034227e0046b98f8dbff5", "PNP.DirectWire.terminalCandidateSaturateTrace_costSnapshot_eq": "a71b030f39a2e1a75045b984451b286d3ed66101bebea61d97693f9ba23ba6a5", "PNP.DirectWire.terminalCandidateSaturateTrace_metadata_transparent": "e30fc653246ef6cd59ec517a9667f819ad013811f758aa855aa9f02a5ee6fc76" }, "theoremAxioms": { "PNP.DirectWire.terminalSaturateTrace_replayRecords_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalSaturateTrace_event_valid": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_ambient_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_costSnapshot_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_metadata_transparent": [ "Quot.sound", "propext" ] } }, { "number": 235, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-235", "id": "residual-terminal-physical-saturation-accounting", "title": "Actual physical saturation accounting and first-obstruction fidelity", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalPhysicalSaturationAccountingFormalized": true, "leanResidualTerminalPhysicalSaturationAccountingAxiomAuditPassed": true, "leanResidualTerminalPhysicalSaturationAccountingAuditedDeclarationCount": 5, "leanResidualTerminalSaturationEventContextTheorem": "PNP.DirectWire.terminalSaturateTrace_event_context", "leanResidualTerminalPhysicalSaturationSupportCostTheorem": "PNP.DirectWire.terminalCandidateSaturateTrace_supportCostBalanced", "leanResidualTerminalPhysicalSaturationActiveOwnerTheorem": "PNP.DirectWire.terminalCandidateSaturateTrace_event_owner", "leanResidualTerminalPhysicalSaturationObstructionTheorem": "PNP.DirectWire.terminalCandidateSaturateTrace_physicalObstruction", "leanResidualTerminalPhysicalSaturationBalanceOrObstructionTheorem": "PNP.DirectWire.terminalCandidateSaturateTrace_balance_or_physicalObstruction", "leanResidualTerminalPhysicalSaturationAccountingScope": "all-finite-systems-candidates-executable-models-seeds-generated-events-fresh-context-unit-physical-support-cost-active-owner-and-canonical-endpoint-first-obstruction-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalSaturateTrace_event_context": "ee22de07094e37ab879f32dcf4cd29ca950e0ff9077b7b673478fecc77c14649", "PNP.DirectWire.terminalCandidateSaturateTrace_supportCostBalanced": "0b3ea6401032e726f0e43acba13490d9308e323109d0a1d3d1d33aae44080e66", "PNP.DirectWire.terminalCandidateSaturateTrace_event_owner": "ed16113c1dc85a8a77affb8544368ef558cfbccaa8cb6d435ef28f480e10ddb1", "PNP.DirectWire.terminalCandidateSaturateTrace_physicalObstruction": "7b0e659ae86824ee35ef8c5a449cf39b44768e7d5b78173f68fa9d1541e4f9ab", "PNP.DirectWire.terminalCandidateSaturateTrace_balance_or_physicalObstruction": "7d2d28cb4e283178d5d491a6213190a8895661a46bb0bf9973ba60d5b1a100c0" }, "theoremAxioms": { "PNP.DirectWire.terminalSaturateTrace_event_context": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_supportCostBalanced": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_event_owner": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_physicalObstruction": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturateTrace_balance_or_physicalObstruction": [ "Quot.sound", "propext" ] } }, { "number": 236, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-236", "id": "residual-terminal-physical-charge-ledger", "title": "Computed physical-charge partition and introduction provenance", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalPhysicalChargeLedgerFormalized": true, "leanResidualTerminalPhysicalChargeLedgerAxiomAuditPassed": true, "leanResidualTerminalPhysicalChargeLedgerAuditedDeclarationCount": 5, "leanResidualTerminalPhysicalChargeLedgerNodupTheorem": "PNP.DirectWire.terminalSaturatePhysicalCharges_nodup", "leanResidualTerminalPhysicalChargeLedgerCompletenessTheorem": "PNP.DirectWire.terminalSaturatePhysicalCharges_complete", "leanResidualTerminalPhysicalChargeLedgerProvenanceTheorem": "PNP.DirectWire.terminalSaturatePhysicalCharges_provenance", "leanResidualTerminalPhysicalChargeLedgerLookupTheorem": "PNP.DirectWire.terminalSaturatePhysicalChargeProvenance?_iff", "leanResidualTerminalPhysicalChargeLedgerSizeTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalCharges_size", "leanResidualTerminalPhysicalChargeLedgerScope": "all-finite-systems-candidates-executable-models-seeds-computed-physical-nand-charge-partition-nodup-completeness-introduction-provenance-lookup-and-total-support-size-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalSaturatePhysicalCharges_nodup": "0a497b58da7516008c21d16102eb4250efb393185ceb94e1ae5a231c0d52b0ca", "PNP.DirectWire.terminalSaturatePhysicalCharges_complete": "8e0e5f6e186440b15ad4d7df71bd695e66d73c2aa78e1c54464055849ebc884f", "PNP.DirectWire.terminalSaturatePhysicalCharges_provenance": "de03b8300d15fd5811d005d572f55ad8cd40c0be743b08c4d0d360937834324a", "PNP.DirectWire.terminalSaturatePhysicalChargeProvenance?_iff": "5452a6276bb56f83bdfb7faadf64cf3a3f74e3b33d64f362f202c0c63af3dcb8", "PNP.DirectWire.terminalCandidateSaturatePhysicalCharges_size": "0f4f2f19bf24e21a369d29a1ac517235c071f3511f0663dd87af3b854625f8fc" }, "theoremAxioms": { "PNP.DirectWire.terminalSaturatePhysicalCharges_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalSaturatePhysicalCharges_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalSaturatePhysicalCharges_provenance": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalSaturatePhysicalChargeProvenance?_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalCharges_size": [ "Quot.sound", "propext" ] } }, { "number": 237, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-11-237", "id": "residual-terminal-saturated-support-context", "title": "Computed saturated-support replacement context and physical slack", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalSaturatedSupportContextFormalized": true, "leanResidualTerminalSaturatedSupportContextAxiomAuditPassed": true, "leanResidualTerminalSaturatedSupportContextAuditedDeclarationCount": 5, "leanResidualTerminalSaturatedSupportContextBoundaryTheorem": "PNP.DirectWire.terminalCandidateSaturate_boundary_isInput", "leanResidualTerminalSaturatedSupportContextSizeTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_size", "leanResidualTerminalSaturatedSupportContextReconstructionTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_equivalent", "leanResidualTerminalSaturatedSupportContextReplacementTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_replace_equivalent", "leanResidualTerminalSaturatedSupportContextSlackTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalSupport_slack_le", "leanResidualTerminalSaturatedSupportContextScope": "all-finite-candidates-executable-models-seeds-production-saturated-supports-computed-physical-complement-context-primary-input-boundary-exact-gate-partition-whole-boolean-reconstruction-equivalent-replacement-and-physical-slack-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalCandidateSaturate_boundary_isInput": "ec26a0d3919ff6dcf860984c92310bb49a1e5d608e863c05be8733603bd5b270", "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_size": "f0bc6f7e663522a203de0c795593b631dbee10e250ea098434e7b43798182f17", "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_equivalent": "86fb01c46c418f630fcf7d85b8b1706bb78c03e0df292f42c877673258555323", "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_replace_equivalent": "b3404c4072cad4b15a86c1b1a58c83869093f77d1ca15684e61c7d0c22b74aca", "PNP.DirectWire.terminalCandidateSaturatePhysicalSupport_slack_le": "70f1c100034d2f37d8e2f6cc4f437b392e5f9c4adacfbb416fff852c763ec742" }, "theoremAxioms": { "PNP.DirectWire.terminalCandidateSaturate_boundary_isInput": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_size": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalContext_replace_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalSupport_slack_le": [ "Quot.sound", "propext" ] } }, { "number": 238, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-238", "id": "residual-terminal-physical-gain", "title": "Computed proper-support physical gain and exact slack descent", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalPhysicalGainFormalized": true, "leanResidualTerminalPhysicalGainAxiomAuditPassed": true, "leanResidualTerminalPhysicalGainAuditedDeclarationCount": 5, "leanResidualTerminalPhysicalGainEquivalenceTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_equivalent", "leanResidualTerminalPhysicalGainSizeTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_size_gain", "leanResidualTerminalPhysicalGainSlackTheorem": "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_slack_gain", "leanResidualTerminalPhysicalGainSearchSoundnessTheorem": "PNP.DirectWire.findTerminalCandidatePhysicalGain_sound", "leanResidualTerminalPhysicalGainSearchFailureTheorem": "PNP.DirectWire.findTerminalCandidatePhysicalGain_eq_none_iff", "leanResidualTerminalPhysicalGainScope": "all-finite-candidates-executable-models-production-saturated-supports-computed-reference-minimum-replacements-exact-physical-size-and-slack-descent-and-complete-proper-positive-search-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_equivalent": "e1da67101c515204dd045a2f04fb5e8b50cd2c930eb6ae526c3192657180af4a", "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_size_gain": "3b1b137f09a7681341f12a83c5de1713d4116c1baa6f98ac0300da039342cf31", "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_slack_gain": "96dac6e6f5ecc546b311cf0bab666075da5143cd31563aa1e09eaf9cfba4de66", "PNP.DirectWire.findTerminalCandidatePhysicalGain_sound": "f5e4ab7db43a4f9476b036cbed4d58aa0a5a46889ff738e76c71bf354ea79479", "PNP.DirectWire.findTerminalCandidatePhysicalGain_eq_none_iff": "de932d3dd29285c67a55cce7e67378b4ecd805f7daf84516e8c0b9ed3cc7f0fd" }, "theoremAxioms": { "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_size_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalCandidateSaturatePhysicalMinimumReplacement_slack_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.findTerminalCandidatePhysicalGain_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.findTerminalCandidatePhysicalGain_eq_none_iff": [ "Quot.sound", "propext" ] } }, { "number": 239, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-239", "id": "residual-terminal-gain-profile-firewall", "title": "Computed full-profile gain acceptance and exact slack descent", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalGainProfileFirewallFormalized": true, "leanResidualTerminalGainProfileFirewallAxiomAuditPassed": true, "leanResidualTerminalGainProfileFirewallAuditedDeclarationCount": 7, "leanResidualTerminalGainProfileFirewallProfileScanTheorem": "PNP.DirectWire.firstTerminalGainProfileMismatch_eq_none_iff", "leanResidualTerminalGainProfileFirewallFirstMismatchTheorem": "PNP.DirectWire.firstTerminalGainProfileMismatch_spec", "leanResidualTerminalGainProfileFirewallFullMinimumTheorem": "PNP.DirectWire.terminalFullProfileMinimum_eq_of_fullRealization", "leanResidualTerminalGainProfileFirewallAcceptanceTheorem": "PNP.DirectWire.classifyTerminalCandidateGainProfile_accepted_iff", "leanResidualTerminalGainProfileFirewallSearchFailureTheorem": "PNP.DirectWire.classifyTerminalCandidateGainProfile_noGain_iff", "leanResidualTerminalGainProfileFirewallRejectionTheorem": "PNP.DirectWire.classifyTerminalCandidateGainProfile_mismatch_iff", "leanResidualTerminalGainProfileFirewallFullSlackTheorem": "PNP.DirectWire.TerminalCandidateFullProfileGain.fullSlack_gain", "leanResidualTerminalGainProfileFirewallScope": "all-finite-candidates-supplied-executable-profile-models-computed-physical-gain-full-coordinate-first-mismatch-acceptance-and-exact-accepted-full-profile-slack-descent-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.firstTerminalGainProfileMismatch_eq_none_iff": "52aa9325d4a4b8f913638324e694e3d80d7640a630e29e2000b040a28d4dfcb8", "PNP.DirectWire.firstTerminalGainProfileMismatch_spec": "0296facc7457cb22362c0ba0417f1d9db05f472c05a7a80785270f1d0778f7a6", "PNP.DirectWire.terminalFullProfileMinimum_eq_of_fullRealization": "e86e3fcdfbc81b6f1a6d14d631dae151b60d34950ac04f4a0b71b5c1c76764f9", "PNP.DirectWire.classifyTerminalCandidateGainProfile_accepted_iff": "5271b9a9fdc0a1e07d5fe34f74d101a6ebd23ca15f7e21cc9779020761caeefa", "PNP.DirectWire.classifyTerminalCandidateGainProfile_noGain_iff": "1d9f1e3ab39bdfed1ef6692e9aef6042a169a2d74f5d5dae632d5ad5ab036e4a", "PNP.DirectWire.classifyTerminalCandidateGainProfile_mismatch_iff": "dfc8ea46b715beacd6afa5b64988becc4d208d8c19ef8191d592bd4f3dc34a20", "PNP.DirectWire.TerminalCandidateFullProfileGain.fullSlack_gain": "52a4af27b6946c6dee5fc9a0d00f3f5b1fc80a7a8a23c7153f0621953fff3ab9" }, "theoremAxioms": { "PNP.DirectWire.firstTerminalGainProfileMismatch_eq_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.firstTerminalGainProfileMismatch_spec": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalFullProfileMinimum_eq_of_fullRealization": [ "propext" ], "PNP.DirectWire.classifyTerminalCandidateGainProfile_accepted_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.classifyTerminalCandidateGainProfile_noGain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.classifyTerminalCandidateGainProfile_mismatch_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalCandidateFullProfileGain.fullSlack_gain": [ "Quot.sound", "propext" ] } }, { "number": 240, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-240", "id": "residual-independent-materializer-cost", "title": "Independent NAND materializer exact minimum-cost additivity", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualIndependentMaterializerCostFormalized": true, "leanResidualIndependentMaterializerCostAxiomAuditPassed": true, "leanResidualIndependentMaterializerCostAuditedDeclarationCount": 7, "leanResidualIndependentMaterializerCostSizeTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_size", "leanResidualIndependentMaterializerCostOriginalOutputsTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_original", "leanResidualIndependentMaterializerCostFreshOutputsTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_materializer", "leanResidualIndependentMaterializerCostLowerBoundTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_lower_bound", "leanResidualIndependentMaterializerCostEquivalenceTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_equivalent", "leanResidualIndependentMaterializerCostMinimumTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_referenceMinimum", "leanResidualIndependentMaterializerCostSlackTheorem": "PNP.DirectWire.appendIndependentNandMaterializers_residualSlack", "leanResidualIndependentMaterializerCostScope": "all-finite-original-candidates-and-bank-sizes-disjoint-fresh-input-nand-materializers-computed-erasure-unrestricted-competitors-exact-reference-minimum-additivity-and-physical-slack-preservation-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.appendIndependentNandMaterializers_size": "b9e62d820791057b85d460f0f0e4fcdf75b548ade178ffb02f6afbe43342007f", "PNP.DirectWire.appendIndependentNandMaterializers_original": "7e65839855b25defa669921d118f54469f1adad851557433c6b2a3916bd0497b", "PNP.DirectWire.appendIndependentNandMaterializers_materializer": "b4ec58852a66b2b707ddac5378b3fce1481889d9e89a3be878cf3345fcdc81a1", "PNP.DirectWire.appendIndependentNandMaterializers_lower_bound": "d775d0bd12c5cb8af9a3ab08fd05a21637f1d724aff0bf3f28c93997db70ccdf", "PNP.DirectWire.appendIndependentNandMaterializers_equivalent": "e4ca1a4bc815ba9e1be215fff9ca41e24e10e90a43f627ea000eee029899ca68", "PNP.DirectWire.appendIndependentNandMaterializers_referenceMinimum": "0b9830efe900d365e70e4150003eb0df18c3da3ba28e17df580edd64db48ccf8", "PNP.DirectWire.appendIndependentNandMaterializers_residualSlack": "d4809059a0690effa9e02fa217a7d6ce6b59faaef074efb2f42a9d728e1e35c2" }, "theoremAxioms": { "PNP.DirectWire.appendIndependentNandMaterializers_size": [], "PNP.DirectWire.appendIndependentNandMaterializers_original": [ "Quot.sound" ], "PNP.DirectWire.appendIndependentNandMaterializers_materializer": [ "Quot.sound", "propext" ], "PNP.DirectWire.appendIndependentNandMaterializers_lower_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.appendIndependentNandMaterializers_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.appendIndependentNandMaterializers_referenceMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.appendIndependentNandMaterializers_residualSlack": [ "Quot.sound", "propext" ] } }, { "number": 241, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-241", "id": "residual-terminal-physical-ownership", "title": "Support-independent physical ownership and exact materializer charges", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanResidualTerminalPhysicalOwnershipFormalized": true, "leanResidualTerminalPhysicalOwnershipAxiomAuditPassed": true, "leanResidualTerminalPhysicalOwnershipAuditedDeclarationCount": 10, "leanResidualTerminalPhysicalOwnershipUnrequestedTheorem": "PNP.DirectWire.terminalPhysicalOwner_none_iff", "leanResidualTerminalPhysicalOwnershipFirstOwnerTheorem": "PNP.DirectWire.terminalPhysicalOwner_first", "leanResidualTerminalPhysicalOwnershipPartitionTheorem": "PNP.DirectWire.terminalOwnedPhysicalGates_partition", "leanResidualTerminalPhysicalOwnershipDisjointTheorem": "PNP.DirectWire.terminalOwnedPhysicalGates_disjoint", "leanResidualTerminalPhysicalOwnershipRestrictionTheorem": "PNP.DirectWire.terminalOwnedPhysicalGates_restrict", "leanResidualTerminalPhysicalOwnershipGateCountTheorem": "PNP.DirectWire.terminalOwnedPhysicalMaterializer_gateCount", "leanResidualTerminalPhysicalOwnershipChargeIdentityTheorem": "PNP.DirectWire.terminalOwnedPhysicalMaterializer_chargeIdentity", "leanResidualTerminalPhysicalOwnershipOpenSemanticsTheorem": "PNP.DirectWire.terminalOwnedPhysicalMaterializer_semantics", "leanResidualTerminalPhysicalOwnershipInducedSemanticsTheorem": "PNP.DirectWire.terminalOwnedPhysicalMaterializer_induced", "leanResidualTerminalPhysicalOwnershipWholeChargeTheorem": "PNP.DirectWire.terminalOwnedPhysicalMaterializer_wholeCharge", "leanResidualTerminalPhysicalOwnershipScope": "all-finite-candidates-raw-request-families-and-supports-first-requester-ambient-ownership-fixed-remainder-disjoint-stable-physical-pieces-actual-extracted-nand-counts-open-semantics-and-exact-charge-total-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalPhysicalOwner_none_iff": "ffc0ed143bf7e48c93f51515386fd85a50d91876ef9079208c85da56384caecc", "PNP.DirectWire.terminalPhysicalOwner_first": "ea71fecbc78798ce11593d9f1a9991444ed2441a909b02e9a9e64fdbb0791ac7", "PNP.DirectWire.terminalOwnedPhysicalGates_partition": "fcc78b43e37b2ecff81821ca824b6846cbd7dedbc034a964e02604780c234792", "PNP.DirectWire.terminalOwnedPhysicalGates_disjoint": "309b77fc6c02991fe447b18c499ffded34920f11e8e5738eb915edbdebceec60", "PNP.DirectWire.terminalOwnedPhysicalGates_restrict": "5ad710531d391c95b4159defd761557215dfc0bceefcbced744060569dee942f", "PNP.DirectWire.terminalOwnedPhysicalMaterializer_gateCount": "fa95da38296729083ca7fc691fb6ddb2519b8cb14a5cdd7131a56baacd838678", "PNP.DirectWire.terminalOwnedPhysicalMaterializer_chargeIdentity": "536ab6d2243bb5599225af8762bebc639928dd957692cc58a4e38c16f7d05fbe", "PNP.DirectWire.terminalOwnedPhysicalMaterializer_semantics": "8de6988c721b8734eea3bea0f9c66a58ef6b149f93a3366e195570422ca02c3b", "PNP.DirectWire.terminalOwnedPhysicalMaterializer_induced": "6382079281a6e01dc636253438900d6528f761ff9c5fc8e2001d02da554fac7a", "PNP.DirectWire.terminalOwnedPhysicalMaterializer_wholeCharge": "2cf21f36ac2063dd4093521f5eb5de20647af79da6848811ce8fae59b33b27a0" }, "theoremAxioms": { "PNP.DirectWire.terminalPhysicalOwner_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalPhysicalOwner_first": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOwnedPhysicalGates_partition": [ "propext" ], "PNP.DirectWire.terminalOwnedPhysicalGates_disjoint": [ "propext" ], "PNP.DirectWire.terminalOwnedPhysicalGates_restrict": [ "propext" ], "PNP.DirectWire.terminalOwnedPhysicalMaterializer_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOwnedPhysicalMaterializer_chargeIdentity": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOwnedPhysicalMaterializer_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOwnedPhysicalMaterializer_induced": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOwnedPhysicalMaterializer_wholeCharge": [ "Quot.sound", "propext" ] } }, { "number": 242, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-242", "id": "pccmin-constructive-nand-sharing", "title": "Constructive whole-program NAND sharing and checked normalization", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanPCCMinConstructiveNANDSharingFormalized": true, "leanPCCMinConstructiveNANDSharingAxiomAuditPassed": true, "leanPCCMinConstructiveNANDSharingAuditedDeclarationCount": 9, "leanPCCMinConstructiveNANDSharingAliasSemanticsTheorem": "PNP.DirectWire.compileNANDSharing_alias_semantics", "leanPCCMinConstructiveNANDSharingGateAccountingTheorem": "PNP.DirectWire.compileNANDSharing_exact_accounting", "leanPCCMinConstructiveNANDSharingEquivalenceTheorem": "PNP.DirectWire.sharingImplementation_equivalent", "leanPCCMinConstructiveNANDSharingGateCountTheorem": "PNP.DirectWire.sharingImplementation_gateCount_le", "leanPCCMinConstructiveNANDSharingReferenceMinimumTheorem": "PNP.DirectWire.sharingImplementation_referenceMinimum", "leanPCCMinConstructiveNANDSharingResidualSlackTheorem": "PNP.DirectWire.sharingImplementation_residualSlack", "leanPCCMinConstructiveNANDSharingStrictGainTheorem": "PNP.DirectWire.sharingImplementation_strictGain_iff", "leanPCCMinConstructiveNANDSharingStrictResidualDescentTheorem": "PNP.DirectWire.sharingImplementation_strictResidualDescent", "leanPCCMinConstructiveNANDSharingNormalizerTheorem": "PNP.DirectWire.nandSharingNormalizer_checked", "leanPCCMinConstructiveNANDSharingScope": "all-finite-nand-programs-and-ordered-outputs-computed-structural-and-commuted-reuse-alias-semantics-exact-fold-accounting-invariant-reference-minimum-residual-descent-and-concrete-normalizer-stage-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.compileNANDSharing_alias_semantics": "4deb034903ad839c8a3b4b239a3eedac0b9015b2ca80f813887ab3fe0da96822", "PNP.DirectWire.compileNANDSharing_exact_accounting": "164deeba19f4e72d48b14460ecf95cab0aaaa5d9f1bd0d7c162197c2254c0c82", "PNP.DirectWire.sharingImplementation_equivalent": "bf6462df6f7b2be0f1e107c0de6e9dbfe0d60f95207d32da437ba4d3e9bba1f8", "PNP.DirectWire.sharingImplementation_gateCount_le": "2e8b717281088e2f705da023dcf9c3e70c36eb734e6b2e1cc21d011f743fe5b4", "PNP.DirectWire.sharingImplementation_referenceMinimum": "1765f52468d594f9b61339121daf6522ab56cc1b1b2ce3c8ea0bc7a5b339a263", "PNP.DirectWire.sharingImplementation_residualSlack": "a5dee1ecca503f2fbc2d154a79fece88bf4c9b22ba1b836c17222e62731cae1d", "PNP.DirectWire.sharingImplementation_strictGain_iff": "5de93eb4cd692308ffce27770919129d605624fc0b0983d46cbe1f6fc675104d", "PNP.DirectWire.sharingImplementation_strictResidualDescent": "78ca908349b5ce03bd5e8585dcfed98eb3a24cd860337fab2681d8e435cc19cf", "PNP.DirectWire.nandSharingNormalizer_checked": "9ad481fa3cf574495fe90302d3f8945fe4917791935b065cbc86f51aef60b7fd" }, "theoremAxioms": { "PNP.DirectWire.compileNANDSharing_alias_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.compileNANDSharing_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.sharingImplementation_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.sharingImplementation_gateCount_le": [ "Quot.sound", "propext" ], "PNP.DirectWire.sharingImplementation_referenceMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.sharingImplementation_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.sharingImplementation_strictGain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.sharingImplementation_strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.nandSharingNormalizer_checked": [ "Quot.sound", "propext" ] } }, { "number": 243, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-243", "id": "concrete-final-report-bridge", "title": "Checked concrete SAT hardness in the active conditional final-report bridge", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanConcreteFinalReportBridgeFormalized": true, "leanConcreteFinalReportBridgeAxiomAuditPassed": true, "leanConcreteFinalReportBridgeAuditedDeclarationCount": 4, "leanConcreteFinalReportBridgeSATHardnessTheorem": "PNP.sat_np_hard_checked", "leanConcreteFinalReportBridgeSATCompletenessTheorem": "PNP.sat_np_complete_checked", "leanConcreteFinalReportBridgePackageConsequenceTheorem": "PNP.accepted_generated_package_implies_p_eq_np", "leanConcreteFinalReportBridgeFinalReportTheorem": "PNP.final_report_bridge", "leanConcreteFinalReportBridgeRequiresSuppliedSATHardness": false, "leanConcreteFinalReportBridgeLoopCertificateExistenceDischarged": false, "leanConcreteFinalReportBridgeScope": "checked-all-input-concrete-cook-levin-hardness-consumed-by-the-active-conditional-final-report-bridge-explicit-proof-bearing-pccmin-loop-existence-still-required" }, "theoremKernelTypeSha256": { "PNP.sat_np_hard_checked": "ebcaa13f070d5b1f8fc0105e0feea71c65010f94a5e135ae0c4abaf4544fb382", "PNP.sat_np_complete_checked": "4ed163e43a3c4fd3be9ea3d1d5c348a0ce4951beb322aca3c617265e63b0fd26", "PNP.accepted_generated_package_implies_p_eq_np": "89cfb0983711ce18a75e458324047e6007ac456dbdc926f09080db41d826379f", "PNP.final_report_bridge": "956062f71216218a1edb59039ae63f85c01564a93e7a1e891754127f3e22c8a5" }, "theoremAxioms": { "PNP.sat_np_hard_checked": [ "Classical.choice", "Quot.sound", "propext" ], "PNP.sat_np_complete_checked": [ "Classical.choice", "Quot.sound", "propext" ], "PNP.accepted_generated_package_implies_p_eq_np": [ "Classical.choice", "Quot.sound", "propext" ], "PNP.final_report_bridge": [ "Classical.choice", "Quot.sound", "propext" ] } }, { "number": 244, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-244", "id": "pccmin-output-cone-pruning", "title": "Derived physical output cones and checked unused-gate pruning", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanPCCMinOutputConePruningFormalized": true, "leanPCCMinOutputConePruningAxiomAuditPassed": true, "leanPCCMinOutputConePruningAuditedDeclarationCount": 11, "leanPCCMinOutputConePruningOutputCoverageTheorem": "PNP.DirectWire.outputConeRecords_output", "leanPCCMinOutputConePruningPredecessorClosureTheorem": "PNP.DirectWire.outputConeRecords_closed", "leanPCCMinOutputConePruningLeastConeTheorem": "PNP.DirectWire.outputConeRecords_least", "leanPCCMinOutputConePruningNoExternalGateTheorem": "PNP.DirectWire.outputConeRecords_noExternalGate", "leanPCCMinOutputConePruningEquivalenceTheorem": "PNP.DirectWire.outputConeImplementation_equivalent", "leanPCCMinOutputConePruningGateCountTheorem": "PNP.DirectWire.outputConeImplementation_gateCount_le", "leanPCCMinOutputConePruningGateAccountingTheorem": "PNP.DirectWire.outputConeImplementation_exact_accounting", "leanPCCMinOutputConePruningReferenceMinimumTheorem": "PNP.DirectWire.outputConeImplementation_referenceMinimum", "leanPCCMinOutputConePruningResidualSlackTheorem": "PNP.DirectWire.outputConeImplementation_residualSlack", "leanPCCMinOutputConePruningStrictGainTheorem": "PNP.DirectWire.outputConeImplementation_strictGain_iff", "leanPCCMinOutputConePruningNormalizerTheorem": "PNP.DirectWire.outputConeNormalizer_checked", "leanPCCMinOutputConePruningFullProfilePreservationProved": false, "leanPCCMinOutputConePruningPolynomialRuntimeProved": false, "leanPCCMinOutputConePruningScope": "all-finite-nand-candidates-derived-least-physical-output-predecessor-cone-checked-support-extraction-original-io-semantics-exact-deletion-accounting-and-physical-normalizer-stage-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.outputConeRecords_output": "4a84fda6540cca8fb6973022a6b2fd87a24e4dcb3d9fb88fdfd7c8a220fb4cd3", "PNP.DirectWire.outputConeRecords_closed": "35b36dfb577ea36b54a521a9821c3e8d8fd9b561aa8621f87160088ad2607005", "PNP.DirectWire.outputConeRecords_least": "acbdad00014ed703ae3b6e5d8752f55e13d47c0238b477892758b9ca0fbb572d", "PNP.DirectWire.outputConeRecords_noExternalGate": "378d1260b7d2ee62fe165ac89564e432ba1747781f13686e17d9a83e75cf47be", "PNP.DirectWire.outputConeImplementation_equivalent": "064356bbc6da79448d31aa75eb34b149ee082822f42a2521b60da9930f85bcb6", "PNP.DirectWire.outputConeImplementation_gateCount_le": "8da639dbcc1460fb5ef3f78e62cc27e8379c52ce5a8181a0ef9fe54644fe95cc", "PNP.DirectWire.outputConeImplementation_exact_accounting": "c794c33214594e260a14552758c307ea23e1c3c945388c3a27a496263cb739a4", "PNP.DirectWire.outputConeImplementation_referenceMinimum": "a607337089e55510c9b9c32b166b739b728b3626fa58c63f043d35817b82308b", "PNP.DirectWire.outputConeImplementation_residualSlack": "8a9a1ad3414ffd5caf2ee0ee7a3bc9f1f7db7ac3654b34eff9d189fdeb5c327b", "PNP.DirectWire.outputConeImplementation_strictGain_iff": "74d077b8e8abb30b93dfefa3d0b836c39794144e2fa3b55883b6ea1040e5ef35", "PNP.DirectWire.outputConeNormalizer_checked": "943e610f7a7ff686071f1adda11a52a5659428fa1fa8649254444ca20e982fd6" }, "theoremAxioms": { "PNP.DirectWire.outputConeRecords_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeRecords_closed": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeRecords_least": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeRecords_noExternalGate": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeImplementation_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeImplementation_gateCount_le": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeImplementation_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeImplementation_referenceMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeImplementation_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeImplementation_strictGain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.outputConeNormalizer_checked": [ "Quot.sound", "propext" ] } }, { "number": 245, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-245", "id": "pccmin-dead-support-context", "title": "Computed dead-support frames and proper physical deletion", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanPCCMinDeadSupportContextFormalized": true, "leanPCCMinDeadSupportContextAxiomAuditPassed": true, "leanPCCMinDeadSupportContextAuditedDeclarationCount": 20, "leanPCCMinDeadSupportContextFrontierSemanticsTheorem": "PNP.DirectWire.outputConeFrontierCandidate_semantics", "leanPCCMinDeadSupportContextEmptyInterfaceTheorem": "PNP.DirectWire.deadSupport_interface_empty", "leanPCCMinDeadSupportContextGatePartitionTheorem": "PNP.DirectWire.deadSupportGateCount_partition", "leanPCCMinDeadSupportContextDeletedCountTheorem": "PNP.DirectWire.deadSupportGateCount_eq_deleted", "leanPCCMinDeadSupportContextBoundaryValuesTheorem": "PNP.DirectWire.deadSupportEnvironment_boundary", "leanPCCMinDeadSupportContextBypassOutputsTheorem": "PNP.DirectWire.deadSupportEnvironment_bypass", "leanPCCMinDeadSupportContextActualExtractionTheorem": "PNP.DirectWire.deadSupportCandidate_extracted", "leanPCCMinDeadSupportContextExtractedProgramTheorem": "PNP.DirectWire.deadSupportCandidate_program", "leanPCCMinDeadSupportContextLocalEquivalenceTheorem": "PNP.DirectWire.deadSupportEmptyReplacement_equivalent", "leanPCCMinDeadSupportContextFramedEquivalenceTheorem": "PNP.DirectWire.deadSupportContext_plug_equivalent", "leanPCCMinDeadSupportContextOriginalFrameSizeTheorem": "PNP.DirectWire.deadSupportContext_original_size", "leanPCCMinDeadSupportContextReplacementGateCountTheorem": "PNP.DirectWire.deadSupportReplacement_gateCount", "leanPCCMinDeadSupportContextReplacementEquivalenceTheorem": "PNP.DirectWire.deadSupportReplacement_equivalent", "leanPCCMinDeadSupportContextReplacementAccountingTheorem": "PNP.DirectWire.deadSupportReplacement_accounting", "leanPCCMinDeadSupportContextResidualSlackTheorem": "PNP.DirectWire.deadSupportReplacement_residualSlack", "leanPCCMinDeadSupportContextStrictGainTheorem": "PNP.DirectWire.deadSupportReplacement_strictGain_iff", "leanPCCMinDeadSupportContextProperAcceptanceTheorem": "PNP.DirectWire.deadSupportProperGain_isSome_iff", "leanPCCMinDeadSupportContextProperGainSoundnessTheorem": "PNP.DirectWire.deadSupportProperGain_sound", "leanPCCMinDeadSupportContextAllDeadRejectionTheorem": "PNP.DirectWire.deadSupportProperGain_none_of_all_dead", "leanPCCMinDeadSupportContextNoDeadRejectionTheorem": "PNP.DirectWire.deadSupportProperGain_none_of_no_dead", "leanPCCMinDeadSupportContextFullProfileAdmissibilityProved": false, "leanPCCMinDeadSupportContextCompletePackageEVerifierProved": false, "leanPCCMinDeadSupportContextPolynomialRuntimeProved": false, "leanPCCMinDeadSupportContextScope": "all-finite-nand-implementations-computed-dead-gate-complement-empty-interface-exact-extracted-support-live-frontier-environment-framed-replacement-and-nonempty-proper-physical-gain-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.outputConeFrontierCandidate_semantics": "3dc1bb632f4ffbc3f0f1c8b32c170e70b6ba9812eb06eb4066c75d9a6f3f0055", "PNP.DirectWire.deadSupport_interface_empty": "906b882fffcfde65b4de880537a04e1ec9dacb5647cbcb9bc8ec4d80abbf83f8", "PNP.DirectWire.deadSupportGateCount_partition": "6edafb52a2e5ff5d1866967dd0a8b4a94b759429dc0d71486ccd5b6d76ad563a", "PNP.DirectWire.deadSupportGateCount_eq_deleted": "82d59d27ed1c3cd19002619b0d1cfbb0606623acafcaf1c6fa659905da8a368b", "PNP.DirectWire.deadSupportEnvironment_boundary": "162da320d61d2549c4fdbf27b8c6d91d1462fa130d351b14d87af2e39fcca254", "PNP.DirectWire.deadSupportEnvironment_bypass": "7a706583784a3a8000d311fc7d744eee0afcda9bbeb244cb59df9ad5aa3f5c68", "PNP.DirectWire.deadSupportCandidate_extracted": "eda366bcc7644aad67a9a8ff4a47b8911fe7d9defe1cfb08e707913c29605cf1", "PNP.DirectWire.deadSupportCandidate_program": "e3b9e0c33c87b292695750a5e2b3b17ff3c190ccbe5b314647ca6367496c7fb2", "PNP.DirectWire.deadSupportEmptyReplacement_equivalent": "a491c8f37fa95a7803005f043458bf5e0d62066c51082781b9d3764acede3e9f", "PNP.DirectWire.deadSupportContext_plug_equivalent": "5de578a40f9d237158105924b2591a08cf0576898fed1eaab43799879c6343ec", "PNP.DirectWire.deadSupportContext_original_size": "4c0b8ad72564b492a3e161db0f6c3d4f5731da4959b699585c8d8dbe5da54d71", "PNP.DirectWire.deadSupportReplacement_gateCount": "e3049d0cee3f4870ea9d8f60100ff98dcd8105310e20579ba4f80b0f53d4870c", "PNP.DirectWire.deadSupportReplacement_equivalent": "d5c1b86dfb34461c8b300d3647fcf54e8cf46b3104122595beb6368b2660bc2a", "PNP.DirectWire.deadSupportReplacement_accounting": "61abe459f6ba20d1aea0ec9b3c26821fbf405e12aea50fdaa986a89c90fb186c", "PNP.DirectWire.deadSupportReplacement_residualSlack": "5adb0248d3e63508b978489c8710df0d8ee4835cd2e8e33ea6d8fd7f4971225c", "PNP.DirectWire.deadSupportReplacement_strictGain_iff": "9620a0e22c4e3cafafdf4ee248b08b0d5205b3e378e4bed1aa743be59a8f7b26", "PNP.DirectWire.deadSupportProperGain_isSome_iff": "c031fe639898d6671d76e28409b5204852aa290dd37c6e294b6a641fd1cc55b2", "PNP.DirectWire.deadSupportProperGain_sound": "51cc13a8b4d0c917107a5199e03f5a5a862e30b01ad4c3d6265c2065daf755a2", "PNP.DirectWire.deadSupportProperGain_none_of_all_dead": "c7b2036d09f1e80c0f2367ed5046c49fc5aea9412e2b59b7404ddc4bad68dc11", "PNP.DirectWire.deadSupportProperGain_none_of_no_dead": "36242686b99f11d533a8fd54ab724dd586c89e621d25d9bea4b0ab3e57d0c40a" }, "theoremAxioms": { "PNP.DirectWire.outputConeFrontierCandidate_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupport_interface_empty": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportGateCount_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportGateCount_eq_deleted": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportEnvironment_boundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportEnvironment_bypass": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportCandidate_extracted": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportCandidate_program": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportEmptyReplacement_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportContext_plug_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportContext_original_size": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportReplacement_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportReplacement_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportReplacement_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportReplacement_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportReplacement_strictGain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportProperGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportProperGain_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportProperGain_none_of_all_dead": [ "Quot.sound", "propext" ], "PNP.DirectWire.deadSupportProperGain_none_of_no_dead": [ "Quot.sound", "propext" ] } }, { "number": 246, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-246", "id": "pccmin-dead-support-full-mode", "title": "Full finite-profile and obligation acceptance for computed dead-support gains", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanPCCMinDeadSupportFullModeFormalized": true, "leanPCCMinDeadSupportFullModeAxiomAuditPassed": true, "leanPCCMinDeadSupportFullModeAuditedDeclarationCount": 8, "leanPCCMinDeadSupportFullModeObligationScanTheorem": "PNP.DirectWire.firstTerminalOpenObligation_eq_none_iff", "leanPCCMinDeadSupportFullModeFirstOpenObligationTheorem": "PNP.DirectWire.firstTerminalOpenObligation_spec", "leanPCCMinDeadSupportFullModeCurrentObligationsTheorem": "PNP.DirectWire.DeadSupportFullModeGain.currentObligationsDischarged", "leanPCCMinDeadSupportFullModeAcceptanceTheorem": "PNP.DirectWire.classifyDeadSupportFullMode_accepted_iff", "leanPCCMinDeadSupportFullModeNoProperSupportTheorem": "PNP.DirectWire.classifyDeadSupportFullMode_noProperSupport_iff", "leanPCCMinDeadSupportFullModeFullProfileMinimumTheorem": "PNP.DirectWire.DeadSupportFullModeGain.fullProfileMinimum", "leanPCCMinDeadSupportFullModeAcceptedSoundnessTheorem": "PNP.DirectWire.DeadSupportFullModeGain.checked", "leanPCCMinDeadSupportFullModeClassifierSoundnessTheorem": "PNP.DirectWire.classifyDeadSupportFullMode_checked", "leanPCCMinDeadSupportFullModeManuscriptCarrierDerived": false, "leanPCCMinDeadSupportFullModeCompletePackageEVerifierProved": false, "leanPCCMinDeadSupportFullModePolynomialRuntimeProved": false, "leanPCCMinDeadSupportFullModeScope": "computed-proper-dead-support-complete-finite-profile-and-observed-obligation-acceptance-over-input-observation-system-no-derived-manuscript-carrier-or-discharge-ledger" }, "theoremKernelTypeSha256": { "PNP.DirectWire.firstTerminalOpenObligation_eq_none_iff": "1a0c93b1d9ce168b0e077280cb41ed9ab682db406f7d6915b2fe6e327a1de60d", "PNP.DirectWire.firstTerminalOpenObligation_spec": "123d777771db64aaaf53b9dd42a834694d86f7088c8d422008be7f445842e8be", "PNP.DirectWire.DeadSupportFullModeGain.currentObligationsDischarged": "4439af8e42be526327a645db512351e9373ca77858c4adb172d5167b23a684d1", "PNP.DirectWire.classifyDeadSupportFullMode_accepted_iff": "b552736e74904695506adb00c52b18047de6cdc4af1890f01d5a66a4b8cca642", "PNP.DirectWire.classifyDeadSupportFullMode_noProperSupport_iff": "d08c20b2c7b9af0a2cdc926dcf66fe1bb7809c1d0cddd3f5ecee698c6454188a", "PNP.DirectWire.DeadSupportFullModeGain.fullProfileMinimum": "feeab8f455701e6dd448e31dab4a596148cc02258492127d0f40cdde76a99f44", "PNP.DirectWire.DeadSupportFullModeGain.checked": "4cad2c9d19dd6d8d490643fe8145e7962898c2cb63eef3af2560f31a21baf729", "PNP.DirectWire.classifyDeadSupportFullMode_checked": "e45814982c40279fd2e49a52e93e7428012a6dc5003e3effc7222977a0fb8e50" }, "theoremAxioms": { "PNP.DirectWire.firstTerminalOpenObligation_eq_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.firstTerminalOpenObligation_spec": [ "Quot.sound", "propext" ], "PNP.DirectWire.DeadSupportFullModeGain.currentObligationsDischarged": [ "Quot.sound", "propext" ], "PNP.DirectWire.classifyDeadSupportFullMode_accepted_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.classifyDeadSupportFullMode_noProperSupport_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.DeadSupportFullModeGain.fullProfileMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.DeadSupportFullModeGain.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.classifyDeadSupportFullMode_checked": [ "Quot.sound", "propext" ] } }, { "number": 247, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-247", "id": "pccmin-constant-propagation", "title": "Computed constant propagation through arbitrary NAND programs", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanPCCMinConstantPropagationFormalized": true, "leanPCCMinConstantPropagationAxiomAuditPassed": true, "leanPCCMinConstantPropagationAuditedDeclarationCount": 10, "leanPCCMinConstantPropagationConstantRuleTheorem": "PNP.DirectWire.constantGateValue_sound", "leanPCCMinConstantPropagationAliasSemanticsTheorem": "PNP.DirectWire.compileNANDConstantPropagation_alias_semantics", "leanPCCMinConstantPropagationGateAccountingTheorem": "PNP.DirectWire.compileNANDConstantPropagation_exact_accounting", "leanPCCMinConstantPropagationEquivalenceTheorem": "PNP.DirectWire.constantPropagationImplementation_equivalent", "leanPCCMinConstantPropagationGateCountTheorem": "PNP.DirectWire.constantPropagationImplementation_gateCount_le", "leanPCCMinConstantPropagationReferenceMinimumTheorem": "PNP.DirectWire.constantPropagationImplementation_referenceMinimum", "leanPCCMinConstantPropagationResidualSlackTheorem": "PNP.DirectWire.constantPropagationImplementation_residualSlack", "leanPCCMinConstantPropagationStrictGainTheorem": "PNP.DirectWire.constantPropagationImplementation_strictGain_iff", "leanPCCMinConstantPropagationResidualDescentTheorem": "PNP.DirectWire.constantPropagationImplementation_strictResidualDescent", "leanPCCMinConstantPropagationNormalizerTheorem": "PNP.DirectWire.nandConstantPropagationNormalizer_checked", "leanPCCMinConstantPropagationFullProfilePreservationProved": false, "leanPCCMinConstantPropagationCompleteNormalizationProved": false, "leanPCCMinConstantPropagationPolynomialRuntimeProved": false, "leanPCCMinConstantPropagationScope": "all-finite-direct-wire-nand-programs-computed-literal-constant-propagation-through-source-aliases-complete-ordered-io-exact-elimination-accounting-physical-normalizer-stage-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.constantGateValue_sound": "0ec6cff2be375dc0eb181e160e267405a485d3e2ac41b4a8cec33b994f02b2a8", "PNP.DirectWire.compileNANDConstantPropagation_alias_semantics": "499c24a8a4455a18159223191f8879034e87f39f45493973fb81c4076c4ced7e", "PNP.DirectWire.compileNANDConstantPropagation_exact_accounting": "50d1f42a8732f6563a48dec3a1c364f41ed9fccfb0b4c7ed72faa382c3013c87", "PNP.DirectWire.constantPropagationImplementation_equivalent": "85b42a5ccf8a28af9ba9b19ee9b73eecc63dfe63ca306777b395881fc6c9aabc", "PNP.DirectWire.constantPropagationImplementation_gateCount_le": "7da5157348a386861cf8b2cb5ef617fc89d16409f8640de9376957b344b3ab29", "PNP.DirectWire.constantPropagationImplementation_referenceMinimum": "9631c6094e82f3e0ce1b4c45bb4fa4e892321fd2746ff3437cddafd9130c9ae3", "PNP.DirectWire.constantPropagationImplementation_residualSlack": "532ee6acbab9c551e3da7a3cb6296b1c405458f6bb821e059826bb3aed1c0981", "PNP.DirectWire.constantPropagationImplementation_strictGain_iff": "f2447341b74dc43f0d98a5fb3a63dc153eef0da71d28017060be06238796d7e6", "PNP.DirectWire.constantPropagationImplementation_strictResidualDescent": "96c02d048c9f50fb371e546364a55c1d5bf364fdcb626b38aafda1f9724fb785", "PNP.DirectWire.nandConstantPropagationNormalizer_checked": "7d26c6a7ceba21244ab334e8524b55ee9ff5e0f046c5c535506d2553f8106b3b" }, "theoremAxioms": { "PNP.DirectWire.constantGateValue_sound": [], "PNP.DirectWire.compileNANDConstantPropagation_alias_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.compileNANDConstantPropagation_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.constantPropagationImplementation_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.constantPropagationImplementation_gateCount_le": [ "Quot.sound", "propext" ], "PNP.DirectWire.constantPropagationImplementation_referenceMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.constantPropagationImplementation_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.constantPropagationImplementation_strictGain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.constantPropagationImplementation_strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.nandConstantPropagationNormalizer_checked": [ "Quot.sound", "propext" ] } }, { "number": 248, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-248", "id": "pccmin-physical-normalization-closure", "title": "Computed closure of constant propagation, NAND sharing and output-cone pruning", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanPCCMinPhysicalNormalizationClosureFormalized": true, "leanPCCMinPhysicalNormalizationClosureAxiomAuditPassed": true, "leanPCCMinPhysicalNormalizationClosureAuditedDeclarationCount": 12, "leanPCCMinPhysicalNormalizationClosurePassEquivalenceTheorem": "PNP.DirectWire.physicalNormalizationPass_equivalent", "leanPCCMinPhysicalNormalizationClosurePassAccountingTheorem": "PNP.DirectWire.physicalNormalizationPass_exact_accounting", "leanPCCMinPhysicalNormalizationClosureSelectedGainTheorem": "PNP.DirectWire.PhysicalNormalizationGain.checked", "leanPCCMinPhysicalNormalizationClosurePrioritySelectionTheorem": "PNP.DirectWire.nextPhysicalNormalizationStep_checked", "leanPCCMinPhysicalNormalizationClosureTraceAccountingTheorem": "PNP.DirectWire.PhysicalNormalizationTrace.checked", "leanPCCMinPhysicalNormalizationClosureComputedClosureTheorem": "PNP.DirectWire.runPhysicalNormalization_checked", "leanPCCMinPhysicalNormalizationClosureQuiescentInputTheorem": "PNP.DirectWire.runPhysicalNormalization_of_quiescent", "leanPCCMinPhysicalNormalizationClosureIdempotenceTheorem": "PNP.DirectWire.runPhysicalNormalization_idempotent", "leanPCCMinPhysicalNormalizationClosureReferenceMinimumTheorem": "PNP.DirectWire.runPhysicalNormalization_referenceMinimum", "leanPCCMinPhysicalNormalizationClosureResidualSlackTheorem": "PNP.DirectWire.runPhysicalNormalization_residualSlack", "leanPCCMinPhysicalNormalizationClosureIterationBoundTheorem": "PNP.DirectWire.runPhysicalNormalization_gainIterations_le_residualSlack", "leanPCCMinPhysicalNormalizationClosureNormalizerTheorem": "PNP.DirectWire.physicalClosureNormalizer_checked", "leanPCCMinPhysicalNormalizationClosureFullProfilePreservationProved": false, "leanPCCMinPhysicalNormalizationClosureCompleteNormalizationProved": false, "leanPCCMinPhysicalNormalizationClosurePolynomialRuntimeProved": false, "leanPCCMinPhysicalNormalizationClosureScope": "all-finite-direct-wire-implementations-computed-priority-three-pass-physical-closure-common-quiescence-actual-strict-trace-exact-savings-idempotent-result-no-complete-manuscript-normalization-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.physicalNormalizationPass_equivalent": "1e98dba1264aa27ff4c269a804a91c3280100aafeb59f4f000c84c1916f3d186", "PNP.DirectWire.physicalNormalizationPass_exact_accounting": "229aea7c24bfd7a753d61ab458d77663ab7afe172c669dae30155cf90dceccdb", "PNP.DirectWire.PhysicalNormalizationGain.checked": "427337b3b71051ea6183892626f713e70e71a95dbc47a589b6d041d5a82d1a33", "PNP.DirectWire.nextPhysicalNormalizationStep_checked": "1790d801558465f07fa0c179acef3b6ef54ce7e749207a96844b0bc38d5166b8", "PNP.DirectWire.PhysicalNormalizationTrace.checked": "a0a622312d96848ad1fa1080be5fe4922be9e260ef640539d021401739cb0ec5", "PNP.DirectWire.runPhysicalNormalization_checked": "dcc99d344b550bc094a11cb3c5276d275222849728f0532089e7b5cdf5b266a4", "PNP.DirectWire.runPhysicalNormalization_of_quiescent": "289992dec9ffe984bb89f69e00a6b4e2fdc7187c4bda3d53130f7d87c6195c8e", "PNP.DirectWire.runPhysicalNormalization_idempotent": "b11d9128d7a75c26f45a83ea6a800200f61acf33709d285bd809d1ae13031664", "PNP.DirectWire.runPhysicalNormalization_referenceMinimum": "962346c00f368bc0320f4008d01920dddab26c57f4cfb6e0c66571c7bfebecb1", "PNP.DirectWire.runPhysicalNormalization_residualSlack": "798ff693e7e90fbfd2d71794a07d1b9fe44c00d9e7509d6f73f412002276106b", "PNP.DirectWire.runPhysicalNormalization_gainIterations_le_residualSlack": "681cc73dd14a8ec8a6df53b1317bfb870911e3b54646d8ce58cccc4cba8378c9", "PNP.DirectWire.physicalClosureNormalizer_checked": "b5ae9aa84bf7be2011daca12a1a9f6213b8182b8a968265d116fecccdaa4509a" }, "theoremAxioms": { "PNP.DirectWire.physicalNormalizationPass_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.physicalNormalizationPass_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalNormalizationGain.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.nextPhysicalNormalizationStep_checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalNormalizationTrace.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.runPhysicalNormalization_checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.runPhysicalNormalization_of_quiescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.runPhysicalNormalization_idempotent": [ "Quot.sound", "propext" ], "PNP.DirectWire.runPhysicalNormalization_referenceMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.runPhysicalNormalization_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.runPhysicalNormalization_gainIterations_le_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.physicalClosureNormalizer_checked": [ "Quot.sound", "propext" ] } }, { "number": 249, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-249", "id": "arbitrary-support-splice", "title": "Computed arbitrary-support literal NAND replacement and topological compilation", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanArbitrarySupportSpliceFormalized": true, "leanArbitrarySupportSpliceAxiomAuditPassed": true, "leanArbitrarySupportSpliceAuditedDeclarationCount": 24, "leanArbitrarySupportSpliceCompilerSuccessTheorem": "PNP.DirectWire.compileRawNandGraph_success_iff", "leanArbitrarySupportSpliceCompilerFailureTheorem": "PNP.DirectWire.compileRawNandGraph_failure_iff", "leanArbitrarySupportSpliceRawOutputSemanticsTheorem": "PNP.DirectWire.CompiledRawNandGraph.candidate_semantics", "leanArbitrarySupportSpliceExactGateCountTheorem": "PNP.DirectWire.ArbitrarySupportSplice.result_gateCount", "leanArbitrarySupportSpliceGraphEquationsTheorem": "PNP.DirectWire.ArbitrarySupportSplice.values_solution", "leanArbitrarySupportSpliceGlobalSemanticsTheorem": "PNP.DirectWire.ArbitrarySupportSplice.result_semantics", "leanArbitrarySupportSplicePartitionTheorem": "PNP.DirectWire.ArbitrarySupportSplice.exterior_accounting", "leanArbitrarySupportSpliceExactAccountingTheorem": "PNP.DirectWire.ArbitrarySupportSplice.result_exact_accounting", "leanArbitrarySupportSpliceStrictGainTheorem": "PNP.DirectWire.ArbitrarySupportSplice.result_strict_gain", "leanArbitrarySupportSpliceProductionOrderTheorem": "PNP.DirectWire.ArbitrarySupportSplice.graph_rank_decreases", "leanArbitrarySupportSpliceProductionSuccessTheorem": "PNP.DirectWire.ArbitrarySupportSplice.production_compiles", "leanArbitrarySupportSpliceProductionAgreementTheorem": "PNP.DirectWire.ArbitrarySupportSplice.production_agreement", "leanArbitrarySupportSpliceUnrestrictedReplacementSuccessProved": false, "leanArbitrarySupportSpliceFullProfilePreservationProved": false, "leanArbitrarySupportSpliceCompletePackageEProved": false, "leanArbitrarySupportSplicePolynomialRuntimeProved": false, "leanArbitrarySupportSpliceScope": "all-finite-actual-supports-computed-literal-exterior-replacement-graph-derived-topological-order-complete-ordered-output-semantics-exact-accounting-cyclic-rejection-production-saturation-success-physical-only" }, "theoremKernelTypeSha256": { "PNP.DirectWire.RawNandCompilationState.readSource_sound": "249ab589fff275624335e93a95c3b2862e7571861f602a9a70b13a65f877b61c", "PNP.DirectWire.RawNandCompilationState.readGate_sound": "2122df5770802861ba07cdbd547afc012daaae5702e26b0ed87181952af491cb", "PNP.DirectWire.RawNandReadyStep.apply_remaining_lt": "a167205196de2bd40e72deecb2cf8d099f4c3e64fc9b638a866d324547db644e", "PNP.DirectWire.RawNandCompilationStop.unresolved_predecessor": "05ebc6f9f02d6a05eeca50202e1cb0b913b033ecfe8e548b43569b8aeb033959", "PNP.DirectWire.RawNandCompilationStop.complete_of_wellFounded": "1bb645c9e89c90ce8195e4185efc1bb97909240430e67450da59cf4087748d0c", "PNP.DirectWire.CompiledRawNandGraph.wellFounded": "4e407ec0b1b11c26e305f4b6933706dbafecb931aee26181165cb570de6e2353", "PNP.DirectWire.compileRawNandGraph_success_iff": "93307f1d06f33a85af1e05f01ec9cb33db389877e5c9f7bd1838b989ae1100b7", "PNP.DirectWire.compileRawNandGraph_failure_iff": "5c942c77b078d5717609c444cea6c87b8bdbd45d707659bccad6c810dabc1d66", "PNP.DirectWire.CompiledRawNandGraph.candidate_gateCount": "e8190898d052060480bd4856f59cc987c79c8f0127fdfbaced645bce19e40156", "PNP.DirectWire.CompiledRawNandGraph.candidate_semantics": "cc989aa0ce66ace1cf344b38d9f00f6cd0c7057f5bddae614e2d4c0c9913aaa1", "PNP.DirectWire.ArbitrarySupportSplice.result_gateCount": "e54d5da539b9ee0e0d8334b9bca202caaea0d91c02a040ca33773eda06c0efe4", "PNP.DirectWire.ArbitrarySupportSplice.compile_success_iff": "50d8a57ea6ec2910278d2f8d31b8b580d18486f4bef6a051ee0bf546e534df8b", "PNP.DirectWire.ArbitrarySupportSplice.compile_failure_iff": "3ccc9106581f2cae3f36f17be8f58d78c0071aa0c39f3d4863f3144970ce558e", "PNP.DirectWire.ArbitrarySupportSplice.replacementSource_eval": "6e1004ed4845279079fee1f84c482fdeb9bad1c0b34174b94215098871f0f553", "PNP.DirectWire.ArbitrarySupportSplice.originalSource_eval": "a78632aaf6fd18c70508d245380e821a57d1961c728ffca10021a3327560042a", "PNP.DirectWire.ArbitrarySupportSplice.values_solution": "510b56c2ce6bb2e14b51d6b5921d6cac369c5b88e127bf54b6ddad1e156af91d", "PNP.DirectWire.ArbitrarySupportSplice.result_semantics": "6940158e70561f97abcff887d83b2ee27c06864ea746b60c80fa4a06b6324200", "PNP.DirectWire.ArbitrarySupportSplice.exterior_accounting": "cfc111a947f4eb06bd738d6258c46e598a3bfcfc7fccabe13aef8a8bb8a8c994", "PNP.DirectWire.ArbitrarySupportSplice.result_exact_accounting": "6da5b36305b6fd26bfb41c1554e744f5c6dd11308b5e20ea9df7829b657ea763", "PNP.DirectWire.ArbitrarySupportSplice.result_strict_gain": "acc58cbe89243294ea56091b30ffa196725aeb3ba18c3577923ba033711b06f3", "PNP.DirectWire.ArbitrarySupportSplice.graph_rank_decreases": "67c8f06262ace5918cb8e3f61c626b82fc4ef041148c7cac0b553fff6238e7ec", "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_primaryBoundary": "f3976f6579060f445aefe21487ac307efdcc929f9b469af1f56fc92cb2a9fb86", "PNP.DirectWire.ArbitrarySupportSplice.production_compiles": "900469aefe05cde3d9a9976d31672a502e532ee629545d7392785b2db9e3a00c", "PNP.DirectWire.ArbitrarySupportSplice.production_agreement": "4184ac9ce3304d128becafaeeaeb180ab9a96b5431e4a3fb3ad7280bf99b6846" }, "theoremAxioms": { "PNP.DirectWire.RawNandCompilationState.readSource_sound": [ "propext" ], "PNP.DirectWire.RawNandCompilationState.readGate_sound": [ "propext" ], "PNP.DirectWire.RawNandReadyStep.apply_remaining_lt": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandCompilationStop.unresolved_predecessor": [ "propext" ], "PNP.DirectWire.RawNandCompilationStop.complete_of_wellFounded": [ "propext" ], "PNP.DirectWire.CompiledRawNandGraph.wellFounded": [], "PNP.DirectWire.compileRawNandGraph_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.compileRawNandGraph_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.candidate_gateCount": [], "PNP.DirectWire.CompiledRawNandGraph.candidate_semantics": [], "PNP.DirectWire.ArbitrarySupportSplice.result_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.compile_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.compile_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.replacementSource_eval": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.originalSource_eval": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.values_solution": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.result_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.exterior_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.result_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.result_strict_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.graph_rank_decreases": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_primaryBoundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.production_compiles": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.production_agreement": [ "Quot.sound", "propext" ] } }, { "number": 250, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-250", "id": "wire-carrier-transport", "title": "Computed wire-backed carrier preservation under physical normalization and replacement", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireCarrierTransportFormalized": true, "leanWireCarrierTransportAxiomAuditPassed": true, "leanWireCarrierTransportAuditedDeclarationCount": 16, "leanWireCarrierTransportPackUnpackTheorem": "PNP.DirectWire.WireCarrier.exposed_unpack", "leanWireCarrierTransportUnpackPackTheorem": "PNP.DirectWire.WireCarrier.unpack_exposed", "leanWireCarrierTransportNormalizationOutputTheorem": "PNP.DirectWire.WireCarrier.normalize_output", "leanWireCarrierTransportNormalizationFieldTheorem": "PNP.DirectWire.WireCarrier.normalize_field", "leanWireCarrierTransportNormalizationAccountingTheorem": "PNP.DirectWire.WireCarrier.normalize_exact_accounting", "leanWireCarrierTransportNormalizationQuiescenceTheorem": "PNP.DirectWire.WireCarrier.normalize_quiescent", "leanWireCarrierTransportNormalizationIdempotenceTheorem": "PNP.DirectWire.WireCarrier.normalize_idempotent", "leanWireCarrierTransportHiddenFieldInterfaceTheorem": "PNP.DirectWire.WireCarrier.field_producer_visible", "leanWireCarrierTransportSpliceOutputTheorem": "PNP.DirectWire.WireCarrier.splice_output", "leanWireCarrierTransportSpliceFieldTheorem": "PNP.DirectWire.WireCarrier.splice_field", "leanWireCarrierTransportSpliceAccountingTheorem": "PNP.DirectWire.WireCarrier.splice_exact_accounting", "leanWireCarrierTransportSpliceStrictGainTheorem": "PNP.DirectWire.WireCarrier.splice_strict_gain", "leanWireCarrierTransportSpliceExecutionTheorem": "PNP.DirectWire.WireCarrier.splice_checked", "leanWireCarrierTransportCyclicRejectionTheorem": "PNP.DirectWire.WireCarrier.splice_failure_iff", "leanWireCarrierTransportProductionBoundaryTheorem": "PNP.DirectWire.WireCarrier.production_boundary_isInput", "leanWireCarrierTransportProductionSuccessTheorem": "PNP.DirectWire.WireCarrier.production_compiles", "leanWireCarrierTransportFullManuscriptCarrierDerived": false, "leanWireCarrierTransportObligationLifecycleProved": false, "leanWireCarrierTransportUnrestrictedReplacementSuccessProved": false, "leanWireCarrierTransportCompletePackageEProved": false, "leanWireCarrierTransportPolynomialRuntimeProved": false, "leanWireCarrierTransportScope": "all-finite-literal-wire-backed-computational-fields-complete-ordered-exposure-computed-normalization-and-arbitrary-support-splice-value-preservation-exact-physical-accounting-derived-production-predecessors-no-full-manuscript-carrier-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireCarrier.exposed_unpack": "52b06e232ee698792723138e1bd7c233a0df92fc0596e5d1cb5a5ad3a6998ab2", "PNP.DirectWire.WireCarrier.unpack_exposed": "e4bc75b87eb806542a29c7a7c6e523ba784ae91d2cdd3f258df74dee3a50190f", "PNP.DirectWire.WireCarrier.normalize_output": "16061da3c8919111c1c6978a464a20b8569b0699b37cd393eb2dcdec5c9056aa", "PNP.DirectWire.WireCarrier.normalize_field": "7db27122f63ded43c385da4a7261d23c7e9879d028553550b08aa876d4792416", "PNP.DirectWire.WireCarrier.normalize_exact_accounting": "a198f6730e3dc53bbc9b1ab5c0422213e3d608a01e5db509eecdba8758f2ff2b", "PNP.DirectWire.WireCarrier.normalize_quiescent": "34ab38584d59be857e7cf3a55c64f5c88f1f90c4dd2f40d67daa464aa8075ecd", "PNP.DirectWire.WireCarrier.normalize_idempotent": "f7cce5f43df79ea96c60e655cb5b86173522fde20c2234a439868221011420c5", "PNP.DirectWire.WireCarrier.field_producer_visible": "bc09f579729f6afb62951d1703ece5a713fe6a4beeed9cc53ca40c6fe3761b84", "PNP.DirectWire.WireCarrier.splice_output": "411dc13ea230fc22b77724331e9e1c33714d660a4a604cfd7898538c8786f74c", "PNP.DirectWire.WireCarrier.splice_field": "4ba4f77a1c9283281452654d90c7345f8d0f8c6dc9191e0605cda7c42484bb0d", "PNP.DirectWire.WireCarrier.splice_exact_accounting": "5f466be2d9ebc3e5d9cf6e0e846f82bbaf1b888e89e12f38adf89aef53fd7d58", "PNP.DirectWire.WireCarrier.splice_strict_gain": "4123bc53c6f2b6de684443b5c59fc548ccec92315b2f414fe8bc2a34a4585be6", "PNP.DirectWire.WireCarrier.splice_checked": "98107b6a054e0da36408a39910ff8938933712f48a4a2f5dd669b98900d303f9", "PNP.DirectWire.WireCarrier.splice_failure_iff": "8267d78155cac9ef72b19406e8a7b9e94064d7c675dddea99d1ef3e7c6fb881e", "PNP.DirectWire.WireCarrier.production_boundary_isInput": "685e00c4d3d3038805c3db5f9c6b028a28ae8ef39c7cadab56e116151fafc1fc", "PNP.DirectWire.WireCarrier.production_compiles": "09f0bee838b9d67f46d451c461a6272810bef6ec49d7b00cd1e4c615cefa8e22" }, "theoremAxioms": { "PNP.DirectWire.WireCarrier.exposed_unpack": [ "Quot.sound" ], "PNP.DirectWire.WireCarrier.unpack_exposed": [ "Quot.sound" ], "PNP.DirectWire.WireCarrier.normalize_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.normalize_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.normalize_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.normalize_quiescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.normalize_idempotent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.field_producer_visible": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.splice_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.splice_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.splice_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.splice_strict_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.splice_checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.splice_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.production_boundary_isInput": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.production_compiles": [ "Quot.sound", "propext" ] } }, { "number": 251, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-251", "id": "wire-obligation-restoration", "title": "Computed lost-wire projection obligations and fully charged restoration", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireObligationRestorationFormalized": true, "leanWireObligationRestorationAxiomAuditPassed": true, "leanWireObligationRestorationAuditedDeclarationCount": 22, "leanWireObligationRestorationProjectedOutputTheorem": "PNP.DirectWire.WireObligationRestoration.projected_output", "leanWireObligationRestorationProjectedKeptFieldTheorem": "PNP.DirectWire.WireObligationRestoration.projected_kept_field", "leanWireObligationRestorationMaterializerForgottenFieldTheorem": "PNP.DirectWire.WireObligationRestoration.materializer_forgotten_field", "leanWireObligationRestorationJoinOutputTheorem": "PNP.DirectWire.WireObligationRestoration.join_output", "leanWireObligationRestorationJoinKeptFieldTheorem": "PNP.DirectWire.WireObligationRestoration.join_kept_field", "leanWireObligationRestorationJoinForgottenFieldTheorem": "PNP.DirectWire.WireObligationRestoration.join_forgotten_field", "leanWireObligationRestorationRestoredOutputTheorem": "PNP.DirectWire.WireObligationRestoration.restored_output", "leanWireObligationRestorationRestoredFieldTheorem": "PNP.DirectWire.WireObligationRestoration.restored_field", "leanWireObligationRestorationExactGateChargeTheorem": "PNP.DirectWire.WireObligationRestoration.restored_exact_gate_charge", "leanWireObligationRestorationGateBoundTheorem": "PNP.DirectWire.WireObligationRestoration.restored_gate_bound", "leanWireObligationRestorationCreatedCoordinatesTheorem": "PNP.DirectWire.WireObligationRestoration.created_exact", "leanWireObligationRestorationDischargedCoordinatesTheorem": "PNP.DirectWire.WireObligationRestoration.discharged_exact", "leanWireObligationRestorationForgottenMaskTheorem": "PNP.DirectWire.WireObligationRestoration.mem_forgottenCoordinates_iff", "leanWireObligationRestorationCreationMembershipTheorem": "PNP.DirectWire.WireObligationRestoration.creation_iff", "leanWireObligationRestorationDischargeMembershipTheorem": "PNP.DirectWire.WireObligationRestoration.discharge_iff", "leanWireObligationRestorationClosedReplayTheorem": "PNP.DirectWire.WireObligationRestoration.replay_closed", "leanWireObligationRestorationFullDischargeValueTheorem": "PNP.DirectWire.WireObligationRestoration.dischargeR8_full_value", "leanWireObligationRestorationGainIffTheorem": "PNP.DirectWire.WireObligationRestoration.gain?_isSome_iff", "leanWireObligationRestorationCheckedGainTheorem": "PNP.DirectWire.WireObligationRestoration.gain_checked", "leanWireObligationRestorationCreationUniquenessTheorem": "PNP.DirectWire.WireObligationRestoration.created_nodup", "leanWireObligationRestorationDischargeUniquenessTheorem": "PNP.DirectWire.WireObligationRestoration.discharged_nodup", "leanWireObligationRestorationDuplicateIdentityRejectionTheorem": "PNP.DirectWire.WireObligationRestoration.replay_rejects_duplicate_ids", "leanWireObligationRestorationFullManuscriptCarrierDerived": false, "leanWireObligationRestorationCompleteObligationCalculusProved": false, "leanWireObligationRestorationGeneralDependencyDAGProved": false, "leanWireObligationRestorationCompletePackageEProved": false, "leanWireObligationRestorationPolynomialRuntimeProved": false, "leanWireObligationRestorationScope": "all-finite-computational-wire-fields-actual-quotient-projection-shared-materializer-full-value-restoration-exact-gate-charge-derived-r5-full-r8-coordinate-ledger-whole-trace-unique-identities-no-full-manuscript-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireObligationRestoration.projected_output": "9db137ff572598f27b8978c1e20592987442afe9518444b13a1a82be7389eafe", "PNP.DirectWire.WireObligationRestoration.projected_kept_field": "18eb453392e344b669686f436529edc8eac10935796c5d660dadd58dae0dd27e", "PNP.DirectWire.WireObligationRestoration.materializer_forgotten_field": "443dd40f055b1440727c3b6bae6e475ed159bf3fbe5d61093d6730f33d7f5950", "PNP.DirectWire.WireObligationRestoration.join_output": "39bf1aac304078048078a936243756c731ef9e036aa97339424f1134457abab9", "PNP.DirectWire.WireObligationRestoration.join_kept_field": "2beb641b17d6f90f1029f1c56ea226ba65d1b4a59e8bc22f39c08f9b1cd671e3", "PNP.DirectWire.WireObligationRestoration.join_forgotten_field": "dbf92adf17c0520daefcd37b20bdae3868600663f73e69ccfd63479f6018b061", "PNP.DirectWire.WireObligationRestoration.restored_output": "f2700308348906c76b750ce766a97d50c2c3e1c59f590ddc475384824b87cd37", "PNP.DirectWire.WireObligationRestoration.restored_field": "64df896b2a0483021625f23df9f82a1b4d3316916a5b3e49acdc52fb3300ea24", "PNP.DirectWire.WireObligationRestoration.restored_exact_gate_charge": "1dce5aeceb99a472a85441e2e20f95970b141bc335e78f0c6cbf8914ae355196", "PNP.DirectWire.WireObligationRestoration.restored_gate_bound": "024165d580947e53951cc622e0da244a7b8b1c4073546afb4688274afa4bfb25", "PNP.DirectWire.WireObligationRestoration.created_exact": "4e4f8fd06ec135760827ee6c7912f228bacb3c130c6265ca4f6a613e24cf947b", "PNP.DirectWire.WireObligationRestoration.discharged_exact": "5768997e5f284d7fcd7f257d1c98475dd57c5c94c0183077411b26e656173b77", "PNP.DirectWire.WireObligationRestoration.mem_forgottenCoordinates_iff": "fd19fd4184326b9f8b1a2d2c366ae70cc639af00735742284e1027676d54a47a", "PNP.DirectWire.WireObligationRestoration.creation_iff": "f1b7532d0e888e57ce1b16f0ddce0fb03687dd335558c639939cde0654bcc0a0", "PNP.DirectWire.WireObligationRestoration.discharge_iff": "4ae3a648df20849a27c29b2ad75f4dc2493b20b56ee7a970431a22d427cd7bab", "PNP.DirectWire.WireObligationRestoration.replay_closed": "fe9eebebe76bf2c9468b1c74b8283cac786fe19c63c2b7e66eb11b38bbb2d842", "PNP.DirectWire.WireObligationRestoration.dischargeR8_full_value": "ece2b699fc6d36735d7a62f772db312386c33ff388e1c0ed2b2a1ecba9bac05f", "PNP.DirectWire.WireObligationRestoration.gain?_isSome_iff": "d0d8ddb1749b477af29863f43640eb7241a06445a9db2aa09f661b1fdaf0ad20", "PNP.DirectWire.WireObligationRestoration.gain_checked": "6371bbe19d03e7455d308a83c48154ad5a8e97f39508b74b05e040314d9d877c", "PNP.DirectWire.WireObligationRestoration.created_nodup": "c13d5f7f593ff543a7d6367f4513a07b09fac14a1bd804494d2b4f58418608ae", "PNP.DirectWire.WireObligationRestoration.discharged_nodup": "de37f4291ba5722db2e4309d9d837e4ed439a819ee82f6fb1fc131be2b87954e", "PNP.DirectWire.WireObligationRestoration.replay_rejects_duplicate_ids": "e946fbe19d83be47720897f76d693bace11654c868189c7bbf1ef43ddcf679e6" }, "theoremAxioms": { "PNP.DirectWire.WireObligationRestoration.projected_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.projected_kept_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.materializer_forgotten_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.join_output": [], "PNP.DirectWire.WireObligationRestoration.join_kept_field": [], "PNP.DirectWire.WireObligationRestoration.join_forgotten_field": [], "PNP.DirectWire.WireObligationRestoration.restored_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.restored_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.restored_exact_gate_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.restored_gate_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.created_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.discharged_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.mem_forgottenCoordinates_iff": [ "propext" ], "PNP.DirectWire.WireObligationRestoration.creation_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.discharge_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.replay_closed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.dischargeR8_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.gain?_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.gain_checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.created_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.discharged_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.replay_rejects_duplicate_ids": [ "Quot.sound", "propext" ] } }, { "number": 252, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-252", "id": "wire-quotient-lift", "title": "Computed quotient replacement lift with matched materializer costs", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireQuotientLiftFormalized": true, "leanWireQuotientLiftAxiomAuditPassed": true, "leanWireQuotientLiftAuditedDeclarationCount": 17, "leanWireQuotientLiftExpandedReferenceTheorem": "PNP.DirectWire.WireQuotientLift.expanded_reference", "leanWireQuotientLiftReferenceChargeTheorem": "PNP.DirectWire.WireQuotientLift.referenceLift_charge", "leanWireQuotientLiftExpandedChargeTheorem": "PNP.DirectWire.WireQuotientLift.expanded_charge", "leanWireQuotientLiftReferenceChargeDifferenceTheorem": "PNP.DirectWire.WireQuotientLift.referenceLift_charge_difference", "leanWireQuotientLiftExpandedChargeDifferenceTheorem": "PNP.DirectWire.WireQuotientLift.expanded_charge_difference", "leanWireQuotientLiftMatchedMaterializerChargeTheorem": "PNP.DirectWire.WireQuotientLift.matched_materializer_charge", "leanWireQuotientLiftRelativeSavingIffTheorem": "PNP.DirectWire.WireQuotientLift.relative_saving_iff", "leanWireQuotientLiftOriginalGainIffTheorem": "PNP.DirectWire.WireQuotientLift.original_gain_iff", "leanWireQuotientLiftExpandedOutputTheorem": "PNP.DirectWire.WireQuotientLift.expanded_output", "leanWireQuotientLiftExpandedKeptFieldTheorem": "PNP.DirectWire.WireQuotientLift.expanded_kept_field", "leanWireQuotientLiftExpandedForgottenFieldTheorem": "PNP.DirectWire.WireQuotientLift.expanded_forgotten_field", "leanWireQuotientLiftExpandedFieldTheorem": "PNP.DirectWire.WireQuotientLift.expanded_field", "leanWireQuotientLiftExpandedEquivalenceTheorem": "PNP.DirectWire.WireQuotientLift.expanded_equivalent", "leanWireQuotientLiftDischargeSourceExactTheorem": "PNP.DirectWire.WireQuotientLift.discharge_source_exact", "leanWireQuotientLiftDischargeFullValueTheorem": "PNP.DirectWire.WireQuotientLift.discharge_full_value", "leanWireQuotientLiftGainIffTheorem": "PNP.DirectWire.WireQuotientLift.checkedGain_isSome_iff", "leanWireQuotientLiftCheckedGainTheorem": "PNP.DirectWire.WireQuotientLift.CheckedGain.checked", "leanWireQuotientLiftFullManuscriptPullExpandProved": false, "leanWireQuotientLiftReferenceLiftIdentifiedWithOriginal": false, "leanWireQuotientLiftAutomaticQuotientAgreementDerived": false, "leanWireQuotientLiftCompleteObligationCalculusProved": false, "leanWireQuotientLiftCompletePackageEProved": false, "leanWireQuotientLiftPolynomialRuntimeProved": false, "leanWireQuotientLiftScope": "all-finite-computational-wire-quotient-compatible-replacements-literal-shared-materializer-full-value-lift-exact-matched-integer-charges-original-cost-gain-test-expanded-source-bound-discharge-no-arbitrary-support-embedding-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireQuotientLift.expanded_reference": "dad34b516523dd4761eed9fe0e51f4ea277af7b09f47963376a231f88769b9cd", "PNP.DirectWire.WireQuotientLift.referenceLift_charge": "8ef5fa5a1c3f72b8696d60b96ef30bf041e06d6e0118eddbd369e9724eff784e", "PNP.DirectWire.WireQuotientLift.expanded_charge": "2c390754add81c66fce0e7f06d9645887fe99f409f56ba5017ff019de0bddafe", "PNP.DirectWire.WireQuotientLift.referenceLift_charge_difference": "161d81be5eddf99fbe120d07fe2e28283f4f1ab98ea1f44bfca25d8008074f7c", "PNP.DirectWire.WireQuotientLift.expanded_charge_difference": "20cc0581c6b78bc09932db012b163951a02c5e74a768868d168ee7798d9ca5e7", "PNP.DirectWire.WireQuotientLift.matched_materializer_charge": "c406464ebafae4e77738d6900db05342b1eb36847dd4c16a949349a336dceba7", "PNP.DirectWire.WireQuotientLift.relative_saving_iff": "f01eace00b52eeaabe4b5144a8d72ae541387ecd4d6aa29b4e7b93ce11d96be8", "PNP.DirectWire.WireQuotientLift.original_gain_iff": "cd38b27471456bec443545e4111706f83a73acfeadc512c9bde1ceb01f6e4ff5", "PNP.DirectWire.WireQuotientLift.expanded_output": "e56816eefc3ae363d597a4f30f061a13912dbbfcc6bbbcdc7c563680de9264b6", "PNP.DirectWire.WireQuotientLift.expanded_kept_field": "68f9c76da6c2c6180c8093c20d9e72ad9e718ddd3bc5b632cfbb1624ba946969", "PNP.DirectWire.WireQuotientLift.expanded_forgotten_field": "1f311380a7b47553cc0b7c9e271589f1cb34ea176ae44f84850935604aff7191", "PNP.DirectWire.WireQuotientLift.expanded_field": "ad7fd204b29e8141d7942bfbed034296c89b8aea9996e92d2e915e6e8326c0af", "PNP.DirectWire.WireQuotientLift.expanded_equivalent": "39f297948af422b3a8643984303c0773bcea23dc75a1a4b834f31245346d6da1", "PNP.DirectWire.WireQuotientLift.discharge_source_exact": "4f253f28d63c4ef390842de5ec99c84a819d2fa3e69b0f67ecaecb5ac7d4547f", "PNP.DirectWire.WireQuotientLift.discharge_full_value": "7b121a128cf884fcad0435492949da493316ec268b54a558c1c5c89ff3745677", "PNP.DirectWire.WireQuotientLift.checkedGain_isSome_iff": "79cbe56d948918e2995435dee395b44858bc98bd351f66b8a341479318d7db93", "PNP.DirectWire.WireQuotientLift.CheckedGain.checked": "61ca863d7794e9ce01dd17ac5f76237d0c0d0019009f62d3c07decfe4f977fd7" }, "theoremAxioms": { "PNP.DirectWire.WireQuotientLift.expanded_reference": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.referenceLift_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.referenceLift_charge_difference": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_charge_difference": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.matched_materializer_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.relative_saving_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.original_gain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_kept_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_forgotten_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.expanded_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.discharge_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.discharge_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.checkedGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireQuotientLift.CheckedGain.checked": [ "Quot.sound", "propext" ] } }, { "number": 253, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-12-253", "id": "wire-frontier-lift", "title": "Computed original-accounted frontier replacement", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireFrontierLiftFormalized": true, "leanWireFrontierLiftAxiomAuditPassed": true, "leanWireFrontierLiftAuditedDeclarationCount": 18, "leanWireFrontierLiftOrdinaryOutputSelectedTheorem": "PNP.DirectWire.WireFrontierLift.ordinary_output_selected", "leanWireFrontierLiftKeptFieldSelectedTheorem": "PNP.DirectWire.WireFrontierLift.kept_field_selected", "leanWireFrontierLiftPredecessorClosureTheorem": "PNP.DirectWire.WireFrontierLift.records_predecessor_closed", "leanWireFrontierLiftSelectedFieldFrontierTheorem": "PNP.DirectWire.WireFrontierLift.selected_field_in_frontier", "leanWireFrontierLiftPrimaryBoundaryTheorem": "PNP.DirectWire.WireFrontierLift.primary_boundary", "leanWireFrontierLiftOriginalChargeTheorem": "PNP.DirectWire.WireFrontierLift.original_charge", "leanWireFrontierLiftCompileIsSomeTheorem": "PNP.DirectWire.WireFrontierLift.compile_isSome", "leanWireFrontierLiftExpandedChargeTheorem": "PNP.DirectWire.WireFrontierLift.expanded_charge", "leanWireFrontierLiftMatchedOriginalChargeTheorem": "PNP.DirectWire.WireFrontierLift.matched_original_charge", "leanWireFrontierLiftOriginalGainIffTheorem": "PNP.DirectWire.WireFrontierLift.original_gain_iff", "leanWireFrontierLiftExpandedOutputTheorem": "PNP.DirectWire.WireFrontierLift.expanded_output", "leanWireFrontierLiftExpandedFieldTheorem": "PNP.DirectWire.WireFrontierLift.expanded_field", "leanWireFrontierLiftExpandedEquivalenceTheorem": "PNP.DirectWire.WireFrontierLift.expanded_equivalent", "leanWireFrontierLiftDischargeSourceExactTheorem": "PNP.DirectWire.WireFrontierLift.discharge_source_exact", "leanWireFrontierLiftDischargeFullValueTheorem": "PNP.DirectWire.WireFrontierLift.discharge_full_value", "leanWireFrontierLiftProperIffExteriorPositiveTheorem": "PNP.DirectWire.WireFrontierLift.proper_iff_exterior_positive", "leanWireFrontierLiftProperGainIffTheorem": "PNP.DirectWire.WireFrontierLift.checkedProperGain_isSome_iff", "leanWireFrontierLiftCheckedProperGainTheorem": "PNP.DirectWire.WireFrontierLift.ProperGain.checked", "leanWireFrontierLiftEveryArbitrarySupportCovered": false, "leanWireFrontierLiftAutomaticLocalAgreementDerived": false, "leanWireFrontierLiftFullManuscriptPullExpandProved": false, "leanWireFrontierLiftCompleteObligationCalculusProved": false, "leanWireFrontierLiftCompletePackageEProved": false, "leanWireFrontierLiftPolynomialRuntimeProved": false, "leanWireFrontierLiftScope": "all-finite-computational-wire-input-derived-quotient-visible-cone-completed-original-frontier-primary-boundary-actual-compiler-full-local-open-agreement-original-exterior-once-exact-integer-charges-strict-proper-gain-no-full-manuscript-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireFrontierLift.ordinary_output_selected": "8931e68e92d35b11528e401a2794cd957f15aa680c3fc0d403792565c3877b60", "PNP.DirectWire.WireFrontierLift.kept_field_selected": "f1e883390878267faaeb4e079fe8a8e6b1beaa818ee6289321b290e4569fd7a3", "PNP.DirectWire.WireFrontierLift.records_predecessor_closed": "aaac754e3944140d3f9ab991fe42cc844199ca686b2df52f3853c289f980dc22", "PNP.DirectWire.WireFrontierLift.selected_field_in_frontier": "4562d68496b552354fc79fa2203f76209b5c82152af04989e379d7661041e2c6", "PNP.DirectWire.WireFrontierLift.primary_boundary": "5f646ed8a46cd2fa78f3546ae15d17d10c7885b90c986df52e58dfd81c92bacd", "PNP.DirectWire.WireFrontierLift.original_charge": "4eb5b3b2bea74fa2ef8f74430443fcf91703578efaa7c5bd240750acab1fe673", "PNP.DirectWire.WireFrontierLift.compile_isSome": "c7c54aca037e1809f3dc247e6b2fdd8400610a8534d0c13421fd92b7e1a68e9f", "PNP.DirectWire.WireFrontierLift.expanded_charge": "e1cd44f5181734485e18c9715033158ca360b888eda0f51e70b366d77760e88a", "PNP.DirectWire.WireFrontierLift.matched_original_charge": "3a44ac86b851eae886ec1c90d7f6a70b18873d9c25053910cf09fdd27c27b16a", "PNP.DirectWire.WireFrontierLift.original_gain_iff": "2f4fcc36271b2b7ccbc96c064df4296c60498f617f0e9a7b0335a2f727ce584b", "PNP.DirectWire.WireFrontierLift.expanded_output": "bf326f0b42446e9c7acb8321afdbba90d86db4221d2a49b46ab390dc6fdf82af", "PNP.DirectWire.WireFrontierLift.expanded_field": "d44019f1b34aea6e5192f1121e790d79176267f1a59f0a6d69153e4a38061378", "PNP.DirectWire.WireFrontierLift.expanded_equivalent": "71984fb9b72d71ad9ea78dd7d83d517064e2ec2a8f911fb1508962c71627c0ba", "PNP.DirectWire.WireFrontierLift.discharge_source_exact": "5648f9e263315b547073b009e005fbeb0dc23065179daa94744fabe0068bb945", "PNP.DirectWire.WireFrontierLift.discharge_full_value": "5f76bac96ea0779b49d2e6c7db6cdc3f3d6a953ba834835e0a449c951a741738", "PNP.DirectWire.WireFrontierLift.proper_iff_exterior_positive": "3ad5423b315def909a850c9f775b9bf51ced9833a9566b82978770b779319441", "PNP.DirectWire.WireFrontierLift.checkedProperGain_isSome_iff": "419ea770c1d5c32e79ec2f3bc59d1d4497d1b447f3e363a5e70e9e2326d5a01e", "PNP.DirectWire.WireFrontierLift.ProperGain.checked": "a3092c4aca64494c0ac7112cf82d000da02b4a4a61ae545f8b74719dc436a2a4" }, "theoremAxioms": { "PNP.DirectWire.WireFrontierLift.ordinary_output_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.kept_field_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.records_predecessor_closed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.selected_field_in_frontier": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.primary_boundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.original_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.compile_isSome": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.expanded_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.matched_original_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.original_gain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.expanded_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.expanded_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.expanded_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.discharge_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.discharge_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.proper_iff_exterior_positive": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.checkedProperGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireFrontierLift.ProperGain.checked": [ "Quot.sound", "propext" ] } }, { "number": 254, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-254", "id": "wire-matched-cancellation", "title": "Computed full-mode wire cancellation", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireMatchedCancellationFormalized": true, "leanWireMatchedCancellationAxiomAuditPassed": true, "leanWireMatchedCancellationAuditedDeclarationCount": 26, "leanWireMatchedCancellationRepresentativeAvailabilityTheorem": "PNP.DirectWire.WireMatchedCancellation.representative_isSome_iff", "leanWireMatchedCancellationRetainedObservationValueTheorem": "PNP.DirectWire.WireMatchedCancellation.observation_value", "leanWireMatchedCancellationRepresentativeFullValueTheorem": "PNP.DirectWire.WireMatchedCancellation.Representative.full_value", "leanWireMatchedCancellationAllResolvedSoundnessTheorem": "PNP.DirectWire.WireMatchedCancellation.allResolved_sound", "leanWireMatchedCancellationAllResolvedChargeTheorem": "PNP.DirectWire.WireMatchedCancellation.charge_allResolved", "leanWireMatchedCancellationUnresolvedMaterializerFieldTheorem": "PNP.DirectWire.WireMatchedCancellation.missing_unresolved_field", "leanWireMatchedCancellationMaterializerChargeBoundTheorem": "PNP.DirectWire.WireMatchedCancellation.charge_bound", "leanWireMatchedCancellationVisibleResolvedFieldTheorem": "PNP.DirectWire.WireMatchedCancellation.visible_resolved_field", "leanWireMatchedCancellationExpandedChargeTheorem": "PNP.DirectWire.WireMatchedCancellation.expanded_charge", "leanWireMatchedCancellationExpandedOutputTheorem": "PNP.DirectWire.WireMatchedCancellation.expanded_output", "leanWireMatchedCancellationExpandedFieldTheorem": "PNP.DirectWire.WireMatchedCancellation.expanded_field", "leanWireMatchedCancellationExpandedEquivalenceTheorem": "PNP.DirectWire.WireMatchedCancellation.expanded_equivalent", "leanWireMatchedCancellationDischargeWitnessFullValueTheorem": "PNP.DirectWire.WireMatchedCancellation.Discharge.full_value", "leanWireMatchedCancellationDischargeSourceExactTheorem": "PNP.DirectWire.WireMatchedCancellation.discharge_source_exact", "leanWireMatchedCancellationDischargeKindIffTheorem": "PNP.DirectWire.WireMatchedCancellation.discharge_isR6_iff", "leanWireMatchedCancellationComputedDischargeFullValueTheorem": "PNP.DirectWire.WireMatchedCancellation.discharge_full_value", "leanWireMatchedCancellationGainIffTheorem": "PNP.DirectWire.WireMatchedCancellation.checkedGain_isSome_iff", "leanWireMatchedCancellationCheckedGainTheorem": "PNP.DirectWire.WireMatchedCancellation.CheckedGain.checked", "leanWireMatchedCancellationCreatedExactTheorem": "PNP.DirectWire.WireMatchedCancellation.created_exact", "leanWireMatchedCancellationDischargedExactTheorem": "PNP.DirectWire.WireMatchedCancellation.discharged_exact", "leanWireMatchedCancellationCreationIffTheorem": "PNP.DirectWire.WireMatchedCancellation.creation_iff", "leanWireMatchedCancellationDischargeIffTheorem": "PNP.DirectWire.WireMatchedCancellation.discharge_iff", "leanWireMatchedCancellationCreatedNodupTheorem": "PNP.DirectWire.WireMatchedCancellation.created_nodup", "leanWireMatchedCancellationDischargedNodupTheorem": "PNP.DirectWire.WireMatchedCancellation.discharged_nodup", "leanWireMatchedCancellationReplayClosedTheorem": "PNP.DirectWire.WireMatchedCancellation.replay_closed", "leanWireMatchedCancellationRejectDuplicateIdsTheorem": "PNP.DirectWire.WireMatchedCancellation.replay_rejects_duplicate_ids", "leanWireMatchedCancellationAllSemanticCancellationsDerived": false, "leanWireMatchedCancellationArbitraryObligationDAGsCovered": false, "leanWireMatchedCancellationAutomaticLocalAgreementDerived": false, "leanWireMatchedCancellationFullManuscriptCarrierProved": false, "leanWireMatchedCancellationCompleteObligationCalculusProved": false, "leanWireMatchedCancellationCompletePackageEProved": false, "leanWireMatchedCancellationPolynomialRuntimeProved": false, "leanWireMatchedCancellationScope": "all-finite-computational-wire-original-visible-source-identity-scan-local-quotient-agreement-derived-full-r6-cancellation-unresolved-shared-r8-materializer-actual-expanded-source-exact-charge-whole-trace-unique-ids-no-complete-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireMatchedCancellation.representative_isSome_iff": "9a0ce14691f7d8efab0f371697999b2d067b00a5bfc9fcd44f862f21bcc4e6ba", "PNP.DirectWire.WireMatchedCancellation.observation_value": "f94cb4b0dc8e6c033764ada12c4f515a90797071f034c88ae12b3d823f08ec68", "PNP.DirectWire.WireMatchedCancellation.Representative.full_value": "b427980991225d6ec290732313658035f0423b39e96246f5f2cc3dcd3eca38f3", "PNP.DirectWire.WireMatchedCancellation.allResolved_sound": "b8d11d28fe4db2ec5cd7e0425e4151719df9a47c68eb71bdc4f36cdeab857cd6", "PNP.DirectWire.WireMatchedCancellation.charge_allResolved": "315efbe39ca329c5d4d6e122ace539f26c3f3d89dbd486cbff820cc4c52d5ae7", "PNP.DirectWire.WireMatchedCancellation.missing_unresolved_field": "66dd6694892b90af070b2842905361dcdd6f7aa20ecb4e9b3b96b44272b43b59", "PNP.DirectWire.WireMatchedCancellation.charge_bound": "1adaf4f65352bbcf5056894a1f581a8d4d2104e789f18e770823c90b6fffacde", "PNP.DirectWire.WireMatchedCancellation.visible_resolved_field": "11a959061c3465bb82fa0daaabc34c0b0af67467602e70fa8838e02910ebbc5b", "PNP.DirectWire.WireMatchedCancellation.expanded_charge": "5c010930b10c343eb99b555161171751238b45c577a7b2ef7a27675d9cb0b2ba", "PNP.DirectWire.WireMatchedCancellation.expanded_output": "50f302457ac646b61330aab04da7d1cdc0ac4ef53ba18b9ab1967c3d9f2c882c", "PNP.DirectWire.WireMatchedCancellation.expanded_field": "fd823a6e1a7a2eb2896ae0f86a9405acb41eb35d5a560e92ce5877157a5d2caa", "PNP.DirectWire.WireMatchedCancellation.expanded_equivalent": "d739a414f98686dfc8eacb28580976115794150dc2339039706874eb98e47488", "PNP.DirectWire.WireMatchedCancellation.Discharge.full_value": "9743c4ea11a1b3ef791893c7c4700e1dfd49d8d342f318241d92e5e104c353ab", "PNP.DirectWire.WireMatchedCancellation.discharge_source_exact": "527fa079d1da2264a7c958b78b3264c08e89da693cbc4d579471d8c0a91b8fd5", "PNP.DirectWire.WireMatchedCancellation.discharge_isR6_iff": "344e9293b8d23622e47cfc82a3d9f4a7311e085d78f1111a58a118c012a6478e", "PNP.DirectWire.WireMatchedCancellation.discharge_full_value": "b2f03c46a68b1d103f2bb60d2ffebcea476463787a73e138b7db27110d4b8398", "PNP.DirectWire.WireMatchedCancellation.checkedGain_isSome_iff": "75d6ee1639773cb2417ca3077af8011f6677d6c042f869b1d6691d7be3865b57", "PNP.DirectWire.WireMatchedCancellation.CheckedGain.checked": "7729efcecab7e56556163bdc2bcf218be41a062a6ee285b9807ae6bd3ac2dea7", "PNP.DirectWire.WireMatchedCancellation.created_exact": "e32e06f39dd7a79aeeb8194892b45d5bf39b86e9014f267b438e7613d26e03c9", "PNP.DirectWire.WireMatchedCancellation.discharged_exact": "485a37483687566eff84234d8322dce65af02f4614c43d62a1c3bcddb4643cc3", "PNP.DirectWire.WireMatchedCancellation.creation_iff": "213a77f56b3cf7580de96510516a7c919f1b983cf81c79d8547f639d754e2ba1", "PNP.DirectWire.WireMatchedCancellation.discharge_iff": "14291497e107583d0464ec07e6ad74851f49fcc1526ef0fd7dc6e5dd7199dbcf", "PNP.DirectWire.WireMatchedCancellation.created_nodup": "6768c54d50fa580f817703b0ebdd6ec8bccc1e149aefc968836a475bc6055986", "PNP.DirectWire.WireMatchedCancellation.discharged_nodup": "92d6396ff619ed082c562af3e0e469c7745091c66a916ff678ed6dd9cd0d4dae", "PNP.DirectWire.WireMatchedCancellation.replay_closed": "1abaf7da81590fa0607285d5e8576843119d5c2dd0c92e0862235f982aa4d53e", "PNP.DirectWire.WireMatchedCancellation.replay_rejects_duplicate_ids": "fbd380c2eb40962a25bccbbcd30b86d60ec182ca41ee71beb486532d92223602" }, "theoremAxioms": { "PNP.DirectWire.WireMatchedCancellation.representative_isSome_iff": [ "propext" ], "PNP.DirectWire.WireMatchedCancellation.observation_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.Representative.full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.allResolved_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.charge_allResolved": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.missing_unresolved_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.charge_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.visible_resolved_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.expanded_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.expanded_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.expanded_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.expanded_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.Discharge.full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.discharge_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.discharge_isR6_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.discharge_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.checkedGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.CheckedGain.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.created_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.discharged_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.creation_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.discharge_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.created_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.discharged_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.replay_closed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireMatchedCancellation.replay_rejects_duplicate_ids": [ "Quot.sound", "propext" ] } }, { "number": 255, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-255", "id": "wire-unary-realization", "title": "Computed unary full-word realization", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireUnaryRealizationFormalized": true, "leanWireUnaryRealizationAxiomAuditPassed": true, "leanWireUnaryRealizationAuditedDeclarationCount": 18, "leanWireUnaryRealizationObservationValueTheorem": "PNP.DirectWire.WireUnaryRealization.observation_value", "leanWireUnaryRealizationNegationIffTheorem": "PNP.DirectWire.WireUnaryRealization.needsNegation_iff", "leanWireUnaryRealizationImplementationValueTheorem": "PNP.DirectWire.WireUnaryRealization.implementation_value", "leanWireUnaryRealizationOutputTheorem": "PNP.DirectWire.WireUnaryRealization.realize_output", "leanWireUnaryRealizationFieldTheorem": "PNP.DirectWire.WireUnaryRealization.realize_field", "leanWireUnaryRealizationEquivalenceTheorem": "PNP.DirectWire.WireUnaryRealization.realize_equivalent", "leanWireUnaryRealizationFullEquivalenceTheorem": "PNP.DirectWire.WireUnaryRealization.realize_full_equivalent", "leanWireUnaryRealizationExactGateCountTheorem": "PNP.DirectWire.WireUnaryRealization.realize_gateCount", "leanWireUnaryRealizationNegationLowerBoundTheorem": "PNP.DirectWire.WireUnaryRealization.negation_requires_gate", "leanWireUnaryRealizationFullMinimumTheorem": "PNP.DirectWire.WireUnaryRealization.realize_minimal", "leanWireUnaryRealizationNonincreaseTheorem": "PNP.DirectWire.WireUnaryRealization.realize_nonincrease", "leanWireUnaryRealizationGateBoundTheorem": "PNP.DirectWire.WireUnaryRealization.realize_gate_bound", "leanWireUnaryRealizationR7WitnessFullValueTheorem": "PNP.DirectWire.WireUnaryRealization.R7Discharge.full_value", "leanWireUnaryRealizationR7SourceExactTheorem": "PNP.DirectWire.WireUnaryRealization.dischargeR7_source_exact", "leanWireUnaryRealizationComputedR7FullValueTheorem": "PNP.DirectWire.WireUnaryRealization.dischargeR7_full_value", "leanWireUnaryRealizationGainIffTheorem": "PNP.DirectWire.WireUnaryRealization.checkedGain_isSome_iff", "leanWireUnaryRealizationGainCompletenessTheorem": "PNP.DirectWire.WireUnaryRealization.checkedGain_complete", "leanWireUnaryRealizationCheckedGainTheorem": "PNP.DirectWire.WireUnaryRealization.CheckedGain.checked", "leanWireUnaryRealizationArbitraryAmbientCutsCovered": false, "leanWireUnaryRealizationAllR7CasesDerived": false, "leanWireUnaryRealizationArbitraryObligationDAGsCovered": false, "leanWireUnaryRealizationFullManuscriptCarrierProved": false, "leanWireUnaryRealizationCompleteObligationCalculusProved": false, "leanWireUnaryRealizationCompletePackageEProved": false, "leanWireUnaryRealizationPolynomialRuntimeProved": false, "leanWireUnaryRealizationScope": "all-unary-computational-wire-actual-two-source-valuations-arbitrary-gate-and-full-observation-counts-computed-zero-or-one-shared-not-complete-full-values-universal-full-word-minimum-source-exact-r7-discharge-complete-whole-word-gain-no-ambient-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireUnaryRealization.observation_value": "0e33500a57b8014755eb324cb94a88a8003b72c517e85b6b7e9992dac62f186a", "PNP.DirectWire.WireUnaryRealization.needsNegation_iff": "83a83a00275421eb25c735e9f8f24785bc9f64ba58065c0bfe8be3340d4b696d", "PNP.DirectWire.WireUnaryRealization.implementation_value": "62a7a8db007388000aa40dc102f35ff142b1a810c3d490728bd4d1795a318f63", "PNP.DirectWire.WireUnaryRealization.realize_output": "092307fb96200f321c54e0765a5bb5cf31be1013de71bf3a708e70d9a51c92e0", "PNP.DirectWire.WireUnaryRealization.realize_field": "4ad51b9f8bb60af80b01543e78080aafbb42d0a5cf812e908ba90ca4233ca484", "PNP.DirectWire.WireUnaryRealization.realize_equivalent": "57b87868b12c3b735c89b6b006d160e423cf327024c5a6b2c3a34220e7b03718", "PNP.DirectWire.WireUnaryRealization.realize_full_equivalent": "cb77aa4f7f9b6269386b9d8fdf342c3bfc377b24e2f7e2d8e95d5b0fc72f4113", "PNP.DirectWire.WireUnaryRealization.realize_gateCount": "b4755d75e4153c374e4db394a5ec4bf6cd1dcce17168a45b796137b439c7bc0f", "PNP.DirectWire.WireUnaryRealization.negation_requires_gate": "0830bed847d01bcb5eb79ae2f6558568880e61075a5d5dc0dfc4e94ea7615214", "PNP.DirectWire.WireUnaryRealization.realize_minimal": "8687f6a8fcc08bcb32f606829cb3fc7758013acbee8d66fc69ad3ca0c1bc3430", "PNP.DirectWire.WireUnaryRealization.realize_nonincrease": "f23591915fb7fc1e714aeb1a108377802de42cc868ff8fe3af087e07e2a4acf6", "PNP.DirectWire.WireUnaryRealization.realize_gate_bound": "8fa89009a88967d4df395926dd7a1f7c4143d1223997b2b4bf62c63fbbd2cb5a", "PNP.DirectWire.WireUnaryRealization.R7Discharge.full_value": "9d0c1905736bf1019e6604996d70fefb515f1e137406ed5503ad0681c35b33ee", "PNP.DirectWire.WireUnaryRealization.dischargeR7_source_exact": "19945f8412e44faedfc91210ef4e83439d564a2824edfc1f90b1a1db07d59e61", "PNP.DirectWire.WireUnaryRealization.dischargeR7_full_value": "cffef514537ebcbd880834578e28877e24ba3c25394b490fab04b0045ca064aa", "PNP.DirectWire.WireUnaryRealization.checkedGain_isSome_iff": "7858c41c4efdbb472ae418a27f5d2329fff99241ac349df86b2feffd9d44b79a", "PNP.DirectWire.WireUnaryRealization.checkedGain_complete": "8a9b3ad847ac134d943f18e2247041be14b9042a8f4aa393bf2fe50a308223f2", "PNP.DirectWire.WireUnaryRealization.CheckedGain.checked": "785fbaa771e7477604ab00a32d2db483d958dade5d53f96e2c88ceea95ccbe75" }, "theoremAxioms": { "PNP.DirectWire.WireUnaryRealization.observation_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.needsNegation_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.implementation_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_full_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_gateCount": [], "PNP.DirectWire.WireUnaryRealization.negation_requires_gate": [], "PNP.DirectWire.WireUnaryRealization.realize_minimal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.realize_gate_bound": [], "PNP.DirectWire.WireUnaryRealization.R7Discharge.full_value": [], "PNP.DirectWire.WireUnaryRealization.dischargeR7_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.dischargeR7_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.checkedGain_isSome_iff": [], "PNP.DirectWire.WireUnaryRealization.checkedGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryRealization.CheckedGain.checked": [ "Quot.sound", "propext" ] } }, { "number": 256, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-256", "id": "wire-unary-frontier", "title": "Computed constant and unary frontier replacement", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireUnaryFrontierFormalized": true, "leanWireUnaryFrontierAxiomAuditPassed": true, "leanWireUnaryFrontierAuditedDeclarationCount": 30, "leanWireUnaryFrontierConstantValueTheorem": "PNP.DirectWire.WireUnaryFrontier.constantWord_value", "leanWireUnaryFrontierConstantGateCountTheorem": "PNP.DirectWire.WireUnaryFrontier.constantWord_gateCount", "leanWireUnaryFrontierUnaryValueTheorem": "PNP.DirectWire.WireUnaryFrontier.unaryWord_value", "leanWireUnaryFrontierUnaryMinimumTheorem": "PNP.DirectWire.WireUnaryFrontier.unaryWord_minimal", "leanWireUnaryFrontierUnaryGateBoundTheorem": "PNP.DirectWire.WireUnaryFrontier.unaryWord_gate_bound", "leanWireUnaryFrontierLocalValueTheorem": "PNP.DirectWire.WireUnaryFrontier.localWord_value", "leanWireUnaryFrontierLocalMinimumTheorem": "PNP.DirectWire.WireUnaryFrontier.localWord_minimal", "leanWireUnaryFrontierLocalNonincreaseTheorem": "PNP.DirectWire.WireUnaryFrontier.localWord_nonincrease", "leanWireUnaryFrontierLocalGateBoundTheorem": "PNP.DirectWire.WireUnaryFrontier.localWord_gate_bound", "leanWireUnaryFrontierReplacementAgreementTheorem": "PNP.DirectWire.WireUnaryFrontier.replacement_agreement", "leanWireUnaryFrontierReplacementMinimumTheorem": "PNP.DirectWire.WireUnaryFrontier.replacement_minimal", "leanWireUnaryFrontierReplacementNonincreaseTheorem": "PNP.DirectWire.WireUnaryFrontier.replacement_nonincrease", "leanWireUnaryFrontierReplacementGateBoundTheorem": "PNP.DirectWire.WireUnaryFrontier.replacement_gate_bound", "leanWireUnaryFrontierZeroBoundaryGateCountTheorem": "PNP.DirectWire.WireUnaryFrontier.replacement_zero_gateCount", "leanWireUnaryFrontierOutputTheorem": "PNP.DirectWire.WireUnaryFrontier.expanded_output", "leanWireUnaryFrontierFieldTheorem": "PNP.DirectWire.WireUnaryFrontier.expanded_field", "leanWireUnaryFrontierEquivalenceTheorem": "PNP.DirectWire.WireUnaryFrontier.expanded_equivalent", "leanWireUnaryFrontierExactChargeTheorem": "PNP.DirectWire.WireUnaryFrontier.expanded_charge", "leanWireUnaryFrontierNonincreaseTheorem": "PNP.DirectWire.WireUnaryFrontier.expanded_nonincrease", "leanWireUnaryFrontierGainIffTheorem": "PNP.DirectWire.WireUnaryFrontier.expanded_gain_iff", "leanWireUnaryFrontierAttemptIffTheorem": "PNP.DirectWire.WireUnaryFrontier.attempt_isSome_iff", "leanWireUnaryFrontierAttemptOutputTheorem": "PNP.DirectWire.WireUnaryFrontier.attempt_output", "leanWireUnaryFrontierAttemptFieldTheorem": "PNP.DirectWire.WireUnaryFrontier.attempt_field", "leanWireUnaryFrontierAttemptNonincreaseTheorem": "PNP.DirectWire.WireUnaryFrontier.attempt_nonincrease", "leanWireUnaryFrontierAttemptChargeTheorem": "PNP.DirectWire.WireUnaryFrontier.attempt_charge", "leanWireUnaryFrontierR7SourceExactTheorem": "PNP.DirectWire.WireUnaryFrontier.dischargeR7_source_exact", "leanWireUnaryFrontierR7FullValueTheorem": "PNP.DirectWire.WireUnaryFrontier.dischargeR7_full_value", "leanWireUnaryFrontierProperGainIffTheorem": "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_isSome_iff", "leanWireUnaryFrontierProperGainCompletenessTheorem": "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_complete", "leanWireUnaryFrontierCheckedProperGainTheorem": "PNP.DirectWire.WireUnaryFrontier.ProperGain.checked", "leanWireUnaryFrontierArbitraryAmbientCutsCovered": false, "leanWireUnaryFrontierAllR7CasesDerived": false, "leanWireUnaryFrontierArbitraryObligationDAGsCovered": false, "leanWireUnaryFrontierFullManuscriptCarrierProved": false, "leanWireUnaryFrontierCompleteObligationCalculusProved": false, "leanWireUnaryFrontierCompletePackageEProved": false, "leanWireUnaryFrontierPolynomialRuntimeProved": false, "leanWireUnaryFrontierScope": "all-finite-computational-wire-source-derived-visible-predecessor-cone-completed-frontier-zero-or-one-primary-boundary-computed-minimum-local-word-actual-original-exterior-once-full-field-preservation-source-exact-r7-proper-strict-gain-no-arbitrary-support-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireUnaryFrontier.constantWord_value": "582c6c6da7e892847079603a2c1e999c56485675a943444c8b3ce863e41d5129", "PNP.DirectWire.WireUnaryFrontier.constantWord_gateCount": "02c30022268edc2f89c7ebdffe570f0d212a3dd21b63a796cacab6f49d47ef93", "PNP.DirectWire.WireUnaryFrontier.unaryWord_value": "095947adf6640b07f3284119fff23335824743c4e75f2adeebc1b070e5ebcff6", "PNP.DirectWire.WireUnaryFrontier.unaryWord_minimal": "9644515dbe2ccf8a8021425df0f39167e4cf22a038a1c2ad8c126011ba303796", "PNP.DirectWire.WireUnaryFrontier.unaryWord_gate_bound": "195c48ead6423dd5bcfc9bc200792004fab15abee61174b71b96ccace8529123", "PNP.DirectWire.WireUnaryFrontier.localWord_value": "bcdc116ead3fb88e37f646a064753ec35b5e3b1178a8df46dcc945e7cd7763ed", "PNP.DirectWire.WireUnaryFrontier.localWord_minimal": "9de87539b360cf8c0040e5d4768a2a55e97383687ca2414022916c4cc9a22183", "PNP.DirectWire.WireUnaryFrontier.localWord_nonincrease": "7a06ee455f9fad686535a2a5f4d8112080bf2c6baf994721eba3a74c8a69dc9a", "PNP.DirectWire.WireUnaryFrontier.localWord_gate_bound": "bf005c2e94935b87a0cd21dd610ddffc40623f6b3da8ef76b52df09d8747ad6e", "PNP.DirectWire.WireUnaryFrontier.replacement_agreement": "5a6ce39f55892427c9cfe2ece32206a856269003ea4bda810911bb5ab85893ef", "PNP.DirectWire.WireUnaryFrontier.replacement_minimal": "1ade002576afaf298c69d90c456ef5dcf632df1b05becd67531e1907e5ac02c2", "PNP.DirectWire.WireUnaryFrontier.replacement_nonincrease": "4b11aeb29500651f8c1dc09bb581bafc090f2a9acb51791ce3f64cc279c422f1", "PNP.DirectWire.WireUnaryFrontier.replacement_gate_bound": "aaae4b28519807c79aa38af67108af95ec1bc30e1d969f9e188cf8052afe1ab2", "PNP.DirectWire.WireUnaryFrontier.replacement_zero_gateCount": "e2777f23b123d0c48b7d0e42400e6014da1a9ffce5dc4995999854bdd58ee444", "PNP.DirectWire.WireUnaryFrontier.expanded_output": "7cf73ecff68ca9b077e40aa7dcbc504d02075a7a5211bcac5c57f54119209508", "PNP.DirectWire.WireUnaryFrontier.expanded_field": "c0ed63d53076dbe42cfcaffee3b4eb437882a597efeed79fb4fd4228c35fcc09", "PNP.DirectWire.WireUnaryFrontier.expanded_equivalent": "91e8aa94ca777f69bd55519d8edbdae015ac8145d978483c41aacb841ce420ab", "PNP.DirectWire.WireUnaryFrontier.expanded_charge": "3a064a55c067237139602b7293bc814d9502dd3f1da2fafc0cb523205816f24b", "PNP.DirectWire.WireUnaryFrontier.expanded_nonincrease": "aaedf60953e5cc274403a301d8dac0a256d840eb2bc45d5bad6c8953cb1336fa", "PNP.DirectWire.WireUnaryFrontier.expanded_gain_iff": "e5649fb91a1558e9051e72261560f136d0a2b2de40c1aa84f336f7882688de95", "PNP.DirectWire.WireUnaryFrontier.attempt_isSome_iff": "2ae8fcec0f69a026cb3401b20e819003fb80aae5a8fe31293aeeabdc60c659ea", "PNP.DirectWire.WireUnaryFrontier.attempt_output": "43115671e93b1bf19c367b8f8eb3a97ea31037b8a53666824101be7777d5124a", "PNP.DirectWire.WireUnaryFrontier.attempt_field": "55dc6f57b5361080f99936d93b325868b463b8c9269e90ab42e9e953f831bf21", "PNP.DirectWire.WireUnaryFrontier.attempt_nonincrease": "daa30772b0fb2b3c92d3772f171487a7644122cb8dd63618b857b24d3f49e521", "PNP.DirectWire.WireUnaryFrontier.attempt_charge": "c13da7ce02b9d415ce896effe5b499a9b2249bede31138071b8f3c162e851519", "PNP.DirectWire.WireUnaryFrontier.dischargeR7_source_exact": "07674631131aa34ff0ec625e1c1955d34fbeb54da913b397adb298da6cabaa40", "PNP.DirectWire.WireUnaryFrontier.dischargeR7_full_value": "b15b4a349ce8c1670d63d9cb844eedac3b76cd855e18f328cd95782a6c5618c8", "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_isSome_iff": "a985b9427b18b7dd80fc8b442e23d5931780297c0743d36f051e3fafc0760769", "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_complete": "b3a94c1864f51e3aa6295526c3435ad710721875c202426d39e40562b44a488f", "PNP.DirectWire.WireUnaryFrontier.ProperGain.checked": "27dfb2128a2da21e7d2b104627b9e7860979c1f3332580f7ac52e1db64948521" }, "theoremAxioms": { "PNP.DirectWire.WireUnaryFrontier.constantWord_value": [ "Quot.sound" ], "PNP.DirectWire.WireUnaryFrontier.constantWord_gateCount": [], "PNP.DirectWire.WireUnaryFrontier.unaryWord_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.unaryWord_minimal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.unaryWord_gate_bound": [], "PNP.DirectWire.WireUnaryFrontier.localWord_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.localWord_minimal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.localWord_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.localWord_gate_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.replacement_agreement": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.replacement_minimal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.replacement_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.replacement_gate_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.replacement_zero_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.expanded_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.expanded_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.expanded_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.expanded_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.expanded_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.expanded_gain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.attempt_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.attempt_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.attempt_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.attempt_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.attempt_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.dischargeR7_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.dischargeR7_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.checkedProperGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryFrontier.ProperGain.checked": [ "Quot.sound", "propext" ] } }, { "number": 257, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-257", "id": "wire-unary-arbitrary-support", "title": "Computed constant and unary replacement on arbitrary completed supports", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireUnaryArbitrarySupportFormalized": true, "leanWireUnaryArbitrarySupportAxiomAuditPassed": true, "leanWireUnaryArbitrarySupportAuditedDeclarationCount": 31, "leanWireUnaryArbitrarySupportPrefixCausalityTheorem": "PNP.DirectWire.terminalOpenGateEvaluation_prefix_congr", "leanWireUnaryArbitrarySupportSingleBoundaryCausalityTheorem": "PNP.DirectWire.terminalOpenGateEvaluation_single_gate_prefix", "leanWireUnaryArbitrarySupportSingleBoundaryRankTheorem": "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_singleGateBoundary", "leanWireUnaryArbitrarySupportConstantSourceTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.constantWord_source", "leanWireUnaryArbitrarySupportUnaryLiteralConstantTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.unaryWord_source_of_constant", "leanWireUnaryArbitrarySupportLocalLiteralConstantTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.localWord_source_of_constant", "leanWireUnaryArbitrarySupportReplacementAgreementTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_agreement", "leanWireUnaryArbitrarySupportReplacementGateBoundTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_gate_bound", "leanWireUnaryArbitrarySupportReplacementMinimumTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_minimal", "leanWireUnaryArbitrarySupportReplacementNonincreaseTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_nonincrease", "leanWireUnaryArbitrarySupportEarlyFrontierConstantTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_early_constant", "leanWireUnaryArbitrarySupportWellFoundedTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.graph_wellFounded", "leanWireUnaryArbitrarySupportCompilerSuccessTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.compile_isSome", "leanWireUnaryArbitrarySupportOriginalChargeTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.original_charge", "leanWireUnaryArbitrarySupportOutputTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_output", "leanWireUnaryArbitrarySupportFieldTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_field", "leanWireUnaryArbitrarySupportEquivalenceTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_equivalent", "leanWireUnaryArbitrarySupportExactChargeTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_charge", "leanWireUnaryArbitrarySupportNonincreaseTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_nonincrease", "leanWireUnaryArbitrarySupportGainIffTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_gain_iff", "leanWireUnaryArbitrarySupportProperExteriorIffTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.proper_iff_exterior_positive", "leanWireUnaryArbitrarySupportAttemptIffTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_isSome_iff", "leanWireUnaryArbitrarySupportAttemptOutputTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_output", "leanWireUnaryArbitrarySupportAttemptFieldTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_field", "leanWireUnaryArbitrarySupportAttemptNonincreaseTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_nonincrease", "leanWireUnaryArbitrarySupportAttemptChargeTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_charge", "leanWireUnaryArbitrarySupportR7SourceExactTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_source_exact", "leanWireUnaryArbitrarySupportR7FullValueTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_full_value", "leanWireUnaryArbitrarySupportProperGainIffTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_isSome_iff", "leanWireUnaryArbitrarySupportProperGainCompletenessTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_complete", "leanWireUnaryArbitrarySupportCheckedProperGainTheorem": "PNP.DirectWire.WireUnaryArbitrarySupport.ProperGain.checked", "leanWireUnaryArbitrarySupportAllBoundaryWidthsCovered": false, "leanWireUnaryArbitrarySupportAllR7CasesDerived": false, "leanWireUnaryArbitrarySupportArbitraryObligationDAGsCovered": false, "leanWireUnaryArbitrarySupportFullManuscriptCarrierProved": false, "leanWireUnaryArbitrarySupportCompleteObligationCalculusProved": false, "leanWireUnaryArbitrarySupportCompletePackageEProved": false, "leanWireUnaryArbitrarySupportPolynomialRuntimeProved": false, "leanWireUnaryArbitrarySupportScope": "all-finite-computational-wire-arbitrary-physical-support-completed-frontier-zero-or-one-actual-boundary-including-external-gate-source-derived-prefix-causality-minimum-local-word-ranked-actual-compiler-original-exterior-once-full-fields-source-exact-r7-proper-gain-no-general-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalOpenGateEvaluation_prefix_congr": "0061f7c437b7e27d395569d35d48fe9855416854bdfb7cd22e4c78821cebff01", "PNP.DirectWire.terminalOpenGateEvaluation_single_gate_prefix": "d245e3b3e3315e77d7e1f0ca38c2bc9ac0ad8bc60ce4d85eb6fbb61dc628dc7f", "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_singleGateBoundary": "131ac4d4b954bfccdfb334f7592d63c49f7b0f8cbef14dfbd9708672f0622d9b", "PNP.DirectWire.WireUnaryArbitrarySupport.constantWord_source": "b18c68167c2cf5438f22a797e59049c228249a41db1df94fb3c68f4a255963cc", "PNP.DirectWire.WireUnaryArbitrarySupport.unaryWord_source_of_constant": "60d8adc847127db61ed6db043d02138664e66b9a200bc99b9b1b3f0510fdeace", "PNP.DirectWire.WireUnaryArbitrarySupport.localWord_source_of_constant": "4b8ba04460c91c0e6ee0f01e22d3c0be608d2ea54dd0224826f961d937f5965b", "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_agreement": "74d4b769ab2f48a65f221ba3e8811d4bc83b47ee8d4e49f70ceefacbda5f5cfd", "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_gate_bound": "ef7907c6929e65f812aa3844e922101642a88044dbcdc1136626452789aa8fef", "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_minimal": "3418c00e0587573e9846fe69fe66c478ed027632bf7d0f50cd3d1485106967d1", "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_nonincrease": "9a691e352f9e7e2343d297c759286c8cee0962cd9a15e4bcf8a890f8027530ac", "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_early_constant": "3220d6d9eda3f54ad07c5fb7db7f0bf00b44327d56638164662a08dbe56e4bfb", "PNP.DirectWire.WireUnaryArbitrarySupport.graph_wellFounded": "657338f0205eadf7e6f37e70791da590374f199c08f737cd117ecfd42b819fb0", "PNP.DirectWire.WireUnaryArbitrarySupport.compile_isSome": "0b40032fd8e0e14732dac199a115ec61ef9290c916860bd70bd3b15f42d92e61", "PNP.DirectWire.WireUnaryArbitrarySupport.original_charge": "9c1feaa37b5a1fef557510998992eb40d5e5da7dde9b473b0b01868cd9cfabe3", "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_output": "ef4023d873287ec9b791acd9fc6756f06f96f287cbc0944dbe960b80c6b21e67", "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_field": "292b86e2253a9767a078cce964dd0896d49a644dd64a322bd85fff531ecf7481", "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_equivalent": "e28606e602cc080a5d5a140f2101ecf705212c55372cedc7d96b63857af0c8b6", "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_charge": "55ec202abef861068266ee283243cfe5064fcf6378328f4df87e59c39f9e278d", "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_nonincrease": "29f691ff3546ab68f504a9d1afa7e6d320ad8c486061be0eff2c5a287dadafe7", "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_gain_iff": "a30977882e20c40433ceafe9b8c2a6c1766563afe36815f233e25c5ddd2fddfd", "PNP.DirectWire.WireUnaryArbitrarySupport.proper_iff_exterior_positive": "59d8d725ad98e586da3887e5ffbdc7f8dba0c98a209dd9d6c1fbb41fb23dca43", "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_isSome_iff": "b3fd2f73e6aa15a4f4f5eee75d4261473c49a1d994ef023bd12e74f9950cebff", "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_output": "c3f76011dd727f6e2479a1074dc8cf1b9f5c2ab4b85306dd038c0fdb1126b881", "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_field": "82d5498fcea1f4c0e8fbdbbc3f0f74cee2a44c97d84ad9b5e987301d5ab30924", "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_nonincrease": "10a5d687494ddb4e1b7f549b0d5de87af50285e7c753b2e63a4f720ef6bdcfb9", "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_charge": "9c3d33ffd1e0e2506aba7e7b4303991bda2bbb8b5f2cb685a7345ff1a8a5544a", "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_source_exact": "17e1f9fe0e9e1ab2675094cb0ac78aef910bd5874ac89abd74fa24f564335764", "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_full_value": "aa59004c5807cf81b93fee7ba5b990c274d19760237740386541a96ad82b587b", "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_isSome_iff": "b5b5fcf8e6bfcc58f1fa6350972dbc222bd0219cad0409163191075f333f39b6", "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_complete": "d6a6a6ab8f1b05050a450e078a96abf2fdd9b1e23557191928fc6ec00603bd41", "PNP.DirectWire.WireUnaryArbitrarySupport.ProperGain.checked": "0b9d4a813bdd0931dc63942366a1e181a2f7d13a84aaf796aeda9b75b6687961" }, "theoremAxioms": { "PNP.DirectWire.terminalOpenGateEvaluation_prefix_congr": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOpenGateEvaluation_single_gate_prefix": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_singleGateBoundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.constantWord_source": [], "PNP.DirectWire.WireUnaryArbitrarySupport.unaryWord_source_of_constant": [ "Quot.sound" ], "PNP.DirectWire.WireUnaryArbitrarySupport.localWord_source_of_constant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_agreement": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_gate_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_minimal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.replacement_early_constant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.graph_wellFounded": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.compile_isSome": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.original_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.expanded_gain_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.proper_iff_exterior_positive": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_nonincrease": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.attempt_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.dischargeR7_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.checkedProperGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryArbitrarySupport.ProperGain.checked": [ "Quot.sound", "propext" ] } }, { "number": 258, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-258", "id": "wire-unary-support-search", "title": "Computed complete search for proper constant and unary R7 gains", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireUnarySupportSearchFormalized": true, "leanWireUnarySupportSearchAxiomAuditPassed": true, "leanWireUnarySupportSearchAuditedDeclarationCount": 36, "leanWireUnarySupportSearchMaximalAdmissibilityTheorem": "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_admissible", "leanWireUnarySupportSearchMaximalContainmentTheorem": "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_contains", "leanWireUnarySupportSearchCanonicalSelectionIffTheorem": "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected_iff", "leanWireUnarySupportSearchCanonicalSelectionTheorem": "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected", "leanWireUnarySupportSearchActualBoundaryTheorem": "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary", "leanWireUnarySupportSearchUnaryBoundaryTheorem": "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary_small", "leanWireUnarySupportSearchCandidateBoundaryTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_boundary", "leanWireUnarySupportSearchCandidatePropernessTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_proper", "leanWireUnarySupportSearchConsumedWireCountTheorem": "PNP.DirectWire.WireUnarySupportSearch.consumedWires_length", "leanWireUnarySupportSearchBoundaryEnumerationCompletenessTheorem": "PNP.DirectWire.WireUnarySupportSearch.boundary_mem_consumedWires", "leanWireUnarySupportSearchBoundaryChoiceCountTheorem": "PNP.DirectWire.WireUnarySupportSearch.boundaryChoices_length", "leanWireUnarySupportSearchCandidateFamilyCountTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_length", "leanWireUnarySupportSearchMaximalFamilyMembershipTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_maximal_mem", "leanWireUnarySupportSearchSingletonFamilyMembershipTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_singleton_mem", "leanWireUnarySupportSearchActualChoiceMembershipTheorem": "PNP.DirectWire.WireUnarySupportSearch.supportChoice_wire_mem", "leanWireUnarySupportSearchActualChoiceCompletenessTheorem": "PNP.DirectWire.WireUnarySupportSearch.supportChoice_of_mem", "leanWireUnarySupportSearchActualChoiceExteriorTheorem": "PNP.DirectWire.WireUnarySupportSearch.supportChoice_external", "leanWireUnarySupportSearchChoiceFamilyMembershipTheorem": "PNP.DirectWire.WireUnarySupportSearch.supportChoice_mem", "leanWireUnarySupportSearchGeneralSupportAdmissibilityTheorem": "PNP.DirectWire.WireUnarySupportSearch.support_admissible", "leanWireUnarySupportSearchGeneralSupportContainmentTheorem": "PNP.DirectWire.WireUnarySupportSearch.support_contained_in_candidate", "leanWireUnarySupportSearchSelectionCountMonotonicityTheorem": "PNP.DirectWire.WireUnarySupportSearch.selected_length_mono", "leanWireUnarySupportSearchSelectionCountBoundTheorem": "PNP.DirectWire.WireUnarySupportSearch.selected_length_le", "leanWireUnarySupportSearchCandidateRecordBoundTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_entry_length", "leanWireUnarySupportSearchExtractedCountMonotonicityTheorem": "PNP.DirectWire.WireUnarySupportSearch.extracted_gateCount_mono", "leanWireUnarySupportSearchSingletonCanonicalizationTheorem": "PNP.DirectWire.WireUnarySupportSearch.singleton_selection", "leanWireUnarySupportSearchGainCanonicalizationTheorem": "PNP.DirectWire.WireUnarySupportSearch.checkedGain_selection_invariant", "leanWireUnarySupportSearchCandidateFamilyCompletenessTheorem": "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_complete", "leanWireUnarySupportSearchSearchCompletenessTheorem": "PNP.DirectWire.WireUnarySupportSearch.findGain_complete", "leanWireUnarySupportSearchSearchFamilyMembershipTheorem": "PNP.DirectWire.WireUnarySupportSearch.findGain_member", "leanWireUnarySupportSearchSearchRecordBoundTheorem": "PNP.DirectWire.WireUnarySupportSearch.findGain_records_bound", "leanWireUnarySupportSearchCheckedResultTheorem": "PNP.DirectWire.WireUnarySupportSearch.GainResult.checked", "leanWireUnarySupportSearchNoResultExclusionTheorem": "PNP.DirectWire.WireUnarySupportSearch.findGain_none_excludes", "leanWireUnarySupportSearchR7SourceExactTheorem": "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_source_exact", "leanWireUnarySupportSearchR7FullValueTheorem": "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_full_value", "leanWireUnarySupportSearchReplacementRecognitionTheorem": "PNP.DirectWire.WireUnarySupportSearch.findReplacement_isSome", "leanWireUnarySupportSearchReplacementSoundnessTheorem": "PNP.DirectWire.WireUnarySupportSearch.findReplacement_sound", "leanWireUnarySupportSearchProperZeroUnaryCompletenessProved": true, "leanWireUnarySupportSearchPhysicalCandidateCountBoundProved": true, "leanWireUnarySupportSearchPhysicalRecordCountBoundProved": true, "leanWireUnarySupportSearchCallerSuppliedFamilyRequired": false, "leanWireUnarySupportSearchAllBoundaryWidthsCovered": false, "leanWireUnarySupportSearchAllR7CasesDerived": false, "leanWireUnarySupportSearchNoResultProvesGlobalMinimality": false, "leanWireUnarySupportSearchArbitraryObligationDAGsCovered": false, "leanWireUnarySupportSearchFullManuscriptCarrierProved": false, "leanWireUnarySupportSearchCompleteObligationCalculusProved": false, "leanWireUnarySupportSearchCompletePackageEProved": false, "leanWireUnarySupportSearchPolynomialRuntimeProved": false, "leanWireUnarySupportSearchScope": "all-finite-computational-wire-source-derived-proper-zero-or-one-actual-boundary-support-search-complete-maximal-and-singleton-candidates-physical-count-bounds-full-field-actual-replacement-source-exact-r7-no-global-minimum-or-total-encoded-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_admissible": "70718895c2c12e9a1b2af6e777e6117f87418fa2b0462269f7545c516502d7cf", "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_contains": "f88938f8c16b9e730c9bbe267d4f8c89ee5cadfbc0045afdc70ad3999383d22e", "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected_iff": "8c1966ce09ff72f86c881dd7f8d03cde5b6532909f13ba4b2bda0171069737d5", "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected": "28310bf0e776eb00c6ddab4969e490171a045f6381b0280d7ca5cfcba8b6b39a", "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary": "c485b8b5321f2d1fa7d8bbec9e8c6c8dafaaeaea118e2531571578f0484d3181", "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary_small": "5fee27f35b298617410c0bb3f73c1b2ba6903840661f08032877aa243a0fc5c9", "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_boundary": "45ea7f1d043b44229e95a189f531c40ca12462ff49e977e06846165473859910", "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_proper": "6c086a77b1c970c1866350cd6b71c59404f725aa71a441ddeb54019d5827091d", "PNP.DirectWire.WireUnarySupportSearch.consumedWires_length": "030e909521cdbb6875562dde63d2d1a1e879440fd034c32e5a32ce79df396d04", "PNP.DirectWire.WireUnarySupportSearch.boundary_mem_consumedWires": "e07d702982967607422305510ad6bd38c998d9c4194f5a122c64ff25afa1b8b4", "PNP.DirectWire.WireUnarySupportSearch.boundaryChoices_length": "6c3daa4bbe197385783bf050624d6941da972ed3dca1c09ea203b62c1ab1ead1", "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_length": "5ce4eb7077f3268b4fa8f7325d231721bff04ac3f601adee25463b6d46a2a272", "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_maximal_mem": "a5a638feff27bbcf22136a6e3f3fe99e258d9bbae8d563dc276b5795979991a6", "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_singleton_mem": "4af1de31fd4bf4d201e49818b9c1e0b9036ac6b530ee3eaa595f90d110912adf", "PNP.DirectWire.WireUnarySupportSearch.supportChoice_wire_mem": "e5a7155113a150e4aaf7b68426b1e90b908c19d2ef957df26e5b91f0893b8717", "PNP.DirectWire.WireUnarySupportSearch.supportChoice_of_mem": "150fae8fa479784aa8b872ee5ee64e33e7ffa0977b0842a74a4c8083a2cef015", "PNP.DirectWire.WireUnarySupportSearch.supportChoice_external": "021b77ef9449c5607058ebe310fc6ca6a4dde395583092f1495482dd3120b571", "PNP.DirectWire.WireUnarySupportSearch.supportChoice_mem": "33c62ed28a83b297c5c587ea70cef6d79ac6bbb6d29be514466fbc83b77a8a9a", "PNP.DirectWire.WireUnarySupportSearch.support_admissible": "6a2f0d90b9e1a74a0bd4978489f13438b4e0d47b2caf32d86d2514292354dac2", "PNP.DirectWire.WireUnarySupportSearch.support_contained_in_candidate": "bdf998053acbc7c9b0ffb39d091d7354c2d67e389bf909fede832f4755e8b6e9", "PNP.DirectWire.WireUnarySupportSearch.selected_length_mono": "458a84c5f76b84a54aba3ea5dd87967669fda126c21624f20a860d6c7aee424e", "PNP.DirectWire.WireUnarySupportSearch.selected_length_le": "eec3020b2c61f8352307c58580448422619506f4b6f007a4792f33eb0a402d57", "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_entry_length": "78bb59833db65bb63a805949322c55631c163ff4a419a3512227e60a2a169b8e", "PNP.DirectWire.WireUnarySupportSearch.extracted_gateCount_mono": "567c07c22d6bf483761fdf3f2064e21a35c0041cfa2b975e2df6560bc6128714", "PNP.DirectWire.WireUnarySupportSearch.singleton_selection": "4ebcad2581a27e2d0a261fcdc656f874fc61f088c8c97c70bf39a77d124e097b", "PNP.DirectWire.WireUnarySupportSearch.checkedGain_selection_invariant": "66cc45fcb13c84e7b8069467b95dc2a0f79bd4dd78f65727b7c0698e7b36adab", "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_complete": "80e9036cfa4a719acd036e4a33a52dcff6ef6ca5e8c91733e761f8fac5394b7c", "PNP.DirectWire.WireUnarySupportSearch.findGain_complete": "2a680bd477e64a55707a1f892fa3567ec338de4762b201287e4b13601728653c", "PNP.DirectWire.WireUnarySupportSearch.findGain_member": "688799871ec61a8a9962bf3c1cfc47793194efe5842cec84a62cbedd9599ae78", "PNP.DirectWire.WireUnarySupportSearch.findGain_records_bound": "995f1f43b1064187a69323a68140af8b49d4526774b38a4f598e9fd50afc560a", "PNP.DirectWire.WireUnarySupportSearch.GainResult.checked": "4d4132cd01b501b8f103399b3c57c47e45342692e0e6054fd3814448326180ba", "PNP.DirectWire.WireUnarySupportSearch.findGain_none_excludes": "7e9d9d59b2ce85081194c5ab4fb513ebfd1c4e62017889c5fd3b7774e769fd1b", "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_source_exact": "dc48bbffd059b2660b83265da71e67eb8891cee01bb97f2a69c2a7f210cacb9c", "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_full_value": "96904c09e21b42e091484c33a93aa8cb2949f6992410fcdce7f524ca36bd1b53", "PNP.DirectWire.WireUnarySupportSearch.findReplacement_isSome": "c5b472a9d7dba978e4fc789aae984d010d13d659da7054cb5ed8d88b3fc67435", "PNP.DirectWire.WireUnarySupportSearch.findReplacement_sound": "1fb66b7bb02ed8dab6d84d4dc001e8fcdf6b07f39a61c7bf95c3105ae850d3c7" }, "theoremAxioms": { "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_admissible": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.maximalSelection_contains": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.gateRecords_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.admissible_boundary_small": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_boundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateRecords_proper": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.consumedWires_length": [ "propext" ], "PNP.DirectWire.WireUnarySupportSearch.boundary_mem_consumedWires": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.boundaryChoices_length": [ "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_length": [ "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_maximal_mem": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_singleton_mem": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.supportChoice_wire_mem": [ "propext" ], "PNP.DirectWire.WireUnarySupportSearch.supportChoice_of_mem": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.supportChoice_external": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.supportChoice_mem": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.support_admissible": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.support_contained_in_candidate": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.selected_length_mono": [ "propext" ], "PNP.DirectWire.WireUnarySupportSearch.selected_length_le": [ "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_entry_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.extracted_gateCount_mono": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.singleton_selection": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.checkedGain_selection_invariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.candidateFamily_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.findGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.findGain_member": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.findGain_records_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.GainResult.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.findGain_none_excludes": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_source_exact": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.GainResult.dischargeR7_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.findReplacement_isSome": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnarySupportSearch.findReplacement_sound": [ "Quot.sound", "propext" ] } } ] }, "milestoneBatchM259M262": { "kind": "PNPLabsCompiledMilestoneBatch0", "batchId": "m259-m262", "reviewedSource": { "commit": "c3d4d9a115a357b44ee8104d129ee15e3174ec7f", "tree": "7bd3bc5854b0307330e9e405b5857de658eba54e", "statusCoordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-262" }, "milestones": [ { "number": 259, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-259", "id": "wire-zero-unary-closure", "title": "Computed full-field zero/unary descent and normalization closure", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireZeroUnaryClosureFormalized": true, "leanWireZeroUnaryClosureAxiomAuditPassed": true, "leanWireZeroUnaryClosureAuditedDeclarationCount": 27, "leanWireZeroUnaryClosureWholeSelectionTheorem": "PNP.DirectWire.WireZeroUnaryClosure.whole_selected", "leanWireZeroUnaryClosureWholeExteriorTheorem": "PNP.DirectWire.WireZeroUnaryClosure.whole_exterior", "leanWireZeroUnaryClosureWholeGateCountTheorem": "PNP.DirectWire.WireZeroUnaryClosure.whole_gateCount", "leanWireZeroUnaryClosureWholeNotProperTheorem": "PNP.DirectWire.WireZeroUnaryClosure.whole_not_proper", "leanWireZeroUnaryClosureZeroExteriorSelectionTheorem": "PNP.DirectWire.WireZeroUnaryClosure.all_gates_of_zero_exterior", "leanWireZeroUnaryClosureWholeGainCheckedTheorem": "PNP.DirectWire.WireZeroUnaryClosure.WholeGain.checked", "leanWireZeroUnaryClosureWholeRecognitionTheorem": "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_isSome_iff", "leanWireZeroUnaryClosureWholeCompletenessTheorem": "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_complete", "leanWireZeroUnaryClosureGainFullFieldTheorem": "PNP.DirectWire.WireZeroUnaryClosure.Gain.full_field", "leanWireZeroUnaryClosureGainBranchBoundaryTheorem": "PNP.DirectWire.WireZeroUnaryClosure.Gain.branch_boundary", "leanWireZeroUnaryClosureGainExactAccountingTheorem": "PNP.DirectWire.WireZeroUnaryClosure.Gain.exact_accounting", "leanWireZeroUnaryClosureCombinedRecognitionTheorem": "PNP.DirectWire.WireZeroUnaryClosure.nextGain_isSome_iff", "leanWireZeroUnaryClosureCombinedNoResultTheorem": "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_iff", "leanWireZeroUnaryClosureCombinedCompletenessTheorem": "PNP.DirectWire.WireZeroUnaryClosure.nextGain_complete", "leanWireZeroUnaryClosureCombinedNoGainExclusionTheorem": "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_excludes", "leanWireZeroUnaryClosureNormalizationAccountingTheorem": "PNP.DirectWire.WireZeroUnaryClosure.normalization_accounting", "leanWireZeroUnaryClosureNormalizationIterationBoundTheorem": "PNP.DirectWire.WireZeroUnaryClosure.normalization_iterations", "leanWireZeroUnaryClosureTraceCheckedTheorem": "PNP.DirectWire.WireZeroUnaryClosure.Trace.checked", "leanWireZeroUnaryClosureTraceSearchCallBoundTheorem": "PNP.DirectWire.WireZeroUnaryClosure.Trace.searchCalls_le", "leanWireZeroUnaryClosureClosureCheckedTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_checked", "leanWireZeroUnaryClosureStoppedClosureTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_of_stopped", "leanWireZeroUnaryClosureClosureIdempotenceTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_idempotent", "leanWireZeroUnaryClosureScopedTerminalNoGainTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_no_smaller_zeroUnary", "leanWireZeroUnaryClosureReferenceMinimumInvarianceTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_referenceMinimum", "leanWireZeroUnaryClosureResidualSlackAccountingTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_residualSlack", "leanWireZeroUnaryClosureResidualSlackIterationBoundTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_gainIterations_le_residualSlack", "leanWireZeroUnaryClosureResidualSlackSearchCallBoundTheorem": "PNP.DirectWire.WireZeroUnaryClosure.run_searchCalls_le_residualSlack", "leanWireZeroUnaryClosureWholeSpanBranchDerived": true, "leanWireZeroUnaryClosureProperAndWholeZeroUnaryCompletenessProved": true, "leanWireZeroUnaryClosureActualGainRestartClosureProved": true, "leanWireZeroUnaryClosureFullComputationalFieldPreservationProved": true, "leanWireZeroUnaryClosureCommonPhysicalAndScopedQuiescenceProved": true, "leanWireZeroUnaryClosureExactGateAndResidualSlackAccountingProved": true, "leanWireZeroUnaryClosureIdempotenceProved": true, "leanWireZeroUnaryClosureCallerSuppliedFamilyRequired": false, "leanWireZeroUnaryClosureReferenceMinimumUsedInExecution": false, "leanWireZeroUnaryClosureAllBoundaryWidthsCovered": false, "leanWireZeroUnaryClosureNoResultProvesGlobalMinimality": false, "leanWireZeroUnaryClosureArbitraryObligationDAGsCovered": false, "leanWireZeroUnaryClosureFullManuscriptCarrierProved": false, "leanWireZeroUnaryClosureCompleteObligationCalculusProved": false, "leanWireZeroUnaryClosureCompletePackageEProved": false, "leanWireZeroUnaryClosurePolynomialRuntimeProved": false, "leanWireZeroUnaryClosureScope": "all-finite-computational-wire-derived-proper-and-whole-zero-or-one-actual-boundary-search-full-field-gain-normalization-restart-closure-common-scoped-quiescence-idempotence-exact-gate-and-residual-slack-accounting-no-global-minimum-or-total-encoded-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireZeroUnaryClosure.whole_selected": "627ed2af0a291160959dfdfdffef55c50e37a7cfd105a90ad442f14a6a3316b3", "PNP.DirectWire.WireZeroUnaryClosure.whole_exterior": "7708c145c0c2744c9e1ffad5ae437c6cbb5c3c25e41106882e907d314f02920a", "PNP.DirectWire.WireZeroUnaryClosure.whole_gateCount": "8ba65817e6cd4204b11dea40084855a5d206734a7936074da29009a21e5b89dd", "PNP.DirectWire.WireZeroUnaryClosure.whole_not_proper": "9261edea78fb386bb0d9f2a27d289ee811466240faabeac73edd53b304e252b1", "PNP.DirectWire.WireZeroUnaryClosure.all_gates_of_zero_exterior": "f6e0a6a8c942babe9a6c4a2c122847d9c0cb579c0a95f39cf641d0ed35ee8c8c", "PNP.DirectWire.WireZeroUnaryClosure.WholeGain.checked": "49101e38b6bd44729b79970b09a8dbbbdbb9f08e2ab737bed58fd85c6899343e", "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_isSome_iff": "b076fb85cd52e4ef7e1c9912fafea8239292188b40c94d3a0be83f5f6c258170", "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_complete": "4a1e1926b4822cac53144d8eeb605e573a784bd563d1693c57365923dfada977", "PNP.DirectWire.WireZeroUnaryClosure.Gain.full_field": "6ca0493b38ac572fb200f5f755a2c0d8f66335b2bd1c0c7e21ec0930cfd8986f", "PNP.DirectWire.WireZeroUnaryClosure.Gain.branch_boundary": "304254a14f540976f80afefa4e1a04b95dd2faecb6793057552f47cd6a4d6248", "PNP.DirectWire.WireZeroUnaryClosure.Gain.exact_accounting": "a2292c1a2c0688d37e617bac3347667c187b65179ada4da9a5d042367ab3266a", "PNP.DirectWire.WireZeroUnaryClosure.nextGain_isSome_iff": "c290308e2dd1315e8681c2a7cb6f2eb9435d84a201da37b9e4d1056e9c78b1f5", "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_iff": "5fe27147e0c3bf33ad3565f8263260e91fc515a107e54ff61c19cb25ff828977", "PNP.DirectWire.WireZeroUnaryClosure.nextGain_complete": "46f73860393736f9c448a7da052e81f1d28a55a5ab2eb0df6de72899583e5c1a", "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_excludes": "03ff2bbcd0acd7ec0490130890ff65f1f080370b54cf1ee7f463d1ada3133ed5", "PNP.DirectWire.WireZeroUnaryClosure.normalization_accounting": "2819cb214714b32bb4ff397ce796ce0eec804851fccd8c00888ef435db0d8acc", "PNP.DirectWire.WireZeroUnaryClosure.normalization_iterations": "a51bb1c4dc17ff26218541339352535154dc686b8abe9dde6eedc6af47db80a2", "PNP.DirectWire.WireZeroUnaryClosure.Trace.checked": "1335284c1871dddfc16326dd24c100b5295b995f1ff0824f9dcdcc2b86ece17d", "PNP.DirectWire.WireZeroUnaryClosure.Trace.searchCalls_le": "effa524e072458b489d5b0b63bfbfda80c6ed36bef9c994bab20b55abc2bcf92", "PNP.DirectWire.WireZeroUnaryClosure.run_checked": "40d101b370ac4db92988e9f7afd0bf2a89659d9dbd499239541267967eb40336", "PNP.DirectWire.WireZeroUnaryClosure.run_of_stopped": "07f7ad369df6552ab65d2df57f78e12b768199d8305db05e17803ca7d961c981", "PNP.DirectWire.WireZeroUnaryClosure.run_idempotent": "87532d20fc451bed56d7de417756ab0bfacf20cbff130e1b7a311fbb1ff52f27", "PNP.DirectWire.WireZeroUnaryClosure.run_no_smaller_zeroUnary": "27f009d236e975d9363719387fae52b4fbbdd9eca95c1002415364b40839a8b9", "PNP.DirectWire.WireZeroUnaryClosure.run_referenceMinimum": "b0f2d9158f66326d240a45af3878debf5f3887af50f584972921fa58958b7c72", "PNP.DirectWire.WireZeroUnaryClosure.run_residualSlack": "264c9273a5c13179bd7c8a454ed997ba20671e6349811d5c55e19874c93c996f", "PNP.DirectWire.WireZeroUnaryClosure.run_gainIterations_le_residualSlack": "8011c9319b179a0b46b5cb0a0685c77d3adecbda8068bd8cba6b34cf6b887a5f", "PNP.DirectWire.WireZeroUnaryClosure.run_searchCalls_le_residualSlack": "e70efefdebc4db243493e6e6a5eb3309cf1205d93cc92486ebab313842372cc9" }, "theoremAxioms": { "PNP.DirectWire.WireZeroUnaryClosure.whole_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.whole_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.whole_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.whole_not_proper": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.all_gates_of_zero_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.WholeGain.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.wholeGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.Gain.full_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.Gain.branch_boundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.Gain.exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.nextGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.nextGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.nextGain_none_excludes": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.normalization_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.normalization_iterations": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.Trace.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.Trace.searchCalls_le": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_of_stopped": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_idempotent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_no_smaller_zeroUnary": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_referenceMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_gainIterations_le_residualSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireZeroUnaryClosure.run_searchCalls_le_residualSlack": [ "Quot.sound", "propext" ] } }, { "number": 260, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-13-260", "id": "source-bounded-physical-boundary", "title": "Source-bounded ordered physical boundary extraction", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanSourceBoundedPhysicalBoundaryFormalized": true, "leanSourceBoundedPhysicalBoundaryAxiomAuditPassed": true, "leanSourceBoundedPhysicalBoundaryAuditedDeclarationCount": 23, "leanSourceBoundedPhysicalBoundaryUniqueMembershipTheorem": "PNP.DirectWire.SourceListOrder.mem_unique", "leanSourceBoundedPhysicalBoundaryUniqueNoDuplicatesTheorem": "PNP.DirectWire.SourceListOrder.unique_nodup", "leanSourceBoundedPhysicalBoundaryUniqueLengthBoundTheorem": "PNP.DirectWire.SourceListOrder.unique_length_le", "leanSourceBoundedPhysicalBoundaryCanonicalMembershipTheorem": "PNP.DirectWire.SourceListOrder.mem_canonical", "leanSourceBoundedPhysicalBoundaryCanonicalNoDuplicatesTheorem": "PNP.DirectWire.SourceListOrder.canonical_nodup", "leanSourceBoundedPhysicalBoundaryCanonicalLengthBoundTheorem": "PNP.DirectWire.SourceListOrder.canonical_length_le", "leanSourceBoundedPhysicalBoundaryCanonicalOrderTheorem": "PNP.DirectWire.SourceListOrder.canonical_ordered", "leanSourceBoundedPhysicalBoundaryOrderedReferenceUniquenessTheorem": "PNP.DirectWire.SourceListOrder.ordered_eq_of_mem", "leanSourceBoundedPhysicalBoundaryCanonicalReferenceTheorem": "PNP.DirectWire.SourceListOrder.canonical_eq_reference", "leanSourceBoundedPhysicalBoundaryCoordinateInjectivityTheorem": "PNP.DirectWire.TerminalSupportWire.orderCode_injective", "leanSourceBoundedPhysicalBoundaryAmbientReferenceOrderTheorem": "PNP.DirectWire.allTerminalSupportWires_strictOrder", "leanSourceBoundedPhysicalBoundarySourceOccurrenceMembershipTheorem": "PNP.DirectWire.Source.mem_terminalWireOccurrences_iff", "leanSourceBoundedPhysicalBoundarySourceOccurrenceBoundTheorem": "PNP.DirectWire.Source.terminalWireOccurrences_length", "leanSourceBoundedPhysicalBoundaryProgramOccurrenceBoundTheorem": "PNP.DirectWire.terminalSourceWireOccurrences_length", "leanSourceBoundedPhysicalBoundaryCrossingSourceCompletenessTheorem": "PNP.DirectWire.terminalBoundaryWire_mem_sourceOccurrences", "leanSourceBoundedPhysicalBoundarySourceDrivenReferenceTheorem": "PNP.DirectWire.terminalBoundaryPortsSourceDriven_eq_reference", "leanSourceBoundedPhysicalBoundarySourceDrivenLengthBoundTheorem": "PNP.DirectWire.terminalBoundaryPortsSourceDriven_length", "leanSourceBoundedPhysicalBoundarySourceDrivenNoDuplicatesTheorem": "PNP.DirectWire.terminalBoundaryPortsSourceDriven_nodup", "leanSourceBoundedPhysicalBoundarySourceDrivenOrderTheorem": "PNP.DirectWire.terminalBoundaryPortsSourceDriven_ordered", "leanSourceBoundedPhysicalBoundaryActiveReferenceTheorem": "PNP.DirectWire.terminalBoundaryPorts_reference", "leanSourceBoundedPhysicalBoundaryActiveLengthBoundTheorem": "PNP.DirectWire.terminalBoundaryPorts_length", "leanSourceBoundedPhysicalBoundaryActiveNoDuplicatesTheorem": "PNP.DirectWire.terminalBoundaryPorts_nodup", "leanSourceBoundedPhysicalBoundaryActiveOrderTheorem": "PNP.DirectWire.terminalBoundaryPorts_ordered", "leanSourceBoundedPhysicalBoundaryActualGateSourceOccurrencesDerived": true, "leanSourceBoundedPhysicalBoundaryExactOrderedReferenceEqualityProved": true, "leanSourceBoundedPhysicalBoundaryOccurrenceAndBoundaryLengthBoundsProved": true, "leanSourceBoundedPhysicalBoundaryDuplicateFreeCanonicalOrderProved": true, "leanSourceBoundedPhysicalBoundaryActiveExtractorUsesSourceOccurrences": true, "leanSourceBoundedPhysicalBoundaryExistingPhysicalInterfacesPreserved": true, "leanSourceBoundedPhysicalBoundaryUnusedInputEnumerationRequired": false, "leanSourceBoundedPhysicalBoundaryCallerSuppliedBoundaryRequired": false, "leanSourceBoundedPhysicalBoundaryCallerSuppliedCompletenessRequired": false, "leanSourceBoundedPhysicalBoundaryRuntimeExecutionIsProofAuthority": false, "leanSourceBoundedPhysicalBoundaryFullManuscriptCarrierProved": false, "leanSourceBoundedPhysicalBoundaryCompleteObligationCalculusProved": false, "leanSourceBoundedPhysicalBoundaryCompletePackageEProved": false, "leanSourceBoundedPhysicalBoundaryGlobalMinimalityProved": false, "leanSourceBoundedPhysicalBoundaryPolynomialRuntimeProved": false, "leanSourceBoundedPhysicalBoundaryScope": "all-finite-program-dimensions-actual-gate-source-derived-physical-crossings-exact-ordered-ambient-reference-equality-duplicate-free-canonical-order-twice-gate-count-occurrence-and-boundary-bounds-active-extraction-no-unused-input-scan-or-total-encoded-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.SourceListOrder.mem_unique": "7a49dd95817c0455891c81ec6ed64a3c2a85b5781329a7679db339569689ed68", "PNP.DirectWire.SourceListOrder.unique_nodup": "fdb6af13cee2da15e3a1bf9db99b9e84632ea80f4d365237d4afc0eaf13c8505", "PNP.DirectWire.SourceListOrder.unique_length_le": "b2aeba847545c7ed287ff77c5c6333cf7d02493e92f4ac7aeda9364ac8e86260", "PNP.DirectWire.SourceListOrder.mem_canonical": "dca5768a25f190fc4611cb1e2054e6141a42e4f0e226eb0d7eceaba7f6629c85", "PNP.DirectWire.SourceListOrder.canonical_nodup": "efa8dd491c242ec16a53d9e5bd3d04b51848b13cc07975f9a4ba330bd7f21586", "PNP.DirectWire.SourceListOrder.canonical_length_le": "f84d3b5d18c0db478a3823e93af8fa9f6e4e5f29882d12965770cf7ae356f2ad", "PNP.DirectWire.SourceListOrder.canonical_ordered": "69011b5c2c4adac5ef23fcb94e92f461ad000e1caebe690499e4d85793d80f1e", "PNP.DirectWire.SourceListOrder.ordered_eq_of_mem": "030006421cdf64692885e8d0413aca2328d1c0abe95581d510690e07f498138c", "PNP.DirectWire.SourceListOrder.canonical_eq_reference": "0f99873639e837a33d8fd74e57f65fc63f8250e4cf40652588b6d54a8daf8a33", "PNP.DirectWire.TerminalSupportWire.orderCode_injective": "c14e48f0535f611e3de7a1bbd5af9f321918215e5da69823c3c986360231b4a2", "PNP.DirectWire.allTerminalSupportWires_strictOrder": "75ca4fb846a495969bed16586007970e011e9c5d3ff81d59243e82acf0c02c3c", "PNP.DirectWire.Source.mem_terminalWireOccurrences_iff": "f31f5bdd51cc3289dc4cd9eac239a507cb73353f3add38f60ae741e1f676a3e5", "PNP.DirectWire.Source.terminalWireOccurrences_length": "4480ea986948d9dc413b1b5681dc0f03a32f2537bf3404fb42106ed271bef8b4", "PNP.DirectWire.terminalSourceWireOccurrences_length": "5d9dcd82ddcf9b34ac1fcf7032b8ec57e1a79dac9eef18cbbf8eabd267a83169", "PNP.DirectWire.terminalBoundaryWire_mem_sourceOccurrences": "90451eea87b5af9e66066b0508f3933a7dcccf79c130391e2be031ad8337df68", "PNP.DirectWire.terminalBoundaryPortsSourceDriven_eq_reference": "65d0debd44a86f70d7febae2421a6526bd5c56eb7a5b64cc0775b6af76c07930", "PNP.DirectWire.terminalBoundaryPortsSourceDriven_length": "7ec44311f450db96fe5a40e401c6650f4e6bec4df250ab0e1d3e613b22bf3e80", "PNP.DirectWire.terminalBoundaryPortsSourceDriven_nodup": "7e5fa7bbee7ccfaaf40761dafdcc3dac3d64b12c0af6ad1b24a483a94b7a7044", "PNP.DirectWire.terminalBoundaryPortsSourceDriven_ordered": "547ca82d8d21213fe160f9f3284932a60032de7cf82d6dc0d6adf33cff17ea77", "PNP.DirectWire.terminalBoundaryPorts_reference": "6833f172589ae02ed7b73f6853916e7101f12ed7adfe923272f648221736fe4a", "PNP.DirectWire.terminalBoundaryPorts_length": "ba62c4628cd68cb6bbbc0abb968f00d067f305738395d8e13378aaceabad89b1", "PNP.DirectWire.terminalBoundaryPorts_nodup": "9d59decf9fe49a6f8553d10b327e375c3f91c53879545748a5bdba607a146ee6", "PNP.DirectWire.terminalBoundaryPorts_ordered": "c38618e05bb7e55cc5a952be125f3d089f7057336d3b0f981c5648e8c5eacd58" }, "theoremAxioms": { "PNP.DirectWire.SourceListOrder.mem_unique": [ "propext" ], "PNP.DirectWire.SourceListOrder.unique_nodup": [ "propext" ], "PNP.DirectWire.SourceListOrder.unique_length_le": [ "propext" ], "PNP.DirectWire.SourceListOrder.mem_canonical": [ "propext" ], "PNP.DirectWire.SourceListOrder.canonical_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.SourceListOrder.canonical_length_le": [ "propext" ], "PNP.DirectWire.SourceListOrder.canonical_ordered": [ "Quot.sound", "propext" ], "PNP.DirectWire.SourceListOrder.ordered_eq_of_mem": [ "propext" ], "PNP.DirectWire.SourceListOrder.canonical_eq_reference": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalSupportWire.orderCode_injective": [ "propext" ], "PNP.DirectWire.allTerminalSupportWires_strictOrder": [ "Quot.sound", "propext" ], "PNP.DirectWire.Source.mem_terminalWireOccurrences_iff": [ "propext" ], "PNP.DirectWire.Source.terminalWireOccurrences_length": [], "PNP.DirectWire.terminalSourceWireOccurrences_length": [ "propext" ], "PNP.DirectWire.terminalBoundaryWire_mem_sourceOccurrences": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPortsSourceDriven_eq_reference": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPortsSourceDriven_length": [ "propext" ], "PNP.DirectWire.terminalBoundaryPortsSourceDriven_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPortsSourceDriven_ordered": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPorts_reference": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPorts_length": [ "propext" ], "PNP.DirectWire.terminalBoundaryPorts_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPorts_ordered": [ "Quot.sound", "propext" ] } }, { "number": 261, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-261", "id": "context-aware-square-transport", "title": "Context-aware nested open-support and four-corner transport", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanContextAwareSquareTransportFormalized": true, "leanContextAwareSquareTransportAxiomAuditPassed": true, "leanContextAwareSquareTransportAuditedDeclarationCount": 14, "leanContextAwareSquareTransportSelectedGateSemanticsTheorem": "PNP.DirectWire.terminalOpenGateEvaluation_pullback", "leanContextAwareSquareTransportRetainedInterfaceSemanticsTheorem": "PNP.DirectWire.terminalOpenSupportSemantics_pullback", "leanContextAwareSquareTransportIdentityTheorem": "PNP.DirectWire.terminalBoundaryPullback_identity", "leanContextAwareSquareTransportCompositionTheorem": "PNP.DirectWire.terminalBoundaryPullback_compose", "leanContextAwareSquareTransportSquareLegGateInclusionTheorem": "PNP.DirectWire.TerminalOptimumLegTransport.selectedGateTransport", "leanContextAwareSquareTransportLeftPathTheorem": "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_left", "leanContextAwareSquareTransportRightPathTheorem": "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_right", "leanContextAwareSquareTransportSquarePathEqualityTheorem": "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_square", "leanContextAwareSquareTransportExtractedRetainedSemanticsTheorem": "PNP.DirectWire.TerminalOptimumLegTransport.extracted_retained_semantics", "leanContextAwareSquareTransportRealizationRetainedSemanticsTheorem": "PNP.DirectWire.TerminalOptimumLegTransport.realization_retained_semantics", "leanContextAwareSquareTransportFullFamilyRetainedSemanticsTheorem": "PNP.DirectWire.TerminalFourCornerOptimumFamily.full_retained_semantics", "leanContextAwareSquareTransportQuotientFamilyRetainedSemanticsTheorem": "PNP.DirectWire.TerminalFourCornerOptimumFamily.quotient_retained_semantics", "leanContextAwareSquareTransportCanonicalFullRetainedSemanticsTheorem": "PNP.DirectWire.TerminalFourCornerCarrier.canonicalFull_retained_semantics", "leanContextAwareSquareTransportCanonicalQuotientRetainedSemanticsTheorem": "PNP.DirectWire.TerminalFourCornerCarrier.canonicalQuotient_retained_semantics", "leanContextAwareSquareTransportComputedBoundaryPullbackDerived": true, "leanContextAwareSquareTransportArbitraryOpenValuationsCovered": true, "leanContextAwareSquareTransportInternalizedWireValuesComputed": true, "leanContextAwareSquareTransportSelectedGateAndInterfaceSemanticsProved": true, "leanContextAwareSquareTransportIdentityAndCompositionProved": true, "leanContextAwareSquareTransportSquareLegMapsDerived": true, "leanContextAwareSquareTransportTwoPathValuationEqualityProved": true, "leanContextAwareSquareTransportRetainedRealizerOutputsProved": true, "leanContextAwareSquareTransportCanonicalFullAndQuotientComparisonProved": true, "leanContextAwareSquareTransportExistingAmbientClassifierPreserved": true, "leanContextAwareSquareTransportCallerSuppliedTransportRequired": false, "leanContextAwareSquareTransportCallerSuppliedCorrectnessRequired": false, "leanContextAwareSquareTransportWholeCircuitValuationsOnly": false, "leanContextAwareSquareTransportArbitraryObserverEqualityProved": false, "leanContextAwareSquareTransportPhysicalMinimumGluingProved": false, "leanContextAwareSquareTransportChargeAndObligationOwnershipProved": false, "leanContextAwareSquareTransportFullManuscriptCarrierProved": false, "leanContextAwareSquareTransportCompleteObligationCalculusProved": false, "leanContextAwareSquareTransportCompletePackageEProved": false, "leanContextAwareSquareTransportGlobalRouteCoverageProved": false, "leanContextAwareSquareTransportUnconditionalZeroSlackProved": false, "leanContextAwareSquareTransportExactGeneralPCCMinProved": false, "leanContextAwareSquareTransportPolynomialRuntimeProved": false, "leanContextAwareSquareTransportRuntimeExecutionIsProofAuthority": false, "leanContextAwareSquareTransportScope": "arbitrary-finite-nested-supports-all-open-boundary-valuations-computed-internalized-wire-substitution-selected-gate-and-interface-preservation-identity-composition-four-corner-path-equality-retained-full-and-quotient-realizer-outputs-no-arbitrary-observer-equality-or-charge-gluing-or-global-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.terminalOpenGateEvaluation_pullback": "35b9c3d02da43f951376e48ccd7d5ba97539be554d23a9d7dddff9cbefae8526", "PNP.DirectWire.terminalOpenSupportSemantics_pullback": "8d84b0ca652c271d873986c35aeb5421bd37dd88fad0fae2cd7de521824ec1a4", "PNP.DirectWire.terminalBoundaryPullback_identity": "71783e1a89e5a590fa9092e9c4af7f9cc28182317428be2530ca32cca13d93d0", "PNP.DirectWire.terminalBoundaryPullback_compose": "e63b7f727d763163014f598b5e4f10b70938b885228aa7092f60f06924fb1f1e", "PNP.DirectWire.TerminalOptimumLegTransport.selectedGateTransport": "393bcf57ffe9063520828c2e67f1216fd79cd810ae5867e3d961c81f278cba5e", "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_left": "5f87fc82783c695cee293545700beacaddf310b740f32262449887be9a438eed", "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_right": "114556b3dc918cb2593f4df380a0dd47df7bc85d14e16d30602810c6466453dc", "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_square": "97f9a8f9208f99f55767cb101eda981fdc64d1dfa0345277fa0a34209ec247ad", "PNP.DirectWire.TerminalOptimumLegTransport.extracted_retained_semantics": "4fd1fe7a44bec0d3dfc5b1cfe2bf20ff2e70c0e877feee6b196e6a39faaba6d3", "PNP.DirectWire.TerminalOptimumLegTransport.realization_retained_semantics": "f68469c854249882dcdb32bf48257c27581d289dc7a7efc323a4ac3025707f70", "PNP.DirectWire.TerminalFourCornerOptimumFamily.full_retained_semantics": "3c817f60b6078fc084d819793d47f4c1d1f8625c85540628c45d8089e71faf05", "PNP.DirectWire.TerminalFourCornerOptimumFamily.quotient_retained_semantics": "11e22a080e7420cc7e6c10c2f6558588bb79bd9274bf7dacccbfba817e30f6d8", "PNP.DirectWire.TerminalFourCornerCarrier.canonicalFull_retained_semantics": "de03dff609d419f5ecc843e92ca627d0430f1407413e8722a16d0679a6fdeb13", "PNP.DirectWire.TerminalFourCornerCarrier.canonicalQuotient_retained_semantics": "a8bcb2bb6dc0154959d37c2fdcb67eb451eea01759caa939b8072996811253d3" }, "theoremAxioms": { "PNP.DirectWire.terminalOpenGateEvaluation_pullback": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOpenSupportSemantics_pullback": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPullback_identity": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalBoundaryPullback_compose": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalOptimumLegTransport.selectedGateTransport": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_left": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_meet_join_right": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerCarrier.boundaryPullback_square": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalOptimumLegTransport.extracted_retained_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalOptimumLegTransport.realization_retained_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerOptimumFamily.full_retained_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerOptimumFamily.quotient_retained_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerCarrier.canonicalFull_retained_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.TerminalFourCornerCarrier.canonicalQuotient_retained_semantics": [ "Quot.sound", "propext" ] } }, { "number": 262, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-14-262", "id": "wire-causal-expansion", "title": "Total source-ordered charged arbitrary-support expansion", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireCausalExpansionFormalized": true, "leanWireCausalExpansionAxiomAuditPassed": true, "leanWireCausalExpansionAuditedDeclarationCount": 29, "leanWireCausalExpansionRankDecreaseTheorem": "PNP.DirectWire.WireCausalExpansion.graph_rank_decreases", "leanWireCausalExpansionGraphWellFoundedTheorem": "PNP.DirectWire.WireCausalExpansion.graph_wellFounded", "leanWireCausalExpansionCompileSuccessTheorem": "PNP.DirectWire.WireCausalExpansion.compile_success", "leanWireCausalExpansionCompiledResultTheorem": "PNP.DirectWire.WireCausalExpansion.compiled_spec", "leanWireCausalExpansionPhysicalGateCountTheorem": "PNP.DirectWire.WireCausalExpansion.expanded_gateCount", "leanWireCausalExpansionAllOpenMaskedOutputTheorem": "PNP.DirectWire.WireCausalExpansion.masked_replacement_output", "leanWireCausalExpansionReplacementSourceValueTheorem": "PNP.DirectWire.WireCausalExpansion.replacementSource_eval", "leanWireCausalExpansionOriginalSourceValueTheorem": "PNP.DirectWire.WireCausalExpansion.originalSource_eval", "leanWireCausalExpansionGraphSolutionTheorem": "PNP.DirectWire.WireCausalExpansion.values_solution", "leanWireCausalExpansionOrderedOutputSemanticsTheorem": "PNP.DirectWire.WireCausalExpansion.expanded_semantics", "leanWireCausalExpansionPaidSavingIffTheorem": "PNP.DirectWire.WireCausalExpansion.expanded_smaller_iff", "leanWireCausalExpansionSingleInterfaceSavingTheorem": "PNP.DirectWire.WireCausalExpansion.single_interface_smaller", "leanWireCausalExpansionInterfaceNoDuplicatesTheorem": "PNP.DirectWire.WireCausalExpansion.interface_nodup", "leanWireCausalExpansionPhysicalProducerIdentityTheorem": "PNP.DirectWire.WireCausalExpansion.interface_owner_injective", "leanWireCausalExpansionExteriorOwnershipTheorem": "PNP.DirectWire.WireCausalExpansion.exteriorPosition_injective", "leanWireCausalExpansionCopyOwnershipTheorem": "PNP.DirectWire.WireCausalExpansion.copyPosition_injective", "leanWireCausalExpansionDisjointOwnershipTheorem": "PNP.DirectWire.WireCausalExpansion.exteriorPosition_ne_copyPosition", "leanWireCausalExpansionRawOwnershipCoverageTheorem": "PNP.DirectWire.WireCausalExpansion.raw_node_ownership", "leanWireCausalExpansionEmittedOwnershipCoverageTheorem": "PNP.DirectWire.WireCausalExpansion.expanded_gate_ownership", "leanWireCausalExpansionActualOutputSourceTheorem": "PNP.DirectWire.WireCausalExpansion.expanded_source", "leanWireCausalExpansionLiteralOutputSharingTheorem": "PNP.DirectWire.WireCausalExpansion.expanded_source_equal", "leanWireCausalExpansionCarrierOutputTheorem": "PNP.DirectWire.WireCausalExpansion.expandedCarrier_output", "leanWireCausalExpansionCarrierFieldTheorem": "PNP.DirectWire.WireCausalExpansion.expandedCarrier_field", "leanWireCausalExpansionCarrierPhysicalGateCountTheorem": "PNP.DirectWire.WireCausalExpansion.expandedCarrier_gateCount", "leanWireCausalExpansionCarrierPaidSavingIffTheorem": "PNP.DirectWire.WireCausalExpansion.expandedCarrier_smaller_iff", "leanWireCausalExpansionProperAndPaidSavingTheorem": "PNP.DirectWire.WireCausalExpansion.expandedCarrier_proper_and_smaller", "leanWireCausalExpansionLiteralFieldSharingTheorem": "PNP.DirectWire.WireCausalExpansion.expandedCarrier_source_equal", "leanWireCausalExpansionR5CoordinateTheorem": "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_coordinate", "leanWireCausalExpansionR5OriginalFullSourceTheorem": "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_fullWitness", "leanWireCausalExpansionArbitrarySupportAndBoundaryWidthsCovered": true, "leanWireCausalExpansionSourceDerivedRankProved": true, "leanWireCausalExpansionUnconditionalCompilationProved": true, "leanWireCausalExpansionCompleteOpenMaskSemanticsProved": true, "leanWireCausalExpansionEveryOrderedOutputPreservedUnderFullAgreement": true, "leanWireCausalExpansionEveryComputationalFieldPreservedUnderFullAgreement": true, "leanWireCausalExpansionUniquePhysicalCopyOwnershipProved": true, "leanWireCausalExpansionEveryEmittedGateOwned": true, "leanWireCausalExpansionLiteralRepeatedSourceSharingProved": true, "leanWireCausalExpansionOriginalR5CoordinateAndFullValueTransportProved": true, "leanWireCausalExpansionExactExteriorPlusCopiesGateCountProved": true, "leanWireCausalExpansionPaidSavingIffProved": true, "leanWireCausalExpansionPropernessSeparate": true, "leanWireCausalExpansionExistingLiteralCompilerPreserved": true, "leanWireCausalExpansionCallerSuppliedRankRequired": false, "leanWireCausalExpansionCallerSuppliedCompilerSuccessRequired": false, "leanWireCausalExpansionCallerSuppliedFinalSemanticsRequired": false, "leanWireCausalExpansionSemanticsWithoutLocalAgreementProved": false, "leanWireCausalExpansionWholeCircuitValuationsOnly": false, "leanWireCausalExpansionQuotientOnlyFieldAgreementSufficient": false, "leanWireCausalExpansionUnpaidLocalSavingTransportProved": false, "leanWireCausalExpansionMatchedKappaPullExpandProved": false, "leanWireCausalExpansionArbitraryObserverEqualityProved": false, "leanWireCausalExpansionFullManuscriptCarrierProved": false, "leanWireCausalExpansionCompleteObligationCalculusProved": false, "leanWireCausalExpansionCompletePackageEProved": false, "leanWireCausalExpansionGlobalRouteCoverageProved": false, "leanWireCausalExpansionUnconditionalSaturatePositiveProved": false, "leanWireCausalExpansionUnconditionalBCELReadyProved": false, "leanWireCausalExpansionUnconditionalZeroSlackProved": false, "leanWireCausalExpansionExactGeneralPCCMinProved": false, "leanWireCausalExpansionPolynomialRuntimeProved": false, "leanWireCausalExpansionRuntimeExecutionIsProofAuthority": false, "leanWireCausalExpansionScope": "arbitrary-finite-computational-supports-and-boundary-widths-source-derived-rank-total-causal-physical-expansion-all-open-mask-semantics-under-full-local-agreement-all-outputs-and-full-fields-exact-exterior-plus-producer-copies-unique-complete-ownership-literal-sharing-original-R5-source-transport-paid-saving-iff-no-matched-kappa-global-route-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireCausalExpansion.graph_rank_decreases": "57644abb11a3b3a89770af0bff4b95d4a4fb6fe89c95b7597c680d636dd64784", "PNP.DirectWire.WireCausalExpansion.graph_wellFounded": "4f5418492f37d279d5f263f809691860e3b09a5d40a7d19b812c05d33c167477", "PNP.DirectWire.WireCausalExpansion.compile_success": "4411fb4ee3c71709b0374fdd9c5af36d12d6796c5bad2dbba107eeb5fef85e3b", "PNP.DirectWire.WireCausalExpansion.compiled_spec": "aaf6be59c4f88a7fead74673109d28700ce16820dd0f9ad83cf42c7f2fda507b", "PNP.DirectWire.WireCausalExpansion.expanded_gateCount": "758d28d24a55d457119e6ae98f54798de7f173d5c9802e4df7ee95561bdc3209", "PNP.DirectWire.WireCausalExpansion.masked_replacement_output": "498f6fec12401d5e8a6ac437fba202351b12399567e9591ba6fc224cdc04e27a", "PNP.DirectWire.WireCausalExpansion.replacementSource_eval": "1ed6dee331e6062b34c11d9ee8a6abba3113b0043e50f7ad7061af1d9a49fbc3", "PNP.DirectWire.WireCausalExpansion.originalSource_eval": "7c2f1c2c8a2be86a7e09aec3d634c6f5c6e1786b93fe7b491d1795a48fa7d7f0", "PNP.DirectWire.WireCausalExpansion.values_solution": "9ce5f997c23c4cdd4fa5eb1b0421d8891f4763b1e9e7045aeedbc5215579a0d8", "PNP.DirectWire.WireCausalExpansion.expanded_semantics": "d6ab0ab4c6510402f806592b8888b9da2c0ee6edc88632c3ed61924e7b7b838d", "PNP.DirectWire.WireCausalExpansion.expanded_smaller_iff": "b8d6d37e0936f1464d863e28cad33536118657cc8b900e6978a45c7bbc2fa0a7", "PNP.DirectWire.WireCausalExpansion.single_interface_smaller": "c9b50726136c91ec59b2a341172622351e1e37c05b9b7a9b865e467dac95e739", "PNP.DirectWire.WireCausalExpansion.interface_nodup": "9d06c6bbc391a4a17d0a10bb418e085458cf36654d08be9efff05237037c29d9", "PNP.DirectWire.WireCausalExpansion.interface_owner_injective": "596fbac80224cdea520d2cfe72826db69f806725ae86dbfe9bec41e071e87819", "PNP.DirectWire.WireCausalExpansion.exteriorPosition_injective": "41595a52bb4e193f3dbe8f6649e0948a0fae4d0e45e46d6a4761aaf70d9c1511", "PNP.DirectWire.WireCausalExpansion.copyPosition_injective": "a5ccf42333c6b2f01b9c8b0a18ce894001dcb8eb157428245b9702b0870dc778", "PNP.DirectWire.WireCausalExpansion.exteriorPosition_ne_copyPosition": "b962ed0a91245467f2ad53ce6f0fefd92cabb01d232985604a76e0e79b202c1c", "PNP.DirectWire.WireCausalExpansion.raw_node_ownership": "7da2fa53475565b8c6561eaef5bd4d8be3ac6f2b435d931175be7ead3d511622", "PNP.DirectWire.WireCausalExpansion.expanded_gate_ownership": "59a10f634f371082d7cf52c73e31806a2225245671020447310930a6dbfa1855", "PNP.DirectWire.WireCausalExpansion.expanded_source": "51d3a08c647d37b79586934fe8ab9264543b9473edfb524b6fbffd20d0a7940a", "PNP.DirectWire.WireCausalExpansion.expanded_source_equal": "40d8e8ecefe37a22b2d076f6ea12a623b4e456230601f6094d2d71005b149d1e", "PNP.DirectWire.WireCausalExpansion.expandedCarrier_output": "fa6da8a64f9d09a4a1f329e28892d99305ed68ebc1aaa309fc7100a302bad3d3", "PNP.DirectWire.WireCausalExpansion.expandedCarrier_field": "8482512bec2fdd91a41de913dec04499cc23fe9dfb4e22a9c8ac1a9d4d7a9691", "PNP.DirectWire.WireCausalExpansion.expandedCarrier_gateCount": "2ea5c2c9ed9ec03102e3197c42330f2943f914e404f208fe8ea58cdb1e4a9744", "PNP.DirectWire.WireCausalExpansion.expandedCarrier_smaller_iff": "407306bfe3a6784147d80e73a8df3fdc25d67030b8a4669a101495b388da9c15", "PNP.DirectWire.WireCausalExpansion.expandedCarrier_proper_and_smaller": "7d70d141e95bba9b84f18ece6d34ed734c461fc71df177093af4cb703eb7aebd", "PNP.DirectWire.WireCausalExpansion.expandedCarrier_source_equal": "5a8220e89738e799ed538c8549e0ded5f5fe6c00a8046957ad23104579d93386", "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_coordinate": "ad550a5727ce90e16c4049b5b586e57dead7e6fc9438db879ca25e8a35760788", "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_fullWitness": "7e01ca8c99d4a13c025db43dc44f130d836c0e5a9c3f09b45640997f1ce0937e" }, "theoremAxioms": { "PNP.DirectWire.WireCausalExpansion.graph_rank_decreases": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.graph_wellFounded": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.compile_success": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.compiled_spec": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expanded_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.masked_replacement_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.replacementSource_eval": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.originalSource_eval": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.values_solution": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expanded_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expanded_smaller_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.single_interface_smaller": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.interface_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.interface_owner_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.exteriorPosition_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.copyPosition_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.exteriorPosition_ne_copyPosition": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.raw_node_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expanded_gate_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expanded_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expanded_source_equal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedCarrier_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedCarrier_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedCarrier_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedCarrier_smaller_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedCarrier_proper_and_smaller": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedCarrier_source_equal": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_coordinate": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCausalExpansion.expandedR5Creation_fullWitness": [ "Quot.sound", "propext" ] } } ] }, "milestoneBatchM263M264": { "kind": "PNPLabsCompiledMilestoneBatch0", "batchId": "m263-m264", "reviewedSource": { "commit": "029153fc5d8bfc84c61d33858d0472bcbf3d3a73", "tree": "d725f0e14d1a4625c0ce991364fa4481ef3c032a", "statusCoordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-264" }, "milestones": [ { "number": 263, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-263", "id": "wire-obligation-history", "title": "Computed dependency-ordered physical obligation histories", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireObligationHistoryFormalized": true, "leanWireObligationHistoryAxiomAuditPassed": true, "leanWireObligationHistoryAuditedDeclarationCount": 46, "leanWireObligationHistoryDependencySchedulerSuccessIffTheorem": "PNP.DependencyScheduler.compile_success_iff", "leanWireObligationHistoryDependencySchedulerFailureIffTheorem": "PNP.DependencyScheduler.compile_failure_iff", "leanWireObligationHistoryRawOrderSuccessIffTheorem": "PNP.DirectWire.WireObligationHistory.orderEvents_success_iff", "leanWireObligationHistoryRawOrderFailureIffTheorem": "PNP.DirectWire.WireObligationHistory.orderEvents_failure_iff", "leanWireObligationHistoryCreationSourceSnapshotTheorem": "PNP.DirectWire.WireObligationHistory.State.create_source_snapshot", "leanWireObligationHistoryActualRestorationChargeTheorem": "PNP.DirectWire.WireObligationHistory.State.restore_gate_charge", "leanWireObligationHistoryNormalizationBalanceTheorem": "PNP.DirectWire.WireObligationHistory.State.normalize_gate_balance", "leanWireObligationHistoryMatchedDischargeBindingTheorem": "PNP.DirectWire.WireObligationHistory.Transition.dischargeRecord_binding", "leanWireObligationHistoryCreationLifecycleTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle", "leanWireObligationHistoryDependencyOrderTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before", "leanWireObligationHistoryExactlyOnceCountTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_count", "leanWireObligationHistoryUniqueEventIdentitiesTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_identities_nodup", "leanWireObligationHistoryFullFieldTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field", "leanWireObligationHistoryOrdinaryOutputTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output", "leanWireObligationHistoryPhysicalGateBalanceTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance", "leanWireObligationHistoryArbitraryFiniteEventGraphsCovered": true, "leanWireObligationHistoryDuplicateAndMissingReferencesRejected": true, "leanWireObligationHistoryIntrinsicCreationDependenciesComputed": true, "leanWireObligationHistoryCyclicGraphsRejected": true, "leanWireObligationHistoryActualEvolvingCarrierExecuted": true, "leanWireObligationHistorySourceBoundCreationAndDischargeRecords": true, "leanWireObligationHistoryCreationClosesStrictlyLater": true, "leanWireObligationHistoryPhysicalNormalizationPreservesOpenSnapshots": true, "leanWireObligationHistoryFullReadsRequireClosedField": true, "leanWireObligationHistoryFinalOpenObligationsRejected": true, "leanWireObligationHistoryComputedSourceIdentityR6": true, "leanWireObligationHistoryActualCapturedMaterializerR8": true, "leanWireObligationHistoryCompleteAppendedMaterializersCharged": true, "leanWireObligationHistoryNoFreeCrossSnapshotSharing": true, "leanWireObligationHistoryAllValuationFullOutputAndFieldPreservation": true, "leanWireObligationHistoryCallerSuppliedOrderRequired": false, "leanWireObligationHistoryCallerSuppliedRankRequired": false, "leanWireObligationHistoryCallerSuppliedStateRequired": false, "leanWireObligationHistoryCallerSuppliedFullWitnessRequired": false, "leanWireObligationHistoryCallerSuppliedChargesRequired": false, "leanWireObligationHistoryAcyclicityImpliesValidLifecycle": false, "leanWireObligationHistoryConfluenceOfUnderspecifiedEventGraphsProved": false, "leanWireObligationHistoryQuotientAgreementClosesObligation": false, "leanWireObligationHistoryR5ProjectionRemovesPhysicalGates": false, "leanWireObligationHistoryFullR7SemanticsProved": false, "leanWireObligationHistoryAllManuscriptRewriteFamiliesProved": false, "leanWireObligationHistoryAllManuscriptNormalizationFamiliesProved": false, "leanWireObligationHistoryArbitraryObserverOrProfileTransportProved": false, "leanWireObligationHistoryMatchedKappaPullExpandProved": false, "leanWireObligationHistoryFullManuscriptCarrierProved": false, "leanWireObligationHistoryCompletePackageEProved": false, "leanWireObligationHistoryGlobalRouteCoverageProved": false, "leanWireObligationHistoryUnconditionalSaturatePositiveProved": false, "leanWireObligationHistoryUnconditionalBCELReadyProved": false, "leanWireObligationHistoryUnconditionalZeroSlackProved": false, "leanWireObligationHistoryExactGeneralPCCMinProved": false, "leanWireObligationHistoryPolynomialRuntimeProved": false, "leanWireObligationHistoryRuntimeExecutionIsProofAuthority": false, "leanWireObligationHistoryScope": "arbitrary-finite-raw-event-graphs-computed-order-actual-evolving-carriers-source-bound-R5-R6-R8-full-read-records-strictly-later-matched-discharge-all-full-outputs-and-fields-exact-charged-materializer-and-normalization-gate-balance-no-complete-package-E-global-route-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DependencyScheduler.ReadyStep.remaining_lt": "44bff5d1be6c8074e99def406e7faecb346441bedc0ac3b4420e4927f5e1373f", "PNP.DependencyScheduler.Schedule.at_injective": "7325e0440ba228aecb1f3ca0bfd787ab82c93ed61aeb267db5b806a17845d360", "PNP.DependencyScheduler.Schedule.order_complete": "c0bc5ea38e5bef5a3db8cfb385afd687f05970189a64219461a71a0c0cdc8e98", "PNP.DependencyScheduler.Schedule.order_length": "ccc28a25035f30ad731ce79d62437d84f497ca2c972ac0ef820cdfe0c6c78e83", "PNP.DependencyScheduler.Schedule.order_nodup": "6fcec66236c25dbcf4e6eb74c07a06f8ffb1408eca6aaab395877ef05942d704", "PNP.DependencyScheduler.Schedule.wellFounded": "ba098126abab3930ba38e3eba6155f6aec86bf83d17d1e9b8e7a7cb9ef872882", "PNP.DependencyScheduler.Stop.complete_of_wellFounded": "08aae73b031ced880c4c698523e670264020780bb2299593f48647c49c8a73dc", "PNP.DependencyScheduler.Stop.unresolved_predecessor": "3dc12cd45be6bcb7141fb81a8f29da69532c3374d724539d5e61f78c209193ac", "PNP.DependencyScheduler.compile_failure_iff": "d49913a5214be6296ea356ed69f4002bbf3adca2218ed7a66f3e35da36f5cf6e", "PNP.DependencyScheduler.compile_success_iff": "ff4041ae74888da57f525b104b237572ed7922572b4619e38611029541d78b8e", "PNP.DirectWire.WireObligationHistory.State.cancel_full_value": "f39bb7ff18787f0445bbbddb90f22badc6cc0c720066e449ab0256e4bcbf73f4", "PNP.DirectWire.WireObligationHistory.State.cancel_gateCount": "c6b668b242c280f4bc4e947acf75953e8b3d486f1ffa620a3357de1e42466dec", "PNP.DirectWire.WireObligationHistory.State.closed_field": "aad78fb5c71f29dcc02113ec8f755d63ca8a3a2d475a3eda1f28ac90c6d3a1b2", "PNP.DirectWire.WireObligationHistory.State.create_gateCount": "c5055ea4079398b0c5de5ba33fead7a9e45e2ffeb9c6b8bed34bd3c42d39cca4", "PNP.DirectWire.WireObligationHistory.State.create_source_snapshot": "5e6a73008b9ba035838fc473c3ce1d8aac10e09a8a343cdb47aeeba1160583ea", "PNP.DirectWire.WireObligationHistory.State.currentAgreement": "13ccc70890d2b8883766af4ec127af0c5db4d32c4f08c14df0a35b89a8338770", "PNP.DirectWire.WireObligationHistory.State.normalize_gate_balance": "40935311cd19f706866b06b3b69c7931faead7274c31c7a9c0257f704b3a75ac", "PNP.DirectWire.WireObligationHistory.State.restore_full_value": "dad270a9a1c3a769c62fca96c301be597773a74ece28bf44218ed6ddec8b5ac2", "PNP.DirectWire.WireObligationHistory.State.restore_gate_charge": "6bb4d07dacd7838eabe2be506c785034ae0f46fb4e02fd85e72037ab5a7845bc", "PNP.DirectWire.WireObligationHistory.OrderedEvents.identities_nodup": "ac8b9a9e2dfa8c944d30f4662958a5d7013379563d60c29150c23bf23dd99d46", "PNP.DirectWire.WireObligationHistory.OrderedEvents.order_complete": "441646f4a5b2cb4a59e2ccfc6c8da1304a4ac9a12168930258a8dbf310937d94", "PNP.DirectWire.WireObligationHistory.OrderedEvents.order_length": "20d3aff2d74b639edf50bd457633a18516b53a83e7649fb05cdf712d4ee4d7d7", "PNP.DirectWire.WireObligationHistory.OrderedEvents.order_nodup": "2abfa0b890cbe1d904f1f8d6fc4896e76d8b14411f872fd45cb3b57b23e6f9fc", "PNP.DirectWire.WireObligationHistory.completeReferences_iff": "355c32c56adc705ed0a0190ec224cca20c12a519c46ad7e13432214a0eaa2791", "PNP.DirectWire.WireObligationHistory.graph_dependency_iff": "89f258096645cbd1c3edddcd44168ac82c80ee6061cdf7fa65a21071d2f13153", "PNP.DirectWire.WireObligationHistory.orderEvents_failure_iff": "1e6aee6d2dcd4caeaed20485b311134540d383f0ff27836ad981c2c1e32de043", "PNP.DirectWire.WireObligationHistory.orderEvents_success_iff": "ae1c23179eb625d7939d2c162f30ba70de98db04c30dc8e7f163195eddba6c12", "PNP.DirectWire.WireObligationHistory.uniqueIDs_iff": "71bcbb813a106280cbc23056655b1e00d003abe9546142102a9252995d14ce06", "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle": "931d176535e4d513f8d0c55154d78e8ceb5046c4f00de10429bcaba5e91bbc66", "PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before": "eb9fd5eeb6da03880e4e567c1150d9f788db315013c32ec064dc78c0e551010d", "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_count": "3cd573f4f6711d7024502c0f32d4e095b2d72c472a2683dd98b6dbde45fcb37a", "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_identities_nodup": "c45b5bc13d7b34725e10435625feec02f58632c53a3de2870daa4b7e3b5a1707", "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field": "c693beecbd081a97a4cbb69a8d352963830e1ef59577d90930adbc208a3f111f", "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output": "b424d42f293c35731c15c87699685a7276d36f6535dc9df10d94038525f92c63", "PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance": "1f6a44c3ae70e9bd68aa2f4c27ee53ca15d367bf7537504601368e758bc05207", "PNP.DirectWire.WireObligationHistory.Execution.creationsClosed_of_finalClosed": "2cc26c978ca29feaab7f93495679a526a087d81e45d41e79b747581f3c2affb9", "PNP.DirectWire.WireObligationHistory.Execution.pending_persists_or_discharged": "d6e413063b471ed85b88a8511c3e00cb1b8fbf74c8342ab840a87b0ef833cee2", "PNP.DirectWire.WireObligationHistory.Execution.record_identities": "99998dc3a2db9727261c6aaa9f719dd7e2e7bc1f07d0b4ed2ada9ceb24736ac5", "PNP.DirectWire.WireObligationHistory.Execution.total_charge": "7f1fa056790d301cbe44e1ff146522fe5a6de86a0b4f6f6ce8973ee63a100df1", "PNP.DirectWire.WireObligationHistory.Execution.total_removed": "f904a4305079095ec645306a1d05def1959dce27fb56cbe806f3869f967d4230", "PNP.DirectWire.WireObligationHistory.State.isClosed_sound": "1e28a1969b79445ff35e88b8ba4bfbd84dcbf8ab4a5c62dccafa824dd5cd28fa", "PNP.DirectWire.WireObligationHistory.Transition.charged_eq": "e43b203250254c6888614c96da96a1969c48c462fcf2b82847f344974b2b6b83", "PNP.DirectWire.WireObligationHistory.Transition.created_pending": "4946de5b4d016cfce8082bf7d22630cb7e7b37867fdc9b668d6213d1e3f3d824", "PNP.DirectWire.WireObligationHistory.Transition.dischargeRecord_binding": "140da6c4f11123758ced882d33305ac808236012f726b61dbee4f11a3298b351", "PNP.DirectWire.WireObligationHistory.Transition.pending_persists_or_discharged": "6b9c4958f407e0ffac3ca7d15254ed0070e775cb4b2ab2e2483e7b6a2c8ee192", "PNP.DirectWire.WireObligationHistory.Transition.removed_eq": "9ec3017bd5fed872a00ee12b52b2e9b3a414623683270daed4fca66aabd839b4" }, "theoremAxioms": { "PNP.DependencyScheduler.ReadyStep.remaining_lt": [ "Quot.sound", "propext" ], "PNP.DependencyScheduler.Schedule.at_injective": [], "PNP.DependencyScheduler.Schedule.order_complete": [ "Quot.sound", "propext" ], "PNP.DependencyScheduler.Schedule.order_length": [ "propext" ], "PNP.DependencyScheduler.Schedule.order_nodup": [ "Quot.sound", "propext" ], "PNP.DependencyScheduler.Schedule.wellFounded": [], "PNP.DependencyScheduler.Stop.complete_of_wellFounded": [], "PNP.DependencyScheduler.Stop.unresolved_predecessor": [], "PNP.DependencyScheduler.compile_failure_iff": [ "Quot.sound", "propext" ], "PNP.DependencyScheduler.compile_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.cancel_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.cancel_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.closed_field": [], "PNP.DirectWire.WireObligationHistory.State.create_gateCount": [ "propext" ], "PNP.DirectWire.WireObligationHistory.State.create_source_snapshot": [ "propext" ], "PNP.DirectWire.WireObligationHistory.State.currentAgreement": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.normalize_gate_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.restore_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.restore_gate_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.OrderedEvents.identities_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.OrderedEvents.order_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.OrderedEvents.order_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.OrderedEvents.order_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.completeReferences_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.graph_dependency_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.orderEvents_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.orderEvents_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.uniqueIDs_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.executed_identities_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Execution.creationsClosed_of_finalClosed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Execution.pending_persists_or_discharged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Execution.record_identities": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Execution.total_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Execution.total_removed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.isClosed_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.charged_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.created_pending": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.dischargeRecord_binding": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.pending_persists_or_discharged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.removed_eq": [ "Quot.sound", "propext" ] } }, { "number": 264, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-15-264", "id": "wire-history-arbitrary-support", "title": "Source-derived closed-history literal arbitrary-support replacement", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireHistoryArbitrarySupportFormalized": true, "leanWireHistoryArbitrarySupportAxiomAuditPassed": true, "leanWireHistoryArbitrarySupportAuditedDeclarationCount": 24, "leanWireHistoryArbitrarySupportExtractionCausalLevelsTheorem": "PNP.DirectWire.extractTerminalSupport_causal_levels", "leanWireHistoryArbitrarySupportExtractionCausalIndexTheorem": "PNP.DirectWire.extractTerminalSupport_causal_index", "leanWireHistoryArbitrarySupportPhysicalNormalizationCausalBoundTheorem": "PNP.DirectWire.CausalBound.physical_normalization_output_bound", "leanWireHistoryArbitrarySupportCapturedRestorationCausalBoundTheorem": "PNP.DirectWire.WireObligationRestoration.join_causalBounds", "leanWireHistoryArbitrarySupportClosedHistoryCausalInvariantTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant", "leanWireHistoryArbitrarySupportClosedHistoryFieldCausalBoundTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound", "leanWireHistoryArbitrarySupportLiteralGraphRankDecreaseTheorem": "PNP.DirectWire.ArbitrarySupportSplice.graph_causal_rank_decreases", "leanWireHistoryArbitrarySupportLiteralGraphWellFoundedTheorem": "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_causalInterfaceBound", "leanWireHistoryArbitrarySupportClosedHistoryEquivalentTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_equivalent", "leanWireHistoryArbitrarySupportDerivedInterfaceBoundTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_causalInterfaceBound", "leanWireHistoryArbitrarySupportClosedHistoryCompilationTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles", "leanWireHistoryArbitrarySupportOrderedOutputSemanticsTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics", "leanWireHistoryArbitrarySupportCompletePhysicalAccountingTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting", "leanWireHistoryArbitrarySupportStrictGainTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain", "leanWireHistoryArbitrarySupportRawConstructorCompleteTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete", "leanWireHistoryArbitrarySupportRawConstructorSoundTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound", "leanWireHistoryArbitrarySupportNoAdditionalRejectionTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff", "leanWireHistoryArbitrarySupportArbitraryFiniteCandidateSupportAndEventDimensionsCovered": true, "leanWireHistoryArbitrarySupportZeroDuplicateOrdinaryOutputsInExtractedCarrier": true, "leanWireHistoryArbitrarySupportCurrentAndPendingSnapshotCausalBoundsDerived": true, "leanWireHistoryArbitrarySupportActualPhysicalNormalizerAndCapturedMaterializerUsed": true, "leanWireHistoryArbitrarySupportSourceIdentityCancellationPreserved": true, "leanWireHistoryArbitrarySupportLiteralOneCopySpliceAfterEveryAcceptedClosedHistory": true, "leanWireHistoryArbitrarySupportEveryOrderedOriginalOutputPreserved": true, "leanWireHistoryArbitrarySupportCompleteMaterializerChargesIncluded": true, "leanWireHistoryArbitrarySupportStrictGainRequiresRemovalsExceedCharges": true, "leanWireHistoryArbitrarySupportSpliceStageAddsNoRejection": true, "leanWireHistoryArbitrarySupportCallerSuppliedReplacementRequired": false, "leanWireHistoryArbitrarySupportCallerSuppliedRankOrOrderRequired": false, "leanWireHistoryArbitrarySupportCallerSuppliedSemanticCertificateRequired": false, "leanWireHistoryArbitrarySupportBooleanEquivalenceAloneEnsuresAcyclicity": false, "leanWireHistoryArbitrarySupportSupportRecordsAndRawEventsDerivedFromEveryInput": false, "leanWireHistoryArbitrarySupportFullR7SemanticsProved": false, "leanWireHistoryArbitrarySupportAllManuscriptRewriteAndNormalizationFamiliesProved": false, "leanWireHistoryArbitrarySupportArbitraryObserverOrFullProfileTransportProved": false, "leanWireHistoryArbitrarySupportMatchedKappaPullExpandProved": false, "leanWireHistoryArbitrarySupportFullManuscriptCarrierProved": false, "leanWireHistoryArbitrarySupportCompletePackageEProved": false, "leanWireHistoryArbitrarySupportTerminalFamiliesDerived": false, "leanWireHistoryArbitrarySupportGloballySuccessfulRewriteStrategyDerived": false, "leanWireHistoryArbitrarySupportGlobalRouteCoverageProved": false, "leanWireHistoryArbitrarySupportUnconditionalSaturatePositiveProved": false, "leanWireHistoryArbitrarySupportUnconditionalBCELReadyProved": false, "leanWireHistoryArbitrarySupportUnconditionalZeroSlackProved": false, "leanWireHistoryArbitrarySupportExactGeneralPCCMinProved": false, "leanWireHistoryArbitrarySupportPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanWireHistoryArbitrarySupportRuntimeExecutionIsProofAuthority": false, "leanWireHistoryArbitrarySupportScope": "arbitrary-finite-source-extraction-closed-R5-R6-R8-history-derived-current-and-snapshot-causality-literal-one-copy-splice-all-ordered-outputs-complete-removal-charge-equation-no-additional-rejection-no-derived-terminal-family-global-route-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.extractTerminalSupport_causal_levels": "123e68b3b62bd7450cceb874b37e9133aa7f5bef061c5fd3a7b86006ab209b36", "PNP.DirectWire.extractTerminalSupport_causal_index": "266f2d202c756ac3d535808efc7288371be039b7bd6f3334471a4eb4a09126dc", "PNP.DirectWire.CausalBound.physical_normalization_output_bound": "a6fb41b87c15347278653ccabf0f339b0021e1ff7f00aaf2a6ae3593f5ff8ab8", "PNP.DirectWire.WireCarrier.normalize_causalBounds": "62d2b55983b9459d9c8a4ec3729e24b6757e22aa464e831b36f780edc19534c0", "PNP.DirectWire.WireObligationRestoration.join_causalBounds": "96a57b1e39fa62e703469131981a9464a954c6e6ef93a968c9363130492cdfef", "PNP.DirectWire.WireObligationHistory.Transition.causalInvariant": "5e8e6b3008a3ae5e6eae219e5642bd71496d4c78a6fe24cc00f06d8579bc25c1", "PNP.DirectWire.WireObligationHistory.Execution.causalInvariant": "7eeda6beaebe55aefa689012673e7b2aad279c3a1f98270a8c045d149109de1d", "PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant": "d766a4d18cd18b8fc41844f5862a1db0293043ad3be6711bf2f183584391b9b7", "PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound": "aa051739783a3bcf78c4cfd030bda11ebb4191071367ac5a9cd09d2f63f2dcb8", "PNP.DirectWire.WireObligationHistory.compileHistory_causal_bounds": "d85cb81dde3ff4b72e81c8fd56bbfd521031f13dc86cad93f30a84b5888f452e", "PNP.DirectWire.ArbitrarySupportSplice.graph_causal_rank_decreases": "401cb888e0fdd3fffd02d24c5f5a46d0ec23a3370a61e1c298b3efa086a83f1a", "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_causalInterfaceBound": "47cf35847af614649c6e8f5d929c8447d2a3fcd036119a9cbdb98ca5f9a12e38", "PNP.DirectWire.ArbitrarySupportSplice.compile_of_causalInterfaceBound": "66036c51abd18c65462094db35c49f463b6e40944fb0f40f06bc4ecdb9a63c79", "PNP.DirectWire.WireHistoryArbitrarySupport.extractedCarrier_gateCount": "5b11e6ffa16f80744a224cc5fcaad6a3d2132ca68567e8e0a1b9aeda0e45eae2", "PNP.DirectWire.WireHistoryArbitrarySupport.extractedCarrier_fieldValue": "c4513e607a0d66901d00b788ed6c1884105fb8e2d8d6bc6d9c96df55583250c5", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_equivalent": "b949f2d62101de6687ded05b81d36f3b11b48ebdd722a7d69a8a2d4eb158124d", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_causalInterfaceBound": "bb37db6c982b6fc8e1a879a0c2c5e8a1669fec6d7939d8ff024b205dcd546903", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles": "24628ba7c42242ba62325ae3a02a86c5da4afa69372ee4a8db95369cb2c54177", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics": "3ff01612253857a44f687e7850d60a8c0895046ef5ab7a5bd4190dab27453031", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting": "ba21db1c802ed21d062b78b1a28939a1cac493aba356401f9981e460e076f323", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain": "e6abcd11b0d7e89b0c908788f665a71b2d7576be1ff9a7396e36821647e91770", "PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete": "e4dbaa109b94d8d0704c04d90f776e755c079b7c6e303cb5097cc985df6a6756", "PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound": "7f2ab5eee8236bc96b3ab1f3d1a0edb44631fef986b0c8f0a67f0f7668ba3def", "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff": "b83a398e1ac68926f820d96f95b7e9e21042f8fabcecbbd0fad685a544eeaffb" }, "theoremAxioms": { "PNP.DirectWire.extractTerminalSupport_causal_levels": [ "Quot.sound", "propext" ], "PNP.DirectWire.extractTerminalSupport_causal_index": [ "Quot.sound", "propext" ], "PNP.DirectWire.CausalBound.physical_normalization_output_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.normalize_causalBounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationRestoration.join_causalBounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Execution.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.compileHistory_causal_bounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.graph_causal_rank_decreases": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.graph_wellFounded_of_causalInterfaceBound": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.compile_of_causalInterfaceBound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.extractedCarrier_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.extractedCarrier_fieldValue": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_causalInterfaceBound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff": [ "Quot.sound", "propext" ] } } ] }, "milestoneBatchM265M280": { "kind": "PNPLabsCompiledMilestoneBatch0", "batchId": "m265-m280", "reviewedSource": { "commit": "f14cb7a87004ebedfa55351f6ba20d68a333cc18", "tree": "1cbaf64d8a7303b154848ec73f38e85e406defca", "statusCoordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-280" }, "milestones": [ { "number": 265, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-265", "id": "computed-r7-history", "title": "Source-derived R7 discharge in raw computational histories", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanComputedR7HistoryFormalized": true, "leanComputedR7HistoryAxiomAuditPassed": true, "leanComputedR7HistoryAuditedDeclarationCount": 41, "leanComputedR7HistoryActualCompilerDependencyBoundTheorem": "PNP.DirectWire.RawNandCausalBound.compile_bounds", "leanComputedR7HistoryWholeCarrierDependencyBoundTheorem": "PNP.DirectWire.WireUnaryCausalBound.expanded_causalBounds", "leanComputedR7HistoryRawRecordRoundTripTheorem": "PNP.DirectWire.WireObligationHistory.decodeRecord_encode", "leanComputedR7HistoryRawRecordSourceTheorem": "PNP.DirectWire.WireObligationHistory.decodeRecord_source", "leanComputedR7HistoryRawListRoundTripTheorem": "PNP.DirectWire.WireObligationHistory.decodeRecords_encode", "leanComputedR7HistoryRawListSourceTheorem": "PNP.DirectWire.WireObligationHistory.decodeRecords_source", "leanComputedR7HistoryRecognitionIffTheorem": "PNP.DirectWire.WireObligationHistory.computeR7_isSome_iff", "leanComputedR7HistoryCapturedFullValueTheorem": "PNP.DirectWire.WireObligationHistory.State.restoreR7_full_value", "leanComputedR7HistoryActualMaterializerChargeTheorem": "PNP.DirectWire.WireObligationHistory.State.restoreR7_gate_charge", "leanComputedR7HistoryOtherPendingSnapshotsTheorem": "PNP.DirectWire.WireObligationHistory.State.restoreR7_other_pending", "leanComputedR7HistoryTransitionCausalInvariantTheorem": "PNP.DirectWire.WireObligationHistory.State.restoreR7_causalInvariant", "leanComputedR7HistorySourceCreationLifecycleTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle", "leanComputedR7HistoryClosedHistoryCompilationTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles", "leanComputedR7HistoryCompletePhysicalAccountingTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting", "leanComputedR7HistoryNoAdditionalRejectionTheorem": "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff", "leanComputedR7HistoryArbitraryFiniteCarrierSupportAndEventDimensionsCovered": true, "leanComputedR7HistoryWholeListCoordinatesPreserved": true, "leanComputedR7HistoryExactZeroUnaryRecognitionDerived": true, "leanComputedR7HistoryCapturedCreationIdentityRequired": true, "leanComputedR7HistoryActualComputedReplacementAndMaterializerUsed": true, "leanComputedR7HistoryCurrentAndPendingSnapshotCausalBoundsDerived": true, "leanComputedR7HistoryCompleteMaterializerChargesIncluded": true, "leanComputedR7HistoryLiteralOneCopySpliceAddsNoRejection": true, "leanComputedR7HistoryCallerSuppliedReplacementRequired": false, "leanComputedR7HistoryCallerSuppliedTruthTableRequired": false, "leanComputedR7HistoryCallerSuppliedRankOrOrderRequired": false, "leanComputedR7HistoryCallerSuppliedSemanticCertificateRequired": false, "leanComputedR7HistoryBooleanEquivalenceAloneBoundsDependencies": false, "leanComputedR7HistorySupportRecordsAndRawEventsDerivedFromEveryInput": false, "leanComputedR7HistoryFullManuscriptR7SemanticsProved": false, "leanComputedR7HistoryAllManuscriptRewriteAndNormalizationFamiliesProved": false, "leanComputedR7HistoryArbitraryObserverOrFullProfileTransportProved": false, "leanComputedR7HistoryCompletePackageEProved": false, "leanComputedR7HistoryTerminalFamiliesDerived": false, "leanComputedR7HistoryGloballySuccessfulRewriteStrategyDerived": false, "leanComputedR7HistoryGlobalRouteCoverageProved": false, "leanComputedR7HistoryUnconditionalSaturatePositiveProved": false, "leanComputedR7HistoryUnconditionalBCELReadyProved": false, "leanComputedR7HistoryUnconditionalZeroSlackProved": false, "leanComputedR7HistoryExactGeneralPCCMinProved": false, "leanComputedR7HistoryPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanComputedR7HistoryRuntimeExecutionIsProofAuthority": false, "leanComputedR7HistoryScope": "arbitrary-finite-computational-carriers-raw-record-lists-exact-zero-unary-recognition-source-derived-R7-captured-creation-full-discharge-actual-materializer-charges-derived-causality-closed-R5-R6-R7-R8-histories-literal-one-copy-splice-no-new-rejection-no-derived-global-strategy-or-complete-manuscript-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.RawNandCompilationState.finish_position": "d132e92cc600951248a7c4d18ccd2536f545fb5d637d63901fe5884e22a78e99", "PNP.DirectWire.RawNandCausalBound.compile_bounds": "6d644822bc7e6a5a5a86b5ba70e882dd3bb62616ad979df6462bad85e5a2273b", "PNP.DirectWire.RawNandCausalBound.candidate_bound": "b4bcf059257172153564d9ad29ab2c7d5b689469ab3e48974667f80cf6cc5ba6", "PNP.DirectWire.ArbitrarySupportSplice.graph_dependency_bounds": "e55461cefebaf2cce8759494d7894d57cd953c21a29f377c6eb8f5ae94fa87cf", "PNP.DirectWire.ArbitrarySupportSplice.result_output_dependency_bound": "0bb8f943b2343b78770051263c7cbf575d5fac297e15fb5f5fa7f35ccdf34006", "PNP.DirectWire.WireUnaryCausalBound.implementation_output_bound": "a498c50f7907bc63d7de888a5055f6a59a7c1a31fe59a596855f1a5e95af7f68", "PNP.DirectWire.WireUnaryCausalBound.constantWord_output_bound": "6d8fbf7f8d2490aaa8e0d1ed8c4a19fa3d6c4c3e4a1ee38659907a7c980373d5", "PNP.DirectWire.WireUnaryCausalBound.localWord_output_bound": "3a1a2b6d7ff7e15070ed812ed62d0cfec00883d78001d1fdef272391807996cd", "PNP.DirectWire.WireUnaryCausalBound.arbitrary_replacement_output_bound": "cfda0022edafc82313990497df2a60e3fa9d8a719157700cb89be2722fb8a263", "PNP.DirectWire.WireUnaryCausalBound.compiled_spec": "d4d6651356de9cf54f61e97387ea2ff19fdc85a78ee619f4c998828a25811765", "PNP.DirectWire.WireUnaryCausalBound.replacement_dependency_bound": "db56391c15729c5acf6174ae0832aec317ce7073f46eb95eb69ecb4912f141ba", "PNP.DirectWire.WireUnaryCausalBound.expanded_exposed_bound": "808d3b5c4ea0f2dcf19d291734763344fdad5f318aad9383d0d674e4992cda8f", "PNP.DirectWire.WireUnaryCausalBound.expanded_causalBounds": "ff684b781c2202031f4c0a68b677fe598fe7b176df45488c5aaf65fabfabcfe7", "PNP.DirectWire.WireUnaryCausalBound.attempt_causalBounds": "e9d2762c2330932afec39766a12d19b088ee74fc0f12671edf734f06d980f22f", "PNP.DirectWire.WireObligationHistory.decodeRecord_encode": "c1c1fc876e31185204ecee23a6e7b19013726a825ba08fb2a9b0ec5f045715ce", "PNP.DirectWire.WireObligationHistory.decodeRecord_source": "08275451007126789a96f6997f750ecc028d5052524aca2ea8fc44013f381090", "PNP.DirectWire.WireObligationHistory.decodeRecords_encode": "b04faf388a4c7a24baa0ae7aa1d0ec33c1608a5bbb859b3ff166a0b07f1338ac", "PNP.DirectWire.WireObligationHistory.decodeRecords_source": "4a14bb1202417fa4aa25e238d7677571d88fb29fe13b7afb110b440eadacd245", "PNP.DirectWire.WireObligationHistory.computeR7_isSome_iff": "3903b0ad1fbbf870510cb9c7fb35ff32ec3bee103f80ec06fa6a2f67e178fe08", "PNP.DirectWire.WireObligationHistory.R7Realization.full_field": "7699f8e957edbd66a9bc5c13240e992e05a399071c6c40bbffced57240455f19", "PNP.DirectWire.WireObligationHistory.R7Realization.exact_charge": "3e3cd9fba51b50d94bf57a05e2ba8720a9db4283a6a8559e1863a0e28771d62d", "PNP.DirectWire.WireObligationHistory.R7Realization.causalBounds": "3ed206f861600cca01fa52d00a7494bb45615a7fb7f5a00851d8129fea8f0268", "PNP.DirectWire.WireObligationHistory.State.restoreR7_gate_charge": "cb3ffbc194c947db003584bcb22fb2c956ad0b9e28ffe0153d5f352dcbbfe4de", "PNP.DirectWire.WireObligationHistory.State.restoreR7_full_value": "a26fa69df0f4160df11ab52c810ee9f4f8cebc0df437f6dc25ffb1e199fce0c0", "PNP.DirectWire.WireObligationHistory.State.restoreR7_other_pending": "aa65f63e76312b2484bea839b25d493f8d4976695f5e9de8443e8697939a5fff", "PNP.DirectWire.WireObligationHistory.State.restoreR7_causalInvariant": "f1a777649c0537a2e5d5bc5a638fd50460e249bb8860bc286003816278397557", "PNP.DirectWire.WireObligationHistory.Transition.causalInvariant": "5e8e6b3008a3ae5e6eae219e5642bd71496d4c78a6fe24cc00f06d8579bc25c1", "PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant": "d766a4d18cd18b8fc41844f5862a1db0293043ad3be6711bf2f183584391b9b7", "PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound": "aa051739783a3bcf78c4cfd030bda11ebb4191071367ac5a9cd09d2f63f2dcb8", "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output": "b424d42f293c35731c15c87699685a7276d36f6535dc9df10d94038525f92c63", "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field": "c693beecbd081a97a4cbb69a8d352963830e1ef59577d90930adbc208a3f111f", "PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance": "1f6a44c3ae70e9bd68aa2f4c27ee53ca15d367bf7537504601368e758bc05207", "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle": "931d176535e4d513f8d0c55154d78e8ceb5046c4f00de10429bcaba5e91bbc66", "PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before": "eb9fd5eeb6da03880e4e567c1150d9f788db315013c32ec064dc78c0e551010d", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles": "24628ba7c42242ba62325ae3a02a86c5da4afa69372ee4a8db95369cb2c54177", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics": "3ff01612253857a44f687e7850d60a8c0895046ef5ab7a5bd4190dab27453031", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting": "ba21db1c802ed21d062b78b1a28939a1cac493aba356401f9981e460e076f323", "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain": "e6abcd11b0d7e89b0c908788f665a71b2d7576be1ff9a7396e36821647e91770", "PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete": "e4dbaa109b94d8d0704c04d90f776e755c079b7c6e303cb5097cc985df6a6756", "PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound": "7f2ab5eee8236bc96b3ab1f3d1a0edb44631fef986b0c8f0a67f0f7668ba3def", "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff": "b83a398e1ac68926f820d96f95b7e9e21042f8fabcecbbd0fad685a544eeaffb" }, "theoremAxioms": { "PNP.DirectWire.RawNandCompilationState.finish_position": [], "PNP.DirectWire.RawNandCausalBound.compile_bounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandCausalBound.candidate_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.graph_dependency_bounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.result_output_dependency_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.implementation_output_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.constantWord_output_bound": [], "PNP.DirectWire.WireUnaryCausalBound.localWord_output_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.arbitrary_replacement_output_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.compiled_spec": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.replacement_dependency_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.expanded_exposed_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.expanded_causalBounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireUnaryCausalBound.attempt_causalBounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.decodeRecord_encode": [ "propext" ], "PNP.DirectWire.WireObligationHistory.decodeRecord_source": [], "PNP.DirectWire.WireObligationHistory.decodeRecords_encode": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.decodeRecords_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.computeR7_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.R7Realization.full_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.R7Realization.exact_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.R7Realization.causalBounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.restoreR7_gate_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.restoreR7_full_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.restoreR7_other_pending": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.restoreR7_causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.field_causal_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.full_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.gate_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.ClosedHistory.dependency_before": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_compiles": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_result_strict_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.compile_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.compile_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryArbitrarySupport.compile_none_iff": [ "Quot.sound", "propext" ] } }, { "number": 266, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-266", "id": "source-derived-history-ownership", "title": "Source-derived physical ownership through computational histories", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanSourceDerivedHistoryOwnershipFormalized": true, "leanSourceDerivedHistoryOwnershipAxiomAuditPassed": true, "leanSourceDerivedHistoryOwnershipAuditedDeclarationCount": 78, "leanSourceDerivedHistoryOwnershipTerminalExtractionPhysicalOriginTheorem": "PNP.DirectWire.terminalExtractionOrigin_gateIndex", "leanSourceDerivedHistoryOwnershipNormalizationPhysicalPartitionTheorem": "PNP.DirectWire.PhysicalGateProvenance.normalized_partition", "leanSourceDerivedHistoryOwnershipClosedHistoryPhysicalOwnershipTheorem": "PNP.DirectWire.WireObligationHistory.ClosedHistory.physical_ownership", "leanSourceDerivedHistoryOwnershipCompilerPhysicalOriginInverseTheorem": "PNP.DirectWire.CompiledRawNandGraph.position_physicalOrigin", "leanSourceDerivedHistoryOwnershipCompilerPhysicalOriginPermutationTheorem": "PNP.DirectWire.CompiledRawNandGraph.physicalOrigins_perm", "leanSourceDerivedHistoryOwnershipAmbientOriginalCoordinatePartitionTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.original_coordinate_partition", "leanSourceDerivedHistoryOwnershipAmbientPhysicalOwnershipTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.physical_ownership", "leanSourceDerivedHistoryOwnershipSourceOnlyConstructorProjectionTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.compileOwned_result", "leanSourceDerivedHistoryOwnershipSourceOnlyConstructorSemanticsTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.semantics", "leanSourceDerivedHistoryOwnershipDerivedEventRequestsDisjointTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventRequests_disjoint", "leanSourceDerivedHistoryOwnershipActualRawEventOwnershipTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_some_iff", "leanSourceDerivedHistoryOwnershipFixedRemainderTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_none_iff", "leanSourceDerivedHistoryOwnershipHistoricalChargeCompletenessTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.charged_origin", "leanSourceDerivedHistoryOwnershipSurvivingAllocationCompletenessTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.live_allocated_event", "leanSourceDerivedHistoryOwnershipSupportRestrictionTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.support_restrict", "leanSourceDerivedHistoryOwnershipActualExtractedGateCountTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_gateCount", "leanSourceDerivedHistoryOwnershipActualChargeIdentityTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_chargeIdentity", "leanSourceDerivedHistoryOwnershipWholeChargeTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_wholeCharge", "leanSourceDerivedHistoryOwnershipIndependentOpenSemanticsTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_semantics", "leanSourceDerivedHistoryOwnershipInducedBoundaryTheorem": "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_induced", "leanSourceDerivedHistoryOwnershipArbitraryFiniteCarrierSupportAndEventDimensionsCovered": true, "leanSourceDerivedHistoryOwnershipLiteralNormalizerRetainedOriginsDerived": true, "leanSourceDerivedHistoryOwnershipRemovedOriginsAreExactComplement": true, "leanSourceDerivedHistoryOwnershipExecutingEventAndLocalGateAllocationLabelsDerived": true, "leanSourceDerivedHistoryOwnershipHistoricalChargesSurviveLaterRemoval": true, "leanSourceDerivedHistoryOwnershipActualTopologicalCompilerPositionsUsed": true, "leanSourceDerivedHistoryOwnershipExteriorPhysicalGatesRetainedExactlyOnce": true, "leanSourceDerivedHistoryOwnershipDerivedEventRequestsDisjoint": true, "leanSourceDerivedHistoryOwnershipSupportRestrictionPreservesOwners": true, "leanSourceDerivedHistoryOwnershipExistingConstructorAcceptanceAndResultPreserved": true, "leanSourceDerivedHistoryOwnershipCallerSuppliedOwnerFamilyRequired": false, "leanSourceDerivedHistoryOwnershipCallerSuppliedProvenanceOrPartitionRequired": false, "leanSourceDerivedHistoryOwnershipCallerSuppliedChargeOrTopologicalOrderRequired": false, "leanSourceDerivedHistoryOwnershipCallerSuppliedSuccessfulSpliceCertificateRequired": false, "leanSourceDerivedHistoryOwnershipArbitraryCountPreservingPermutationIsProvenance": false, "leanSourceDerivedHistoryOwnershipHistoricalChargesEqualSurvivingOwnedSize": false, "leanSourceDerivedHistoryOwnershipSupportRecordsAndRawEventsDerivedFromEveryInput": false, "leanSourceDerivedHistoryOwnershipCompleteManuscriptCarrierAndRewriteCalculusProved": false, "leanSourceDerivedHistoryOwnershipArbitraryObserverOrFullProfileTransportProved": false, "leanSourceDerivedHistoryOwnershipMatchedKappaArbitrarySupportPullExpandProved": false, "leanSourceDerivedHistoryOwnershipCompletePackageEProved": false, "leanSourceDerivedHistoryOwnershipTerminalFamiliesDerived": false, "leanSourceDerivedHistoryOwnershipGloballySuccessfulRewriteStrategyDerived": false, "leanSourceDerivedHistoryOwnershipGlobalRouteCoverageProved": false, "leanSourceDerivedHistoryOwnershipUnconditionalSaturatePositiveProved": false, "leanSourceDerivedHistoryOwnershipUnconditionalBCELReadyProved": false, "leanSourceDerivedHistoryOwnershipUnconditionalZeroSlackProved": false, "leanSourceDerivedHistoryOwnershipExactGeneralPCCMinProved": false, "leanSourceDerivedHistoryOwnershipPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanSourceDerivedHistoryOwnershipRuntimeExecutionIsProofAuthority": false, "leanSourceDerivedHistoryOwnershipScope": "arbitrary-finite-computational-histories-source-derived-literal-normalization-origins-executing-event-local-allocation-labels-live-removed-charged-nodup-partition-actual-topological-splice-positions-one-copy-exterior-disjoint-derived-requests-support-stable-extracted-charges-no-supplied-owner-or-partition-no-global-strategy-or-complete-manuscript-calculus-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.PhysicalGateProvenance.constantOrigins_positions": "14202cb776a0455c81fcba3d15fea773506814911656848a6cc8636189e749d1", "PNP.DirectWire.PhysicalGateProvenance.sharingOrigins_positions": "60f68297d2d2a96a4360598a88c458f8e86b23f670c78258abb0f85727446b50", "PNP.DirectWire.PhysicalGateProvenance.constantOrigin_alias": "ce323ad0fc1ce93cc3535dcd40d83378d998210dec0eec0cf3e4ee2d51d5f102", "PNP.DirectWire.PhysicalGateProvenance.constantOrigin_injective": "cb2bf5bfb8f7cccda8ee66ee5639fe74778ee3f9952af0065b9be0ce712cb86b", 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"PNP.DirectWire.PhysicalGateProvenance.normalizedOrigin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.constantOrigins_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.constantOrigins_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.sharingOrigins_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.sharingOrigins_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.passRemoved_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.pass_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.traceRemoved_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.trace_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.normalizedRemoved_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.PhysicalGateProvenance.normalized_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.PhysicalOwnership.append_origin_left": [], "PNP.DirectWire.WireObligationHistory.PhysicalOwnership.append_origin_right": [], "PNP.DirectWire.WireObligationHistory.PhysicalOwnership.append_live": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.PhysicalOwnership.normalize_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.PhysicalOwnership.normalize_removed_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.restore_physical_positions": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.realize_physical_positions": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.allocations_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.physical_charged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.Transition.physical_removed_length": [ "Quot.sound", "propext" ], 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"PNP.DirectWire.CompiledRawNandGraph.position_surjective": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.position_physicalOrigin": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.physicalOrigin_position": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.physicalOrigin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.physicalOrigin_surjective": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.physicalOrigins_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.CompiledRawNandGraph.physicalOrigins_perm": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandCompilationState.finish_physicalOrigin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.liftOrigin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.original_coordinate_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.rawNodeOrigin_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.rawNodeOrigin_history": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.physicalOrigin_position": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.physical_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.compileOwned_result": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventRequests_member": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventRequests_disjoint": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_some_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.charged_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.live_allocated_event": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.eventOwner_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.support_membership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.support_restrict": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_chargeIdentity": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_wholeCharge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireHistoryAmbientOwnership.OwnedCompilation.materializer_induced": [ "Quot.sound", "propext" ] } }, { "number": 267, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-16-267", "id": "descendant-history-ownership", "title": "Persistent physical ownership through descendant histories", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanDescendantHistoryOwnershipFormalized": true, "leanDescendantHistoryOwnershipAxiomAuditPassed": true, "leanDescendantHistoryOwnershipAuditedDeclarationCount": 84, "leanDescendantHistoryOwnershipRawRecordRoundTripTheorem": "PNP.DirectWire.WireDescendantHistory.decodeRecords_encode", "leanDescendantHistoryOwnershipRawRecordSourceTheorem": "PNP.DirectWire.WireDescendantHistory.decodeRecords_source", "leanDescendantHistoryOwnershipRawEventRoundTripTheorem": "PNP.DirectWire.WireDescendantHistory.decodeEvents_encode", "leanDescendantHistoryOwnershipRawEventSourceTheorem": "PNP.DirectWire.WireDescendantHistory.decodeEvents_source", "leanDescendantHistoryOwnershipActualStageResultTheorem": "PNP.DirectWire.WireDescendantHistory.StageCompilation.existing_result", "leanDescendantHistoryOwnershipLiteralPhysicalPositionTheorem": "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_physicalOrigin_position", "leanDescendantHistoryOwnershipOriginalCoordinateLiftTheorem": "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_original", "leanDescendantHistoryOwnershipAllocatedCoordinateLiftTheorem": "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_allocated", "leanDescendantHistoryOwnershipPhysicalOwnershipTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.physical_ownership", "leanDescendantHistoryOwnershipPhysicalOriginInjectiveTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_origin_injective", "leanDescendantHistoryOwnershipCompleteProgramSemanticsTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.semantics", "leanDescendantHistoryOwnershipActualExecutionSizeBalanceTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.gate_balance", "leanDescendantHistoryOwnershipHistoricalChargePersistenceTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charge_survives", "leanDescendantHistoryOwnershipInvalidLaterStagePropagationTheorem": "PNP.DirectWire.WireDescendantHistory.compile_tail_none", "leanDescendantHistoryOwnershipRawEventKeyDistinctnessTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.inputEventKeys_nodup", "leanDescendantHistoryOwnershipHistoricalChargeRawEventTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_charged_origin", "leanDescendantHistoryOwnershipSurvivingAllocationRawEventTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_live_allocated_event", "leanDescendantHistoryOwnershipDerivedEventRequestsDisjointTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventRequests_disjoint", "leanDescendantHistoryOwnershipActualRawEventOwnershipTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_some_iff", "leanDescendantHistoryOwnershipFixedOriginalRemainderTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_none_iff", "leanDescendantHistoryOwnershipSupportRestrictionTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.support_restrict", "leanDescendantHistoryOwnershipExtractedGateCountTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_gateCount", "leanDescendantHistoryOwnershipExtractedChargeIdentityTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_chargeIdentity", "leanDescendantHistoryOwnershipWholeSurvivingChargeTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_wholeCharge", "leanDescendantHistoryOwnershipOpenPieceSemanticsTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_semantics", "leanDescendantHistoryOwnershipInducedPieceBoundaryTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_induced", "leanDescendantHistoryOwnershipFinalNetGainTheorem": "PNP.DirectWire.WireDescendantHistory.GainResult.strictGain", "leanDescendantHistoryOwnershipFinalResidualDescentTheorem": "PNP.DirectWire.WireDescendantHistory.GainResult.strictResidualDescent", "leanDescendantHistoryOwnershipFinalGainAcceptanceIffTheorem": "PNP.DirectWire.WireDescendantHistory.compileGain_exists_iff", "leanDescendantHistoryOwnershipArbitraryFiniteDimensionsAndStageListsCovered": true, "leanDescendantHistoryOwnershipCurrentDescendantCoordinatesDecodedFromRawInput": true, "leanDescendantHistoryOwnershipActualLiteralCompilerPositionsCompose": true, "leanDescendantHistoryOwnershipStageEventAndLocalAllocationIdentitiesDerived": true, "leanDescendantHistoryOwnershipHistoricalChargesSurviveLaterRemoval": true, "leanDescendantHistoryOwnershipActualExecutionTotalsMatchPersistentLedger": true, "leanDescendantHistoryOwnershipLiveRemovedPartitionHasNoDuplicateIdentities": true, "leanDescendantHistoryOwnershipReusedLocalEventNumbersRemainStageDistinct": true, "leanDescendantHistoryOwnershipAllAllocationsTraceToActualInputEvents": true, "leanDescendantHistoryOwnershipDerivedEventRequestsDisjoint": true, "leanDescendantHistoryOwnershipSupportRestrictionPreservesOwners": true, "leanDescendantHistoryOwnershipMalformedLaterStageRejectsCompleteProgram": true, "leanDescendantHistoryOwnershipFinalNetGainAllowsIntermediateExpansion": true, "leanDescendantHistoryOwnershipExistingClosedLocalHistoryLanguagePreserved": true, "leanDescendantHistoryOwnershipCallerSuppliedIntermediateImplementationsRequired": false, "leanDescendantHistoryOwnershipCallerSuppliedOwnerFamilyRequired": false, "leanDescendantHistoryOwnershipCallerSuppliedProvenanceOrPartitionRequired": false, "leanDescendantHistoryOwnershipCallerSuppliedChargeOrRankRequired": false, "leanDescendantHistoryOwnershipCallerSuppliedSuccessfulHistoryCertificateRequired": false, "leanDescendantHistoryOwnershipSemanticOracleUsedByFinalGainAdapter": false, "leanDescendantHistoryOwnershipHistoricalChargesEqualSurvivingOwnedSize": false, "leanDescendantHistoryOwnershipEachIntermediateStageMustStrictlyDecrease": false, "leanDescendantHistoryOwnershipAcceptedPrefixReturnedAfterLaterRejection": false, "leanDescendantHistoryOwnershipRawStagesDerivedFromEveryInput": false, "leanDescendantHistoryOwnershipOpenObligationsTransportedAcrossSupports": false, "leanDescendantHistoryOwnershipCompleteManuscriptCarrierAndRewriteCalculusProved": false, "leanDescendantHistoryOwnershipMatchedKappaArbitrarySupportPullExpandProved": false, "leanDescendantHistoryOwnershipProperSupportVerifyDWProved": false, "leanDescendantHistoryOwnershipCompleteChargeSoundnessProved": false, "leanDescendantHistoryOwnershipCompletePackageEProved": false, "leanDescendantHistoryOwnershipTerminalFamiliesDerived": false, "leanDescendantHistoryOwnershipGloballySuccessfulRewriteStrategyDerived": false, "leanDescendantHistoryOwnershipGlobalRouteCoverageProved": false, "leanDescendantHistoryOwnershipUnconditionalSaturatePositiveProved": false, "leanDescendantHistoryOwnershipUnconditionalBCELReadyProved": false, "leanDescendantHistoryOwnershipUnconditionalZeroSlackProved": false, "leanDescendantHistoryOwnershipExactGeneralPCCMinProved": false, "leanDescendantHistoryOwnershipPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanDescendantHistoryOwnershipRuntimeExecutionIsProofAuthority": false, "leanDescendantHistoryOwnershipScope": "arbitrary-finite-raw-stage-sequences-actual-descendant-decoding-persistent-stage-event-local-physical-origins-exact-live-removed-historical-charge-partition-derived-input-event-owners-support-stable-extracted-charges-final-net-gain-with-intermediate-expansion-no-supplied-intermediates-or-owners-or-oracles-no-open-obligation-transport-or-global-strategy-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireDescendantHistory.decodeRecord_encode": "fc87b5800aec8b69970acee761f33a36668c50afe06a23065b35de69a9fc13b6", 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"PNP.DirectWire.WireDescendantHistory.GainResult.strictGain": "a39fe16e118191baf32ff61fd7abc2d0657024634156b1306bd83072bd06bf08", "PNP.DirectWire.WireDescendantHistory.GainResult.strictResidualDescent": "e4a0a30f2560efd0dea139ef89fb35feffab6efa11adf500369d9ca3cf7f9d65", "PNP.DirectWire.WireDescendantHistory.compileGain_compile_none": "d11fe443478ffdd979f08205e96c6879ea9555c49fa4926cc69efe4bfb0ce3b8", "PNP.DirectWire.WireDescendantHistory.compileGain_no_gain": "5cbb7812dc8e1b5ffdbecc9e88230e1f02dcabfe64d41f9cd423970ecb0a2f63", "PNP.DirectWire.WireDescendantHistory.compileGain_complete": "c5e568e7077d2fa367476cac0c996c87be3d1ade4d4b00cb9c1d80ef40d163e1", "PNP.DirectWire.WireDescendantHistory.compileGain_exists_iff": "502966e15396548e91df5737beba0e5a8a06aca59914b77cbcb28849d65ae666" }, "theoremAxioms": { "PNP.DirectWire.WireDescendantHistory.decodeRecord_encode": [ "propext" ], "PNP.DirectWire.WireDescendantHistory.decodeRecord_source": [], "PNP.DirectWire.WireDescendantHistory.decodeRecords_encode": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.decodeRecords_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.decodeAction_encode": [ "propext" ], "PNP.DirectWire.WireDescendantHistory.decodeAction_source": [], "PNP.DirectWire.WireDescendantHistory.decodeEvent_encode": [ "propext" ], "PNP.DirectWire.WireDescendantHistory.decodeEvent_source": [], "PNP.DirectWire.WireDescendantHistory.decodeEvents_encode": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.decodeEvents_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.records_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.events_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.existing_result": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.physicalOrigin_position": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.gate_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.charged_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.event_identity_unique": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileStage_records_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileStage_events_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileStage_history_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.gate_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compile_nil": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compile_cons": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compile_stage_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compile_tail_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compile_cons_some": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compile_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.createdBefore_mono": [], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.initial_wellFormed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.accounted_before": [ "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.origin_before": [ "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.origin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_original": [], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_allocated": [], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.liftOrigin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.lift_originals": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_live": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_charged_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_removed_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_physicalOrigin_position": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_charge_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.PersistentOwnership.advance_wellFormed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_nil": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_cons": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_wellFormed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charged_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_removed_length": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charge_survives": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_nil": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_wellFormed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_origin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_charged_before": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.inputEventKeys_nil": [], "PNP.DirectWire.WireDescendantHistory.inputEventKeys_cons": [], "PNP.DirectWire.WireDescendantHistory.inputEventKeys_bounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.rawEventIdentities_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.inputEventKeys_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.inputEventKeys_unique": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.carry_charged_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_charged_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.ledger_live_allocated_event": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventRequests_member": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventRequests_disjoint": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_some_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.eventOwner_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.support_membership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.support_restrict": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_chargeIdentity": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_wholeCharge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.materializer_induced": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.GainResult.strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.GainResult.strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileGain_compile_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileGain_no_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileGain_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.compileGain_exists_iff": [ "Quot.sound", "propext" ] } }, { "number": 268, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-268", "id": "proper-descendant-certificates", "title": "Source-only proper-support certificates for descendant programs", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanProperDescendantCertificatesFormalized": true, "leanProperDescendantCertificatesAxiomAuditPassed": true, "leanProperDescendantCertificatesAuditedDeclarationCount": 33, "leanProperDescendantCertificatesArbitraryLabelCausalBoundTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.output_dependency_bound", "leanProperDescendantCertificatesDerivedOuterCompilationTheorem": "PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_compiles", "leanProperDescendantCertificatesCompleteOuterCompilationTheorem": "PNP.DirectWire.WireDescendantProperSupport.compile_complete", "leanProperDescendantCertificatesProperSupportIffTheorem": "PNP.DirectWire.WireDescendantProperSupport.proper_iff_exterior_positive", "leanProperDescendantCertificatesAmbientHistoricalAccountingTheorem": "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.charge_accounting", "leanProperDescendantCertificatesCompleteAcceptanceIffTheorem": "PNP.DirectWire.WireDescendantCertificate.verify_exists_iff", "leanProperDescendantCertificatesSourceRoundTripTheorem": "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.records_source", "leanProperDescendantCertificatesOrdinaryOutputPreservationTheorem": "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.output", "leanProperDescendantCertificatesLiteralFieldPreservationTheorem": "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.field", "leanProperDescendantCertificatesStrictGainTheorem": "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictGain", "leanProperDescendantCertificatesStrictResidualDescentTheorem": "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictResidualDescent", "leanProperDescendantCertificatesFailedCompleteProgramRejectionTheorem": "PNP.DirectWire.WireDescendantCertificate.verify_run_none", "leanProperDescendantCertificatesWholeSupportRejectionTheorem": "PNP.DirectWire.WireDescendantCertificate.verify_not_proper", "leanProperDescendantCertificatesNondecreaseRejectionTheorem": "PNP.DirectWire.WireDescendantCertificate.verify_no_gain", "leanProperDescendantCertificatesArbitraryFiniteDimensionsAndProgramsCovered": true, "leanProperDescendantCertificatesRawSourceOnlyCertificate": true, "leanProperDescendantCertificatesCompleteProgramRequired": true, "leanProperDescendantCertificatesOuterAcyclicityDerivedFromExecution": true, "leanProperDescendantCertificatesProperPhysicalSupportRequired": true, "leanProperDescendantCertificatesStrictFinalLocalSavingRequired": true, "leanProperDescendantCertificatesAllOrdinaryOutputsAndLiteralFieldsPreserved": true, "leanProperDescendantCertificatesExteriorOccursExactlyOnce": true, "leanProperDescendantCertificatesActualHistoricalChargeRemovalBalancePreserved": true, "leanProperDescendantCertificatesIntermediateExpansionAllowed": true, "leanProperDescendantCertificatesCallerSuppliedCorrectnessOrIntermediateCircuitRequired": false, "leanProperDescendantCertificatesCallerSuppliedOrderOrSuccessfulSpliceRequired": false, "leanProperDescendantCertificatesCallerSuppliedCostsOrOwnersRequired": false, "leanProperDescendantCertificatesAcceptedPrefixReturnedAfterLaterRejection": false, "leanProperDescendantCertificatesRejectedCertificateProvesLocalMinimality": false, "leanProperDescendantCertificatesAcceptedCertificateForEveryNonminimalInputProved": false, "leanProperDescendantCertificatesGloballySuccessfulStrategyDerived": false, "leanProperDescendantCertificatesFullManuscriptVerifyDWProved": false, "leanProperDescendantCertificatesFullManuscriptProfilesAndRuleFamiliesProved": false, "leanProperDescendantCertificatesOpenObligationsTransportedAcrossSupports": false, "leanProperDescendantCertificatesCompleteChargeSoundnessProved": false, "leanProperDescendantCertificatesCompletePackageEProved": false, "leanProperDescendantCertificatesTerminalFamiliesDerived": false, "leanProperDescendantCertificatesGlobalRouteCoverageProved": false, "leanProperDescendantCertificatesUnconditionalSaturatePositiveProved": false, "leanProperDescendantCertificatesUnconditionalBCELReadyProved": false, "leanProperDescendantCertificatesUnconditionalZeroSlackProved": false, "leanProperDescendantCertificatesExactGeneralPCCMinProved": false, "leanProperDescendantCertificatesPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanProperDescendantCertificatesRuntimeExecutionIsProofAuthority": false, "leanProperDescendantCertificatesScope": "arbitrary-finite-computational-wire-carriers-source-only-raw-records-and-complete-descendant-programs-derived-causal-literal-splice-proper-support-strict-final-saving-all-output-and-field-preservation-exact-historical-costs-intermediate-expansion-no-global-certificate-discovery-or-full-manuscript-profiles-or-polynomial-runtime" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_dependencyInterfaceBound": "7e91a6ba071a60d7acf5537dbbbe7b92588c7600b8794ff29854f641389e8269", "PNP.DirectWire.WireDescendantHistory.StageCompilation.output_dependency_bound": "6e06d53b0ca176147a923beda5e13fc201257842680b13b7eb0f4e21223d0a5a", "PNP.DirectWire.WireDescendantHistory.CompiledRun.output_dependency_bound": "3bdab1852a89654374cec56b8b06c23c1d5cc963d33ff2842a254db07836af98", "PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_causalInterfaceBound": "9df4cab63a5443ed3c4383553ff5ab1cd7e5a3983b2010d83240b1070703e5d3", "PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_compiles": "47a4a1c20244f1b93aa6fa03c58b88b07ccd74498e37eb645adcf966d095f65e", "PNP.DirectWire.WireDescendantProperSupport.proper_iff_exterior_positive": "d9d08cfb9dadac80b033e39f4954d427cc8003d8cd3d11aae930bb0b6aabb20c", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.open_equivalent": "1554f92d8ccf86c4c94a7040f18a301073fd5f2b22e704da9e7c3d2652b2a9fe", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.output": "3d4007aa676175bca9da0e38c0fa81c4f55bba457806bbb6d8e76ff919f74b98", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.field": "1c982a9e13a376f2b044aa8e95655cea80ea5b09b61717cb7c91612d6bdf67d7", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gateCount": "33ddeedba50fed2e7aeaf3b1d6fdb85128563c912e933424241f611ee8559003", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.charge_accounting": "43cf1de7e6f4a89dac1ecaca41999c83bfb01c5c210adc9c82f9ca8a9b93665f", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gain_iff_local_gain": "f2e0f4bf14a3821fd89e9c15ed3ebaa66038e58d2022e7162257f22cb3d9f6ae", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gain_iff_net_charges": "254edea2db6faf6de9ff5991a1101fa5e98da7f95c4f249d54bf545b1c8de7b5", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.strictGain": "d52506d1fa99a40e31e1f65e2f346737f9650244c325df8e11db6053f5edc84c", "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.strictResidualDescent": "9e078fc6943070e2127e757c87e5128553104a268aa22d0d44a8072ff0d9d99c", "PNP.DirectWire.WireDescendantProperSupport.compile_complete": "f4fbc6327c464ccd90383ce7238d5fb48985e9d1075e44e99ee14febd197f77d", "PNP.DirectWire.WireDescendantProperSupport.compile_exists_iff": "3595a28d541c127f3f9d1c1de45133e52de421ee6dedf8a6ba4b4d2bb70d89c1", "PNP.DirectWire.WireDescendantProperSupport.compile_none_iff": "14ee8d6504fbb3d36d05a30c16804bb64c150c8cd1ffb3650c089d072e9e9e59", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.records_source": "438bd94195840fc2351650b23668de3ba131db36ca00a0afb7cb2edd51957d35", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.proper_support": "e65ada18451c48e87f3809e321a796e32610f9c00d5bcefee226644ef366aa59", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.output": "613f0f18269563e29aba6060065e1b52e3c6becc1e8da84472f6491519266eb7", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.field": "60e21b2c8a882cb82bf741e7692504669c9b5e9bd293e11ed11e23edb9ac2d65", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.gateCount": "7d350b53d51481dc1fe2d5cb4155b5c7aaf6b613052aa6112b9f1174d066ab07", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.charge_accounting": "adb98588ffdceb1296a68ddd61343e8d7939ffca2f812a5d44028ea8f5e9a401", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictGain": "d285a884b421f2610155e13482363543697a2250a40c1c302c7c46b4016f4732", "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictResidualDescent": "b48c42a7f286f32d4c890f51d3c74b020fb19f9f3a24185e58fe5438a3855b46", "PNP.DirectWire.WireDescendantCertificate.verify_complete": "b9601cb040f7386418b4a280b37d283aecdf0792bee24994e9cc194583976d34", "PNP.DirectWire.WireDescendantCertificate.verify_exists_iff": "9eef87d6e1313ff9dda9650d8ef55854860a6b3f63686952b60d79caaeaf36a4", "PNP.DirectWire.WireDescendantCertificate.verify_sound": "a5ed083668d903a2e924c74f98357e3a846172464fa52e82eca97baee2e9a25b", "PNP.DirectWire.WireDescendantCertificate.verify_decode_none": "67515c26c4d5ea9d26bb89b38dea576d8697c0986dea37797c608fd550c67837", "PNP.DirectWire.WireDescendantCertificate.verify_run_none": "23b902698feb58606e2b576acb188dffc1d3517874bf49a8a892be7c851df74a", "PNP.DirectWire.WireDescendantCertificate.verify_not_proper": "6ae7df30920172cc87b581bb315bbd8fba9db594b35e52f85f30f03dc33b0389", "PNP.DirectWire.WireDescendantCertificate.verify_no_gain": "5de9ff869d71ff419c095435550f6276df8087016ebd6bf1da647f65743930c4" }, "theoremAxioms": { "PNP.DirectWire.WireHistoryArbitrarySupport.closedHistory_dependencyInterfaceBound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.StageCompilation.output_dependency_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.output_dependency_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_causalInterfaceBound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantHistory.CompiledRun.extracted_compiles": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.proper_iff_exterior_positive": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.open_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.charge_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gain_iff_local_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.gain_iff_net_charges": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.SplicedRun.strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.compile_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.compile_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantProperSupport.compile_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.records_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.proper_support": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.charge_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.CheckedCertificate.strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_decode_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_run_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_not_proper": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireDescendantCertificate.verify_no_gain": [ "Quot.sound", "propext" ] } }, { "number": 269, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-269", "id": "open-obligation-programs", "title": "Open obligations across complete descendant-support programs", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanOpenObligationProgramsFormalized": true, "leanOpenObligationProgramsAxiomAuditPassed": true, "leanOpenObligationProgramsAuditedDeclarationCount": 144, "leanOpenObligationProgramsPendingSnapshotPreservationTheorem": "PNP.DirectWire.WireOpenSupportSplice.transfer_pending", "leanOpenObligationProgramsCompleteDependencyOrderTheorem": "PNP.DirectWire.WireOpenProgram.orderEvents_success_iff", "leanOpenObligationProgramsCompleteExecutionAcceptanceTheorem": "PNP.DirectWire.WireOpenProgram.compile_exists_iff", "leanOpenObligationProgramsFinalClosureTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.closed", "leanOpenObligationProgramsCreationLifecycleTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle", "leanOpenObligationProgramsFullFieldRestorationTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field", "leanOpenObligationProgramsCompleteOuterCompilationTheorem": "PNP.DirectWire.WireOpenProperSupport.compile_complete", "leanOpenObligationProgramsActualCompilerOwnershipTheorem": "PNP.DirectWire.WireOpenProperSupport.ownership_compiled_position", "leanOpenObligationProgramsCompleteAcceptanceIffTheorem": "PNP.DirectWire.WireOpenCertificate.verify_exists_iff", "leanOpenObligationProgramsSourceRoundTripTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source", "leanOpenObligationProgramsOrdinaryOutputPreservationTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output", "leanOpenObligationProgramsLiteralFieldPreservationTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field", "leanOpenObligationProgramsHistoricalAccountingTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting", "leanOpenObligationProgramsPhysicalOwnershipTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership", "leanOpenObligationProgramsStrictGainTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain", "leanOpenObligationProgramsStrictResidualDescentTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent", "leanOpenObligationProgramsFailedCompleteProgramRejectionTheorem": "PNP.DirectWire.WireOpenCertificate.verify_program_none", "leanOpenObligationProgramsWholeSupportRejectionTheorem": "PNP.DirectWire.WireOpenCertificate.verify_not_proper", "leanOpenObligationProgramsNondecreaseRejectionTheorem": "PNP.DirectWire.WireOpenCertificate.verify_no_gain", "leanOpenObligationProgramsArbitraryFiniteDimensionsAndProgramsCovered": true, "leanOpenObligationProgramsRawSourceOnlyCertificate": true, "leanOpenObligationProgramsInitialStateInternallyDerived": true, "leanOpenObligationProgramsCompleteRawMixedProgramRequired": true, "leanOpenObligationProgramsComputedDependencyOrderRequired": true, "leanOpenObligationProgramsIntrinsicCreationReferencesRequired": true, "leanOpenObligationProgramsSamePendingSnapshotsPreserved": true, "leanOpenObligationProgramsOpenObligationsTransportedAcrossSupports": true, "leanOpenObligationProgramsFullModeR6R7R8DischargeRequired": true, "leanOpenObligationProgramsFinalAmbientLedgerClosureRequired": true, "leanOpenObligationProgramsOuterAcyclicityDerivedFromExecution": true, "leanOpenObligationProgramsProperPhysicalSupportRequired": true, "leanOpenObligationProgramsStrictFinalLocalSavingRequired": true, "leanOpenObligationProgramsAllOrdinaryOutputsAndLiteralFieldsPreserved": true, "leanOpenObligationProgramsExteriorOccursExactlyOnce": true, "leanOpenObligationProgramsActualHistoricalChargeRemovalBalancePreserved": true, "leanOpenObligationProgramsPhysicalOwnershipComputed": true, "leanOpenObligationProgramsActualCompilerPositionMapsUsed": true, "leanOpenObligationProgramsComputedOuterPositionNamespaces": true, "leanOpenObligationProgramsLaterRemovedAllocationChargesRetained": true, "leanOpenObligationProgramsIntermediateExpansionAllowed": true, "leanOpenObligationProgramsInnerClosedHistoryLanguagePreserved": true, "leanOpenObligationProgramsCallerSuppliedCorrectnessOrIntermediateCircuitRequired": false, "leanOpenObligationProgramsCallerSuppliedInitialStateOrSnapshotRequired": false, "leanOpenObligationProgramsCallerSuppliedOrderOrSuccessfulSpliceRequired": false, "leanOpenObligationProgramsCallerSuppliedCostsOrOwnersRequired": false, "leanOpenObligationProgramsAcceptedPrefixReturnedAfterLaterRejection": false, "leanOpenObligationProgramsRejectedCertificateProvesLocalMinimality": false, "leanOpenObligationProgramsAcceptedCertificateForEveryNonminimalInputProved": false, "leanOpenObligationProgramsGloballySuccessfulStrategyDerived": false, "leanOpenObligationProgramsFullManuscriptVerifyDWProved": false, "leanOpenObligationProgramsFullManuscriptProfilesAndRuleFamiliesProved": false, "leanOpenObligationProgramsCompleteChargeSoundnessProved": false, "leanOpenObligationProgramsCompletePackageEProved": false, "leanOpenObligationProgramsTerminalFamiliesDerived": false, "leanOpenObligationProgramsGlobalRouteCoverageProved": false, "leanOpenObligationProgramsUnconditionalSaturatePositiveProved": false, "leanOpenObligationProgramsUnconditionalBCELReadyProved": false, "leanOpenObligationProgramsUnconditionalZeroSlackProved": false, "leanOpenObligationProgramsExactGeneralPCCMinProved": false, "leanOpenObligationProgramsPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanOpenObligationProgramsRuntimeExecutionIsProofAuthority": false, "leanOpenObligationProgramsScope": 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"PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_complete": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_decode_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_program_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_not_proper": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_no_gain": [ "Quot.sound", "propext" ] } }, { "number": 270, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-270", "id": "structural-reindexing-support-transport", "title": "Structural reordering and arbitrary-support replacement transport", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanStructuralReindexingFormalized": true, "leanStructuralReindexingAxiomAuditPassed": true, "leanStructuralReindexingAuditedDeclarationCount": 108, "leanStructuralReindexingActualCompilerSourceFidelityTheorem": "PNP.DirectWire.RawNandWireStructure.compile_sources", "leanStructuralReindexingRawSwapDecodeTheorem": "PNP.DirectWire.StructuralReindexing.GateRenaming.decode_isSome", "leanStructuralReindexingDerivedCompilationTheorem": "PNP.DirectWire.StructuralReindexing.compiled_accepted", "leanStructuralReindexingLiteralSourceTheorem": "PNP.DirectWire.StructuralReindexing.result_sources", "leanStructuralReindexingLiteralOutputTheorem": "PNP.DirectWire.StructuralReindexing.result_output_source", "leanStructuralReindexingArbitraryRecordRoundTripTheorem": "PNP.DirectWire.StructuralReindexing.forward_backward_records", "leanStructuralReindexingBoundaryCorrespondenceTheorem": "PNP.DirectWire.StructuralReindexing.descendant_boundary", "leanStructuralReindexingInterfaceCorrespondenceTheorem": "PNP.DirectWire.StructuralReindexing.descendant_interface", "leanStructuralReindexingIndependentOpenSemanticsTheorem": "PNP.DirectWire.StructuralReindexing.open_support_pullback", "leanStructuralReindexingReplacementCompatibilityTheorem": "PNP.DirectWire.StructuralReindexing.pullReplacement_compatible", "leanStructuralReindexingMatchedSurchargeTheorem": "PNP.DirectWire.StructuralReindexing.matched_surcharge", "leanStructuralReindexingExactSignedSavingTheorem": "PNP.DirectWire.StructuralReindexing.replacement_saving_preserved", "leanStructuralReindexingRawDependencyCorrespondenceTheorem": "PNP.DirectWire.StructuralReindexing.splice_dependencies", "leanStructuralReindexingAcyclicityEquivalenceTheorem": "PNP.DirectWire.StructuralReindexing.splice_wellFounded_iff", "leanStructuralReindexingCompilationEquivalenceTheorem": "PNP.DirectWire.StructuralReindexing.splice_compile_success_iff", "leanStructuralReindexingRejectionEquivalenceTheorem": "PNP.DirectWire.StructuralReindexing.splice_compile_failure_iff", "leanStructuralReindexingActualPhysicalPositionTheorem": "PNP.DirectWire.StructuralReindexing.splice_physical_position", "leanStructuralReindexingCompiledLiteralSourcesTheorem": "PNP.DirectWire.StructuralReindexing.splice_compiled_sources", "leanStructuralReindexingCompiledLiteralOutputTheorem": "PNP.DirectWire.StructuralReindexing.splice_compiled_output_source", "leanStructuralReindexingComputedPredecessorAcceptanceTheorem": "PNP.DirectWire.StructuralReindexing.pullCompiledSplice_accepted", "leanStructuralReindexingCompleteReplacementTransportTheorem": "PNP.DirectWire.StructuralReindexing.literal_replacement_transport", "leanStructuralReindexingArbitraryFiniteDimensionsAndDescendantRecordsCovered": true, "leanStructuralReindexingCompleteCheckedRawSwapSequenceRequired": true, "leanStructuralReindexingActualCompilerPlacementAndInverseUsed": true, "leanStructuralReindexingCanonicalPortAndOwnershipBijectionsDerived": true, "leanStructuralReindexingAllIndependentBoundaryValuationsCovered": true, "leanStructuralReindexingLiteralInputAndOutputReplacementRewiring": true, "leanStructuralReindexingBothMatchedSignedSurchargesZero": true, "leanStructuralReindexingExactLocalAndWholeSignedSavingPreserved": true, "leanStructuralReindexingBothDependencyAndRejectionDirectionsProved": true, "leanStructuralReindexingAcceptedDescendantSpliceRequiredForCompiledPullback": true, "leanStructuralReindexingOpenReplacementCompatibilityRequiredForSemantics": true, "leanStructuralReindexingCallerSuppliedPredecessorCompilerOrOrderRequired": false, "leanStructuralReindexingCallerSuppliedTransportMapsRequired": false, "leanStructuralReindexingCallerSuppliedSourceFidelityRequired": false, "leanStructuralReindexingPaddingUsed": false, "leanStructuralReindexingAllCompatibleSplicesAcyclicProved": false, "leanStructuralReindexingArbitraryPermutationEncodingComplete": false, "leanStructuralReindexingFullManuscriptProfileSemanticsProved": false, "leanStructuralReindexingAllNormalizationAndMaterializerRulesProved": false, "leanStructuralReindexingFullManuscriptVerifyDWProved": false, "leanStructuralReindexingCompleteChargeSoundnessAndPackageEProved": false, "leanStructuralReindexingGlobalCertificateDiscoveryProved": false, "leanStructuralReindexingTerminalFamiliesDerived": false, "leanStructuralReindexingGlobalRouteCoverageProved": false, "leanStructuralReindexingUnconditionalSaturatePositiveProved": false, "leanStructuralReindexingUnconditionalBCELReadyProved": false, "leanStructuralReindexingUnconditionalZeroSlackProved": false, "leanStructuralReindexingExactGeneralPCCMinProved": false, "leanStructuralReindexingPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanStructuralReindexingRuntimeExecutionIsProofAuthority": false, "leanStructuralReindexingScope": "arbitrary-finite-checked-raw-swaps-and-descendant-records-derived-canonical-port-and-ownership-bijections-independent-open-semantics-literal-replacement-rewiring-zero-matched-surcharge-exact-signed-saving-bidirectional-raw-dependency-and-acceptance-actual-compiled-physical-transport-no-full-profiles-or-materializers-or-global-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.RawNandWireStructure.initial_faithful": "e7042f7084f9f6041f83b01963bf2030de0acc306654e9e2ab3d4e0cb8d0b285", "PNP.DirectWire.RawNandWireStructure.apply_faithful": "f60df4d336d71a0c71c724985145147576843d0b53320b5e06fefe3655aeecda", "PNP.DirectWire.RawNandWireStructure.run_faithful": "847686fee173489bf2754901e7b62ad529541016c09f92ccd15bc579c7187aab", "PNP.DirectWire.RawNandWireStructure.finish_sources": "c2db6b1569ad4f93208f71419227ea4f4dbed991a277ffcbed3fa2de33769d3b", 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"PNP.DirectWire.StructuralReindexing.splice_compiled_sources": "b5d8ea1ed268f9b85b5a7113936cf714aecd03796a74dc9a3e439bd777ca1014", "PNP.DirectWire.StructuralReindexing.splice_compiled_output_source": "39b559176c54d63583f72cb73092e59fe2c9baa4573ce466162acd3027f21999", "PNP.DirectWire.StructuralReindexing.splice_compiled_gate_count": "2f949b88ca9475a55b12c54c653a0c080945cd5f0451c21dd4a9f851d4ac547e", "PNP.DirectWire.StructuralReindexing.splice_compiled_semantics": "a1e9bf9938337fcef53f595b9c03e1b5ecf1cc94a28e41a5db9fedd3f29e697d", "PNP.DirectWire.StructuralReindexing.pull_splice_isSome": "2052b46d2ed1b72774821fb8b12b1f660eb4f50dc2ee214a73358b625b83859f", "PNP.DirectWire.StructuralReindexing.pullCompiledSplice_accepted": "d2c8151aa777fcc563ed5692a587449e65de7e51ddfa73b7fd4afc0f9c9a5bd8", "PNP.DirectWire.StructuralReindexing.literal_replacement_transport": "6f6ba6fd10ae2025274a65566740f5f230222c092badfc6ceb17eb00b116b7f5", "PNP.DirectWire.terminalOpenGateEvaluation_sourceEquation": "d3c53e7e15227c609b625667699798e5f151715bef508d181575f265b8402764", "PNP.DirectWire.terminalOpenWireValue_boundary_get": "87a7979757248c52077a0b0400846e4d8a295a863bd99c933dc3f7161c0ec9b6", "PNP.DirectWire.terminalOpenWireValue_external_absent": "466fa8b9f64fef0ba0769d78b981f0e35c890ed20dd8fdbf897315a653c95ad7", "PNP.DirectWire.ArbitrarySupportSplice.boundarySource_input": "6756b4ea8cadeacc264dbc2e956df0bffe34980cdf8bb07ba5830e0a6c135195", "PNP.DirectWire.ArbitrarySupportSplice.boundarySource_gate": "7ac4e0b759c4cad50eb22be05168881e77fe1f0a0ed6eba7d64f006f76a0f49d", "PNP.DirectWire.ArbitrarySupportSplice.originalSource_exterior": "506c4ff0744cc8dc5328c013f1c8437f90b45bc0c4812b835cfcb3a75df309f5", "PNP.DirectWire.ArbitrarySupportSplice.originalSource_interface": "93ff230f571633713e0da734a4b3795d4cd069c5e411c953ca07ea9281a2c049" }, "theoremAxioms": { "PNP.DirectWire.RawNandWireStructure.initial_faithful": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandWireStructure.apply_faithful": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandWireStructure.run_faithful": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandWireStructure.finish_sources": [ "propext" ], "PNP.DirectWire.RawNandWireStructure.compile_sources": [ "Quot.sound", "propext" ], "PNP.DirectWire.RawNandWireStructure.physicalOrigin_sources": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.GateRenaming.forward_injective": [], "PNP.DirectWire.StructuralReindexing.GateRenaming.backward_injective": [], "PNP.DirectWire.StructuralReindexing.GateRenaming.decode_isSome": [ "propext" ], "PNP.DirectWire.StructuralReindexing.sourceMap_compose": [], "PNP.DirectWire.StructuralReindexing.sourceMap_eq_gate_iff": [], "PNP.DirectWire.StructuralReindexing.sourceMap_eval": [], "PNP.DirectWire.StructuralReindexing.graph_edge_ordered": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.graph_wellFounded": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.compile_isSome": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.compiled_accepted": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.backward_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forward_backward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forwardGate_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.backwardGate_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.translated_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.result_sources": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.result_output_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.result_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.graph_solution": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.result_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.attempt_isSome": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.attempt_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.attempt_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.backward_forward_wire": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forward_backward_wire": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.backward_forward_record": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forward_backward_record": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forwardRecord_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.backward_forward_records": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forward_backward_records": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.forwardRecord_mem": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.selected_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.external_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.backward_forward_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.sourceMap_forward_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.source_wire_map": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.source_wire_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.uses_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.boundary_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.externalConsumer_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.globalOutput_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.interface_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.boundary_ports_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.interface_ports_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.descendant_boundary": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.descendant_interface": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.selected_backward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pull_push_boundary_valuation": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.push_pull_boundary_valuation": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.selected_gate_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.exterior_gate_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.external_wire_value_preserved": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.open_gate_preserved": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.open_support_preserved": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.open_support_pullback": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.extracted_support_preserved": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.renameInputs_gateSources": [ "propext" ], "PNP.DirectWire.StructuralReindexing.pullReplacement_program": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pullReplacement_gate_sources": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pullReplacement_output_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pullReplacement_gate_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pullReplacement_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pullReplacement_compatible": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.support_gate_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.support_surcharge_zero": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.replacement_surcharge_zero": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.matched_surcharge": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.replacement_saving_preserved": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.strict_gain_pullback": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.spliceForward_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.spliceForward_replacement": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.spliceBackward_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.spliceBackward_replacement": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_backward_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_forward_backward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_boundarySource_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_replacementSource_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_sources": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_output_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_dependencies": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_wellFounded_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_compile_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_compile_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_physical_backward_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_physical_forward_backward": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_physical_position": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_physical_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_physical_replacement": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_compiled_sources": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_compiled_output_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_compiled_gate_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.splice_compiled_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pull_splice_isSome": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.pullCompiledSplice_accepted": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.literal_replacement_transport": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOpenGateEvaluation_sourceEquation": [ "propext" ], "PNP.DirectWire.terminalOpenWireValue_boundary_get": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalOpenWireValue_external_absent": [ "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.boundarySource_input": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.boundarySource_gate": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.originalSource_exterior": [ "Quot.sound", "propext" ], "PNP.DirectWire.ArbitrarySupportSplice.originalSource_interface": [ "Quot.sound", "propext" ] } }, { "number": 271, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-17-271", "id": "structural-open-program-integration", "title": "Structural reordering in complete source-only replacement programs", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanStructuralProgramsFormalized": true, "leanStructuralProgramsAxiomAuditPassed": true, "leanStructuralProgramsAuditedDeclarationCount": 63, "leanStructuralProgramsGateCausalLabelTheorem": "PNP.DirectWire.StructuralReindexing.result_gate_level", "leanStructuralProgramsLiteralFieldSourceTheorem": "PNP.DirectWire.WireCarrier.reindex_field_source", "leanStructuralProgramsPendingSnapshotTheorem": "PNP.DirectWire.WireObligationHistory.State.reindex_pending", "leanStructuralProgramsRawCurrentCarrierDecodeTheorem": "PNP.DirectWire.WireStructuralState.execute_isSome", "leanStructuralProgramsRawRejectionTheorem": "PNP.DirectWire.WireStructuralState.execute_failure_iff", "leanStructuralProgramsLocalPhysicalOwnershipTheorem": "PNP.DirectWire.WireStructuralState.Receipt.physical_ownership", "leanStructuralProgramsHistoricalOriginTheorem": "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_origin", "leanStructuralProgramsHistoricalChargesTheorem": "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged", "leanStructuralProgramsHistoricalRemovalsTheorem": "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed", "leanStructuralProgramsCompleteProgramLifecycleTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle", "leanStructuralProgramsCompleteProgramCausalInvariantTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant", "leanStructuralProgramsCompleteProgramPhysicalOwnershipTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership", "leanStructuralProgramsCompleteCertificateSoundnessTheorem": "PNP.DirectWire.WireOpenCertificate.verify_sound", "leanStructuralProgramsStrictResidualDescentTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent", "leanStructuralProgramsCheckedRawStructuralActionsDerived": true, "leanStructuralProgramsCurrentCarrierBoundsUsed": true, "leanStructuralProgramsCompleteRawSwapSequenceRequired": true, "leanStructuralProgramsExactPendingSnapshotsPreserved": true, "leanStructuralProgramsLiteralFieldSourcesPreserved": true, "leanStructuralProgramsWholeOutputAndFieldSemanticsPreserved": true, "leanStructuralProgramsAllInputCausalLabelsPreserved": true, "leanStructuralProgramsStructuralAllocationsAndRemovalsZero": true, "leanStructuralProgramsPreviousGlobalOwnersPreserved": true, "leanStructuralProgramsCompleteChargeAndRemovalHistoryPreserved": true, "leanStructuralProgramsCompleteAcceptedProgramRequired": true, "leanStructuralProgramsClosedFinalLedgerRequired": true, "leanStructuralProgramsProperSupportRequired": true, "leanStructuralProgramsStrictSignedSavingRequired": true, "leanStructuralProgramsCallerSuppliedOrderingOrMapsRequired": false, "leanStructuralProgramsCallerSuppliedCausalOrOwnershipWitnessRequired": false, "leanStructuralProgramsReorderingAloneEarnsStrictSaving": false, "leanStructuralProgramsAcceptsSuccessfulPrefixAfterFailedTail": false, "leanStructuralProgramsFullManuscriptProfileSemanticsProved": false, "leanStructuralProgramsAllNormalizationAndMaterializerRulesProved": false, "leanStructuralProgramsFullManuscriptVerifyDWProved": false, "leanStructuralProgramsCompleteChargeSoundnessAndPackageEProved": false, "leanStructuralProgramsGlobalCertificateDiscoveryProved": false, "leanStructuralProgramsTerminalFamiliesDerived": false, "leanStructuralProgramsGlobalRouteCoverageProved": false, "leanStructuralProgramsUnconditionalSaturatePositiveProved": false, "leanStructuralProgramsUnconditionalBCELReadyProved": false, "leanStructuralProgramsUnconditionalZeroSlackProved": false, "leanStructuralProgramsExactGeneralPCCMinProved": false, "leanStructuralProgramsPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanStructuralProgramsRuntimeExecutionIsProofAuthority": false, "leanStructuralProgramsScope": "arbitrary-finite-source-only-complete-programs-computed-current-carrier-raw-structural-actions-literal-field-wires-exact-causal-labels-pending-snapshots-zero-local-cost-prior-global-owners-and-history-closed-ledger-proper-support-strict-saving-no-global-discovery-or-full-manuscript-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.StructuralReindexing.result_gate_level": "a50c0086d15fbd4074b697f5d2ee0a2cc4a3c560b6a897cf4b7d428f6b923147", "PNP.DirectWire.StructuralReindexing.result_source_level": "ab67b74a2c57b018dbd7a0e0d8c87bba4879f725e29d2e8d349f46a909a3752f", "PNP.DirectWire.StructuralReindexing.result_output_level": "0ed0ad0cbc5890423ea42d55462642efdab463ad9dd1c140fe676fb0a118091c", "PNP.DirectWire.WireCarrier.reindex_exposed": "9dedb06fca17bd740917e249b8cea30323d0231377bf46cad60dc391863fd75f", "PNP.DirectWire.WireCarrier.reindex_gateCount": "0d947c176309c42bf07dbecf927a7b8d98d522647e9ef37f5800f7d833347e09", "PNP.DirectWire.WireCarrier.reindex_backward_forward": "e7020fbef713b2c69e5836482cf13b749a97795e147b01bf8f2fd32ef28ac619", "PNP.DirectWire.WireCarrier.reindex_forward_backward": "9078f22fd69aa63d2673a856d3322e82cc1dd15392917a9e6f2a9b5533add29a", "PNP.DirectWire.WireCarrier.reindex_output": "cf09ed635d35b9cd9552ec65eb1ae014ca8bb05414823cab5dc75ffb7579ea79", "PNP.DirectWire.WireCarrier.reindex_field": "4612b606e7507e946f29548e3970060804ac6adcf0df141759023d91661407e6", "PNP.DirectWire.WireCarrier.reindex_field_source": "4b052def21f902eae394a407393e26c5b0e97383909175a8b630fef6b8dfd6f7", "PNP.DirectWire.WireCarrier.reindex_exposed_level": "d6a1f8cddc0bcb52ad1cb75b4c47ba4012f780e5e91c61e9a99b6bff2e7614b7", "PNP.DirectWire.WireCarrier.reindex_output_level": "1eff3d5235aa20f4143d929928e6aaac7bbbbbd3036937bedecfdb9019228bfd", "PNP.DirectWire.WireCarrier.reindex_field_level": "a4f2a92d2d54f64d54afc354e3b5d1fa89956729c517a9e9a94a37b2f31972c6", "PNP.DirectWire.WireCarrier.reindex_causalBounds": "9a740ded5a4cd5450f45e36b76ec58c424d1f66ac143c3dcfa49af71838d4fb2", "PNP.DirectWire.WireObligationHistory.State.reindex_pending": "6858e7c2cb1d0d1c8fa9d5a8b0450b2c43b30e63f189f6aea40d2df5443904b3", "PNP.DirectWire.WireObligationHistory.State.reindex_charged": "3278b0893f6fcfb33cb9ac19e3ad546142dfe3bcf241b1e8333cebbd6a775217", "PNP.DirectWire.WireObligationHistory.State.reindex_removed": "45128e8072c56c21232374f0726840652ef9ae56017b29f1c6deecf61094b843", "PNP.DirectWire.WireObligationHistory.State.reindex_gateCount": "c8dd434a6e1b1f51b4814a2615bb6c4c1baa921798c60eaa86ad3592549ac3ec", "PNP.DirectWire.WireObligationHistory.State.reindex_causalInvariant": "e8de8997cc2dec275f6d660c0ccc3edac2611801728268f621bf2fd7d8c72d7b", "PNP.DirectWire.WireStructuralState.execute_isSome": "4035c397504a98fa0dfec573d7b3d6b24c8202b1b02d6a5dc4af9a0112935012", "PNP.DirectWire.WireStructuralState.execute_failure_iff": "c07429575f8c1aa7e0e81ca4040f14d70f72946450f9fc9109f98ab397854ec0", "PNP.DirectWire.WireStructuralState.Receipt.ownership_origin": "4092333a17356c304128b3f2e0a7e28203538f6eccf21065545a97d5bc3277bd", "PNP.DirectWire.WireStructuralState.Receipt.ownership_origin_forward": "e603acdc3c620f7162b839f84eccdd7f7b1567769d226eaa7b2ab7bf0f6a5bda", "PNP.DirectWire.WireStructuralState.Receipt.ownership_origin_injective": "1e22876ed58d059f7df324d13f989c964f9f0deac5ad3019a08c9e057cfff529", "PNP.DirectWire.WireStructuralState.Receipt.ownership_live_members": "ccb499ea94d177c368edec9e3fd18fc0ef3e9edbd71bee3d6523b9a1fd97baae", "PNP.DirectWire.WireStructuralState.Receipt.ownership_not_allocated": "2ed955adbb23fe72e448ffc1cb1cccd479e2c47a79d722d4a0d56c794cfc5485", "PNP.DirectWire.WireStructuralState.Receipt.ownership_charged": "b3a38a8a73eea8ab001c4b22f4f6966900a9bedfe7856af3bc96b1f24d8fd60b", "PNP.DirectWire.WireStructuralState.Receipt.ownership_removed": "228b4fcbbcbeb56497770b0c5b40e6d70ae73d8230b940bf0cac4f6ca4f96af4", "PNP.DirectWire.WireStructuralState.Receipt.ownership_wellFormed": "f9fef5f8077cd879ed5c275ddc21b46ab741ea12052d20bc939cf996d45c8a0f", "PNP.DirectWire.WireStructuralState.Receipt.physical_ownership": "3ccd99b194af7c85675e7d978e91c68be26394005f26001b9c9a19400f276dee", "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_origin": "e92c140a15b6a707bafcaaadb2a9a25eef3768908749814d35c26e08c02cb979", "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged": "88cea4855d7a80e52fb1ef445208021ad6babff0a45d2f993f6fef31d0ff4a6a", "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed": "12169fcda0c9ce0a4c4d421f867f039406516295425022212b8e06be0749c22a", "PNP.DirectWire.WireOpenProgram.orderEvents_success_iff": "e1b2b9787c19111793f9f90668214efb7c6eff4d421e77aa91f3476f3fc89d72", "PNP.DirectWire.WireOpenProgram.orderEvents_failure_iff": "8d3ebe6d609705e5320540cdcf174fb14bfcaf8aae8595d70ed1893c8dedc95a", "PNP.DirectWire.WireOpenProgram.execute_failed_tail": "c852f45d97e5d2309875f6ba6f2a62aa22f4293c81781f6d7df84cae93f2bb72", "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_output": "9cea32cc78cee0b2c900d6de17291ab5a16954b5b0bcc3cc13c7966bb8002990", "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field": "f7f2e0b981060c9871f68d80e139e2cd1035d277449dead2f13c9c5881518bef", "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle": "9669cc796d490317f08119fd24b916dda275ff271609709f0ffe92e057a8fb2d", "PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_count": "45c2da7f85d2cf6b15e999f771315afdd40b625fc3443eca9a715f768594202b", "PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_identities_nodup": "35b434faefbe1677549ab531bffc512dc5a55890aec21d3ad8d43ec198101168", "PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant": "93a3cdc341e0720cc8327ae38b59cf4a0e419540c23ac76916af0fac7fc557ad", "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership": "15204bb313e0909e10d02a1b740d478b508ce7d129322a15015f90648e12e562", "PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_origin_injective": "7be2e11b1cce85296ad1dfd57f1ef683118d51ea34962fbaf7b56163241cea8d", "PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_charge_origin": "3d637bfdf13b74e29f7d946f218bb8aa0ff6873271eccfc1ab546da6027b1fe0", "PNP.DirectWire.WireOpenProgram.compile_exists_iff": "1e58bf5b50338a0b30d0fe144e44e7c1a2b000c78e460d0a25a72efa4398da75", "PNP.DirectWire.WireOpenProgram.compile_none_iff": "7682645460be03c064cbc89ad7d53075275e646683bf6395d7749f8cc2ab72a5", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source": "437a61a53cd319f887eda93378e0f109fd709c1d9747deb8fd4e77c0e463f326", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.proper_support": "5c6f2e9d804360f72b08750c57d10d96f9512522c6fba908887347c5ac83d067", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output": "5f046bbe098419e59655fce686ee1bfd685ba68791cc61e8c7dca3a35e0c1dc2", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field": "cc8f761bd78a436e5b62f69e746761285b29662707461d4060366e94c3a607b6", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting": "2264e7418f8b4391813ad064cbb043a4d2e27480fbb091497a4602d1d6206cce", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain": "2f7d4f8fcdd07d5f5d87cdbd71bfa6b741458bb71a57152549a2dc4089b9848e", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent": "47f9cc054c7a8c2c40750548184fc3c5c32ad95f3ed5872d9945af8cc7f6f21d", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership": "3ed94e0bc4fff18f80da2ed5a796492e2c320c3cf028ac18cc6a6f61e18cdaed", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger": "052af36b3ec051738c97181fbfe929297367ef4a5fa2066056b7299fceb0a461", "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle": "150b92266e1ffaff1bc2c238a570e17dcf21c2f1ffeba8912edab47fc0f68786", "PNP.DirectWire.WireOpenCertificate.verify_exists_iff": "607dd11f68d99c899559f22b3de54a7da719c006b7bf5f6c31980c9a082b36b0", "PNP.DirectWire.WireOpenCertificate.verify_sound": "614ff8c704c825a45e251875ff486386ac4e7c9c968a8da47a213bf8ce071994", "PNP.DirectWire.WireOpenCertificate.verify_decode_none": "98f44c362e63209904315e4cb49ab0888848f3354629b75e38b89a6ee853ec41", "PNP.DirectWire.WireOpenCertificate.verify_program_none": "590354c6341019bdcf9ed9d6dc48f45d703a8cc7dc4825820714a1cbb46d73aa", "PNP.DirectWire.WireOpenCertificate.verify_not_proper": "38f9ab062e770785bfd5f6ea282de7061e1dd1b1a8d2a787e51f52cbe212be62", "PNP.DirectWire.WireOpenCertificate.verify_no_gain": "e4b610ddb95904ac15f56a5426179f601c7bbda8394423a0b6a8ee5d99ebeb49" }, "theoremAxioms": { "PNP.DirectWire.StructuralReindexing.result_gate_level": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.result_source_level": [ "Quot.sound", "propext" ], "PNP.DirectWire.StructuralReindexing.result_output_level": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_exposed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_backward_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_forward_backward": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_field_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_exposed_level": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_output_level": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_field_level": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireCarrier.reindex_causalBounds": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.reindex_pending": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.reindex_charged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.reindex_removed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.reindex_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireObligationHistory.State.reindex_causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.execute_isSome": [ "propext" ], "PNP.DirectWire.WireStructuralState.execute_failure_iff": [ "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_origin_forward": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_origin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_live_members": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_not_allocated": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_charged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_removed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.ownership_wellFormed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireStructuralState.Receipt.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.orderEvents_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.orderEvents_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.execute_failed_tail": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_identities_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_origin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_charge_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.compile_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.compile_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.proper_support": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_decode_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_program_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_not_proper": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_no_gain": [ "Quot.sound", "propext" ] } }, { "number": 272, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-18-272", "id": "computational-recoding-program-integration", "title": "Computational recoding in complete source-only replacement programs", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanComputationalRecodingFormalized": true, "leanComputationalRecodingAxiomAuditPassed": true, "leanComputationalRecodingAuditedDeclarationCount": 88, "leanComputationalRecodingStructuralExactEncodingTheorem": "PNP.DirectWire.StructuralReindexing.GateRenaming.decode_encode", "leanComputationalRecodingStructuralEncodingLengthTheorem": "PNP.DirectWire.StructuralReindexing.GateRenaming.encode_length_le", "leanComputationalRecodingLiteralInverseCheckTheorem": "PNP.DirectWire.WireCarrierRecoding.check_iff", "leanComputationalRecodingLiteralGateBalanceTheorem": "PNP.DirectWire.WireCarrierRecoding.result_gate_balance", "leanComputationalRecodingCausalGuardTheorem": "PNP.DirectWire.WireCarrier.dependencyGuard_iff", "leanComputationalRecodingPendingSnapshotTheorem": "PNP.DirectWire.WireObligationHistory.State.recode_pending", "leanComputationalRecodingLocalPhysicalOwnershipTheorem": "PNP.DirectWire.WireRecodingState.Receipt.physical_ownership", "leanComputationalRecodingRawDecodeRoundTripTheorem": "PNP.DirectWire.WireRecodingInput.decode_encode", "leanComputationalRecodingRawAcceptanceTheorem": "PNP.DirectWire.WireRecodingInput.execute_success_iff", "leanComputationalRecodingCompleteProgramGateBalanceTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.gate_balance", "leanComputationalRecodingCompleteProgramLifecycleTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle", "leanComputationalRecodingCompleteProgramPhysicalOwnershipTheorem": "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership", "leanComputationalRecodingCompleteCertificateSoundnessTheorem": "PNP.DirectWire.WireOpenCertificate.verify_sound", "leanComputationalRecodingStrictResidualDescentTheorem": "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent", "leanComputationalRecodingExistingRawCodecReused": true, "leanComputationalRecodingBothDimensionsChecked": true, "leanComputationalRecodingCompleteLiteralRecodersRequired": true, "leanComputationalRecodingBothFullInverseEquationsChecked": true, "leanComputationalRecodingAllInputCausalLabelsChecked": true, "leanComputationalRecodingOrdinaryOutputsAndHiddenFieldsCovered": true, "leanComputationalRecodingExactPendingSnapshotsPreserved": true, "leanComputationalRecodingLiteralEncoderDecoderGatesCharged": true, "leanComputationalRecodingActualNormalizerDeletionMapsUsed": true, "leanComputationalRecodingDerivedEncoderDecoderAllocationPhases": true, "leanComputationalRecodingHistoricalChargesAndOwnersPreserved": true, "leanComputationalRecodingCompleteAcceptedProgramRequired": true, "leanComputationalRecodingClosedFinalLedgerRequired": true, "leanComputationalRecodingProperSupportRequired": true, "leanComputationalRecodingStrictSignedSavingRequired": true, "leanComputationalRecodingCallerSuppliedCorrectnessOrderCausalOrOwnerWitnessRequired": false, "leanComputationalRecodingRecodingDischargesOpenObligations": false, "leanComputationalRecodingSemanticReversibilityImpliesPhysicalCancellation": false, "leanComputationalRecodingSemanticReversibilityAloneEarnsSaving": false, "leanComputationalRecodingInverseCheckEnumeratesAllFieldValuations": true, "leanComputationalRecodingFullManuscriptProfileSemanticsProved": false, "leanComputationalRecodingAllRecodingAndNormalizationRulesProved": false, "leanComputationalRecodingFullManuscriptVerifyDWProved": false, "leanComputationalRecodingCompleteChargeSoundnessAndPackageEProved": false, "leanComputationalRecodingGlobalCertificateDiscoveryProved": false, "leanComputationalRecodingTerminalFamiliesDerived": false, "leanComputationalRecodingGlobalRouteCoverageProved": false, "leanComputationalRecodingUnconditionalSaturatePositiveProved": false, "leanComputationalRecodingUnconditionalBCELReadyProved": false, "leanComputationalRecodingUnconditionalZeroSlackProved": false, "leanComputationalRecodingExactGeneralPCCMinProved": false, "leanComputationalRecodingPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanComputationalRecodingRuntimeExecutionIsProofAuthority": false, "leanComputationalRecodingScope": "arbitrary-finite-source-only-complete-programs-existing-raw-codec-both-literal-recoders-exact-inverse-and-syntactic-causal-checks-pending-snapshots-actual-allocations-deletions-and-global-ownership-closed-ledger-proper-support-strict-saving-no-global-discovery-full-manuscript-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.StructuralReindexing.GateRenaming.decode_encode": "6660efe22c09761b56b9f6868aecb0d5999fb0293e6d24651c9af3f597d8fccc", "PNP.DirectWire.StructuralReindexing.GateRenaming.encode_length_le": "40e8aa3e2cafa08891074bb9146c43e7b245a630ab6a02e735d94055842172fd", "PNP.DirectWire.StructuralReindexing.GateRenaming.validCode_encode": "86c582cc582c38d6ace241f6b588e092cbca557c25e2edeb08d2585afd4f33e1", 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], "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_charged": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.ProgramOwnership.advance_structural_removed": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.orderEvents_success_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.orderEvents_failure_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.execute_failed_tail": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.full_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_count": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.executed_identities_nodup": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_origin_injective": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.ownership_charge_origin": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.compile_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.compile_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.records_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.proper_support": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.output": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.field": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.charge_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.strictResidualDescent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.closed_ledger": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.CheckedCertificate.creation_lifecycle": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_exists_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_decode_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_program_none": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_not_proper": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenCertificate.verify_no_gain": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.Transition.charged_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.Transition.removed_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.Transition.causalInvariant": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.Transition.local_physical_ownership": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireOpenProgram.CompiledProgram.gate_balance": [ "Quot.sound", "propext" ] } }, { "number": 273, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-18-273", "id": "source-derived-zero-cost-exposure", "title": "Source-derived zero-cost alias exposure", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanSourceDerivedZeroCostExposureFormalized": true, "leanSourceDerivedZeroCostExposureAxiomAuditPassed": true, "leanSourceDerivedZeroCostExposureAuditedDeclarationCount": 22, "leanSourceDerivedZeroCostExposureMinimumTheorem": "PNP.DirectWire.ZeroCostExposure.referenceMinimum_extend", "leanSourceDerivedZeroCostExposureSlackTheorem": "PNP.DirectWire.ZeroCostExposure.residualSlack_extend", "leanSourceDerivedZeroCostExposureRecognitionTheorem": "PNP.DirectWire.ZeroCostExposure.recognize_success_iff", "leanSourceDerivedZeroCostExposureGateRefusalTheorem": "PNP.DirectWire.ZeroCostExposure.recognize_gate_none_iff", "leanSourceDerivedZeroCostExposureTupleAcceptanceTheorem": "PNP.DirectWire.ZeroCostExposure.compileLayout_available_iff", "leanSourceDerivedZeroCostExposureCarrierMinimumTheorem": "PNP.DirectWire.WireCarrier.exposed_referenceMinimum_of_checkLayout", "leanSourceDerivedZeroCostExposureCarrierSlackTheorem": "PNP.DirectWire.WireCarrier.exposed_residualSlack_of_checkLayout", "leanSourceDerivedZeroCostExposureCarrierPreservationTheorem": "PNP.DirectWire.WireCarrier.checked_exposure_preserves_problem", "leanSourceDerivedZeroCostExposureArbitraryFiniteDimensionsCovered": true, "leanSourceDerivedZeroCostExposureLiteralInputConstantAndOldOutputAliasesCovered": true, "leanSourceDerivedZeroCostExposureBothRealizationTransfersProved": true, "leanSourceDerivedZeroCostExposureActualSourceRecognitionComputed": true, "leanSourceDerivedZeroCostExposureEveryRequestedFieldChecked": true, "leanSourceDerivedZeroCostExposureActualCarrierMinimumAndSlackPreserved": true, "leanSourceDerivedZeroCostExposureCallerSuppliedObserverMinimumOrCorrectnessRequired": false, "leanSourceDerivedZeroCostExposureConstructorOrRecognizerEnumeratesSemanticMinima": false, "leanSourceDerivedZeroCostExposureAllSemanticallyFreeExposuresRecognized": false, "leanSourceDerivedZeroCostExposureRefusalImpliesPackageERoute": false, "leanSourceDerivedZeroCostExposureNoPhysicalGateIncreaseAloneImpliesZeroCost": false, "leanSourceDerivedZeroCostExposureUniquePhysicalChargeAloneForcesMinimumIncrease": false, "leanSourceDerivedZeroCostExposureArbitraryPositiveCostTransparencyProved": false, "leanSourceDerivedZeroCostExposureFullManuscriptProfileSemanticsProved": false, "leanSourceDerivedZeroCostExposureTerminalFamiliesDerived": false, "leanSourceDerivedZeroCostExposureGlobalRouteCoverageProved": false, "leanSourceDerivedZeroCostExposureUnconditionalSaturatePositiveProved": false, "leanSourceDerivedZeroCostExposureUnconditionalBCELReadyProved": false, "leanSourceDerivedZeroCostExposureUnconditionalZeroSlackProved": false, "leanSourceDerivedZeroCostExposureExactGeneralPCCMinProved": false, "leanSourceDerivedZeroCostExposurePolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanSourceDerivedZeroCostExposureScope": "arbitrary-finite-literal-input-constant-old-output-alias-extension-projection-exact-minimum-slack-source-derived-tuple-recognition-actual-carrier-no-semantic-completeness-positive-cost-global-route-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.ZeroCostExposure.Reference.toSource_eval": "18a33b06fc291b34cb074d9688282210f4c21a2708a0c4ab924f8dd985335bab", "PNP.DirectWire.ZeroCostExposure.extend_gateCount": "668882a9bee592090a6cec5f6f2c005121d7682ffb9daa2c5996f8c4d68dee42", "PNP.DirectWire.ZeroCostExposure.project_gateCount": "315753fe80872380b5de8fdca1acf5d866c46416b5e009aeeda8fcc0522f68ae", "PNP.DirectWire.ZeroCostExposure.extend_original": "f735eb48df9890020c841808534c329a72147c759c301d871f21553788157c1f", "PNP.DirectWire.ZeroCostExposure.extend_field": "e9c748c782da7b3b5800c4720fe32cc1fc2d064c15a57ad05109aa844805e6ec", "PNP.DirectWire.ZeroCostExposure.project_semantics": "5cb6faa5210bc24c6aeaabeb999b2a3927da180a0fbf7be9c07cd10b7119bf38", "PNP.DirectWire.ZeroCostExposure.extend_equivalent": "aa61a3a9de83ed22b63685b40b6252144097ae47ce12e57379c69b4e0ae4b74d", "PNP.DirectWire.ZeroCostExposure.project_equivalent": "1cb9297b40140397fc91a2ce4e347ec69b6a9fbe3eee1850d3c1e2a4ed029949", "PNP.DirectWire.ZeroCostExposure.project_extend_equivalent": "95ed0c663bfa2ce81f7763f170bab6e3ff26cf9ac9f0e5ce87ff7e8c084f1f41", "PNP.DirectWire.ZeroCostExposure.referenceMinimum_extend": "e70b4f616f47d81708dfa5b8531191b6942b71ba7c98a2512597416aa98fce55", "PNP.DirectWire.ZeroCostExposure.residualSlack_extend": "11201b09ca4b92710181dde08fb4fbded4bfb4287ad300290472eb7a090a2cdd", "PNP.DirectWire.ZeroCostExposure.compileLayout_success_iff": "0a80a0b6ab49c9d96899615f2bfea720c3c609b514fa2c2909fa7ab0aa892f25", "PNP.DirectWire.ZeroCostExposure.compileLayout_sound": "f62382d60b18888943122868a9e6fbe45f4ec8574fa71dfc4d159b8aba448f11", "PNP.DirectWire.ZeroCostExposure.recognize_success_iff": "7ab1cec4a649def55ddef0b39b50192de5909625fdc73ad330ed49c521f0fbb1", "PNP.DirectWire.ZeroCostExposure.recognize_isSome_iff": "e86ee10c9054890003e5c6b8e9ef7c53b0d1c4ade0eb1238011988ea4506b60d", "PNP.DirectWire.ZeroCostExposure.recognize_none_iff": "c1dd878bb5e68de979dd4a96d5f25d1aefc035ed17e2fcf7408b976de6d936ef", "PNP.DirectWire.ZeroCostExposure.recognize_gate_none_iff": "e877cd0cdd33656f9b03cfedab16e3416385a5fba0ff74e177ba6687471da183", "PNP.DirectWire.ZeroCostExposure.checkLayout_iff": "bb17be20fa7299b6c7eaf7ac27f95bae162d39fe6099a07d46e1eba7d69be8d4", "PNP.DirectWire.ZeroCostExposure.compileLayout_available_iff": "32b03086b0cb2a74ad96b70307963768468c8e43f39e4ac11fb0ea655e6febae", "PNP.DirectWire.WireCarrier.exposed_referenceMinimum_of_checkLayout": "df88d190913b101113192fbe892aef9f7109efaf2717c40433ca0833867d1dfa", "PNP.DirectWire.WireCarrier.exposed_residualSlack_of_checkLayout": "2b0c5ec9087e8f70a023a82fbb930615453c26be4b9addefb45b3b1fb20cba95", "PNP.DirectWire.WireCarrier.checked_exposure_preserves_problem": "2ed10a640a706bb5f1965313859d77148125723d97ea25fb117286ffce7f691c" }, "theoremAxioms": { "PNP.DirectWire.ZeroCostExposure.Reference.toSource_eval": [], "PNP.DirectWire.ZeroCostExposure.extend_gateCount": [], "PNP.DirectWire.ZeroCostExposure.project_gateCount": [], "PNP.DirectWire.ZeroCostExposure.extend_original": [], "PNP.DirectWire.ZeroCostExposure.extend_field": [], "PNP.DirectWire.ZeroCostExposure.project_semantics": [], "PNP.DirectWire.ZeroCostExposure.extend_equivalent": [], "PNP.DirectWire.ZeroCostExposure.project_equivalent": [], "PNP.DirectWire.ZeroCostExposure.project_extend_equivalent": [], "PNP.DirectWire.ZeroCostExposure.referenceMinimum_extend": [], "PNP.DirectWire.ZeroCostExposure.residualSlack_extend": [], "PNP.DirectWire.ZeroCostExposure.compileLayout_success_iff": [], "PNP.DirectWire.ZeroCostExposure.compileLayout_sound": [], "PNP.DirectWire.ZeroCostExposure.recognize_success_iff": [ "Quot.sound" ], "PNP.DirectWire.ZeroCostExposure.recognize_isSome_iff": [ "Quot.sound" ], "PNP.DirectWire.ZeroCostExposure.recognize_none_iff": [ "Quot.sound" ], "PNP.DirectWire.ZeroCostExposure.recognize_gate_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ZeroCostExposure.checkLayout_iff": [ "Quot.sound" ], "PNP.DirectWire.ZeroCostExposure.compileLayout_available_iff": [ "Quot.sound" ], "PNP.DirectWire.WireCarrier.exposed_referenceMinimum_of_checkLayout": [], "PNP.DirectWire.WireCarrier.exposed_residualSlack_of_checkLayout": [], "PNP.DirectWire.WireCarrier.checked_exposure_preserves_problem": [] } }, { "number": 274, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-274", "id": "wire-profile-exposure-balance", "title": "Wire-backed computational profiles and exposure balance", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireProfileExposureFormalized": true, "leanWireProfileExposureAxiomAuditPassed": true, "leanWireProfileExposureAuditedDeclarationCount": 35, "leanWireProfileExposureFullComparisonTheorem": "PNP.DirectWire.WireProfile.full_iff", "leanWireProfileExposureQuotientComparisonTheorem": "PNP.DirectWire.WireProfile.quotient_iff", "leanWireProfileExposureFullLiftTheorem": "PNP.DirectWire.WireProfile.full_lift_iff", "leanWireProfileExposureAttainedQuotientWitnessTheorem": "PNP.DirectWire.WireProfile.quotientWitness_matches", "leanWireProfileExposureExposureBalanceTheorem": "PNP.DirectWire.WireProfile.exposure_states_balance", "leanWireProfileExposureExactTransferTheorem": "PNP.DirectWire.WireProfile.exposure_moves_exact_slack_to_defect", "leanWireProfileExposureNonLiftabilityTheorem": "PNP.DirectWire.WireProfile.exposure_loss_has_unliftable_quotient_witness", "leanWireProfileExposureOrdinarySlackTheorem": "PNP.DirectWire.WireProfile.source_slack_balance", "leanWireProfileExposureNormalizationTheorem": "PNP.DirectWire.WireProfile.normalize_fullEquivalent", "leanWireProfileExposureCheckedSpliceTheorem": "PNP.DirectWire.WireProfile.splice_fullEquivalent", "leanWireProfileExposureArbitraryFiniteDimensionsCovered": true, "leanWireProfileExposureOrdinaryOutputsPreservedInBothModes": true, "leanWireProfileExposureActualWireValuesAtAllValuations": true, "leanWireProfileExposureMinimaAndAttainedWitnessesDerived": true, "leanWireProfileExposureExposureTransfersSlackToDefect": true, "leanWireProfileExposureCallerSuppliedObserverOrMinimumRequired": false, "leanWireProfileExposureQuotientWitnessAloneIsFullReplacement": false, "leanWireProfileExposureAllGateFieldsAreCanonicalTerminalFamily": false, "leanWireProfileExposureCompleteManuscriptProfileGrammarProved": false, "leanWireProfileExposureForcedCostTransparencyProved": false, "leanWireProfileExposureCompletePackageEOrGlobalRoutesProved": false, "leanWireProfileExposureTerminalFamiliesDerived": false, "leanWireProfileExposureUnconditionalSaturatePositiveProved": false, "leanWireProfileExposureUnconditionalBCELReadyProved": false, "leanWireProfileExposureUnconditionalZeroSlackProved": false, "leanWireProfileExposureExactPolynomialPCCMinProved": false, "leanWireProfileExposurePolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanWireProfileExposureReferenceMinimizationIsExhaustive": true, "leanWireProfileExposureScope": "arbitrary-finite-actual-wire-profile-values-all-input-valuations-mandatory-ordinary-outputs-full-quotient-lift-attained-minima-exact-exposure-slack-defect-transfer-checked-normalization-splice-no-full-manuscript-global-route-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireProfile.mask_implementation": "a5e99322915e0ca88895287bf073d302b2b29df82ebdcdf7a84982461d861a05", "PNP.DirectWire.WireProfile.mask_fieldValue": "02bd6191dfb811c25056a049e8e86fa16ada2242ad981e9d302c3be1da8df54e", "PNP.DirectWire.WireProfile.full_iff": "5d698934e56bdcf88b7dcf60eafac3eab9e7db32ea6bf3f9d38f5fa1ff31ff8f", "PNP.DirectWire.WireProfile.quotient_iff": "fccf2f775e403e158d93d6139963ae4158be4993b4d8f377e840eb0733e2d928", "PNP.DirectWire.WireProfile.full_to_quotient": "48950dc3e4b866af61a3e6444bd32cbceae0a46c0957f77cb4fa5e9d54f0f989", "PNP.DirectWire.WireProfile.full_lift_iff": "aaa96b36a3742f3fbf460ac282c6dcea4aa6b136e03c129162f243d303ba25d5", "PNP.DirectWire.WireProfile.fullWitness_gateCount": "099dc96ab5aaa8b8f55d148aae45bf022e4a6d4bfa2d72183f93cd91edf7e188", "PNP.DirectWire.WireProfile.fullWitness_matches": "b7afccdcdb9354ae51800ae53cd96073283c7994b327a4b6a28618dc7c8b2969", "PNP.DirectWire.WireProfile.fullMinimum_le_physical": "0d3ec56776d0c9c8f43c66d71bf0209cf5080d34347aca3d0eedeaae9bd975f2", "PNP.DirectWire.WireProfile.quotientMinimum_le_full": "bc1adee3880f8b44318713263f3b979a747c83c909a77a5b9c58357d010b54d0", "PNP.DirectWire.WireProfile.quotientWitness_gateCount": "652ff627431bbb569f5e42ca2d542dd1424e11a522427ae3040d546825e8e7ed", "PNP.DirectWire.WireProfile.quotientWitness_matches": "eebcc528071e48f3c185e9e70535081af327c58a3294bc6ad14583cfbf39ddad", "PNP.DirectWire.WireProfile.quotient_candidate_lower_bound": "834f4fc9ffa0ba6d873d5ddd4bbad11e4f3a7f93a5ae9bd0cea1670a65f827c7", "PNP.DirectWire.WireProfile.full_candidate_lower_bound": "2b3886e4849ac17ef8565b28f1bd0907293a8a46dd7a922f14689cd3a4d63348", "PNP.DirectWire.WireProfile.fullSlack_add_projectionDefect": "19fe9cf0cbb7a6364face3057ca7d7007fb703836df32eb59ad9efe7b6a7e132", "PNP.DirectWire.WireProfile.exposure_balance": "f687b4f65e9d51beb3024edb123c1ff2204fed3b8adbd26df53cc12ffca3a439", "PNP.DirectWire.WireProfile.exposure_preserves_positive_alternative": "c54845f73cc4c477d4335448949eafb39c53c853ce1da97b9d522d634a50ce32", "PNP.DirectWire.WireProfile.quotient_minimum_cannot_lift_of_positive_defect": "edb1bb6409b16c4bc54f0b3ef32d76a35ccf551487d39a41642d7973fee1f43c", "PNP.DirectWire.WireProfile.exposure_loss_has_unliftable_quotient_witness": "7f3d9d4c895acc696bc99ac5648a6c49e5ab20c9f19553031d12c27fe53b57ed", "PNP.DirectWire.WireProfile.allGateFields_value": "54b34f81e456e694484f290a71c634f4a45b016993e8208744b7a096b59b27b9", "PNP.DirectWire.WireProfile.allGateFields_positive_alternative": "e9281676603a9b4eb5d0739ca3bf71e44a0fe8623f6f7d8ba4015ae0c41be575", "PNP.DirectWire.WireProfile.quotientMinimum_forget_all": "edd5a27a002e25340fe7ca068bd95007b60d9e4c5a703d0034b0e1e9a26ded26", "PNP.DirectWire.WireProfile.source_slack_balance": "ff2ba7a5fb4b772b4ee011f7ef07f7170de32acbdf025fb7e342d7934c8fad12", "PNP.DirectWire.WireProfile.source_positive_alternative": "285b87162a99076953ebe58aeeb633e9feba45114f232ad4b00d6202411714c6", "PNP.DirectWire.WireProfile.mask_absorb_equivalent": "2cf73c7192313cbdbd76735b7b77042b777f74f8b5e649976c8069093a876e46", "PNP.DirectWire.WireProfile.quotientMinimum_mask_active": "b79c9065239510e20587a22cb40b765d2201744deb19f5607789d1fa44858a23", "PNP.DirectWire.WireProfile.fullMinimum_mask_mono": "43029536c1d99c3cfec5ca745449d974a430bf361fefd2b93e2ffceb236e1576", "PNP.DirectWire.WireProfile.exposure_states_balance": "e654e8bd8a28e49091b5bb146f72a4f9268c497b82839c77a542aa3a3b4bbae6", "PNP.DirectWire.WireProfile.exposure_moves_exact_slack_to_defect": "7b4fbd1ffde330cac1106dfce09549e1c44646f640e9d9c3f1cbf132a20c61e3", "PNP.DirectWire.WireProfile.normalize_fullEquivalent": "aae04d9117416a78c56fb98de5f4181f7fe92fd593051bc841c2e02f7161b78b", "PNP.DirectWire.WireProfile.fullMinimum_normalize": "7ab5397d66beaca752e9f08856b3b8746e2bcffcc9637d923abde103af56fe5e", "PNP.DirectWire.WireProfile.quotientMinimum_normalize": "019da02696fa365128110df9065f50101439921957a98b46c6397b9f34d67045", "PNP.DirectWire.WireProfile.splice_fullEquivalent": "2c6287494db7ca5d8bdfb46f0aa27f842ac5c7fd2927f8c687ca9ced370d77d1", "PNP.DirectWire.WireProfile.fullMinimum_splice": "f1ca47b85073fa3b09587f992d21cb51635fdf7831d9536bbea7f4b9be28b564", "PNP.DirectWire.WireProfile.quotientMinimum_splice": "7fc79932a7744ce1ff140a2c4df84342b54cd79fae1b4a3380a78b73da3b2634" }, "theoremAxioms": { "PNP.DirectWire.WireProfile.mask_implementation": [], "PNP.DirectWire.WireProfile.mask_fieldValue": [], "PNP.DirectWire.WireProfile.full_iff": [], "PNP.DirectWire.WireProfile.quotient_iff": [], "PNP.DirectWire.WireProfile.full_to_quotient": [], "PNP.DirectWire.WireProfile.full_lift_iff": [], "PNP.DirectWire.WireProfile.fullWitness_gateCount": [], "PNP.DirectWire.WireProfile.fullWitness_matches": [ "Quot.sound" ], "PNP.DirectWire.WireProfile.fullMinimum_le_physical": [], "PNP.DirectWire.WireProfile.quotientMinimum_le_full": [ "Quot.sound" ], "PNP.DirectWire.WireProfile.quotientWitness_gateCount": [], "PNP.DirectWire.WireProfile.quotientWitness_matches": [ "Quot.sound" ], "PNP.DirectWire.WireProfile.quotient_candidate_lower_bound": [], "PNP.DirectWire.WireProfile.full_candidate_lower_bound": [], "PNP.DirectWire.WireProfile.fullSlack_add_projectionDefect": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.exposure_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.exposure_preserves_positive_alternative": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.quotient_minimum_cannot_lift_of_positive_defect": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.exposure_loss_has_unliftable_quotient_witness": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.allGateFields_value": [], "PNP.DirectWire.WireProfile.allGateFields_positive_alternative": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.quotientMinimum_forget_all": [], "PNP.DirectWire.WireProfile.source_slack_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.source_positive_alternative": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.mask_absorb_equivalent": [], "PNP.DirectWire.WireProfile.quotientMinimum_mask_active": [], "PNP.DirectWire.WireProfile.fullMinimum_mask_mono": [ "Quot.sound" ], "PNP.DirectWire.WireProfile.exposure_states_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.exposure_moves_exact_slack_to_defect": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.normalize_fullEquivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.fullMinimum_normalize": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.quotientMinimum_normalize": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.splice_fullEquivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.fullMinimum_splice": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfile.quotientMinimum_splice": [ "Quot.sound", "propext" ] } }, { "number": 275, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-275", "id": "wire-profile-restoration-cost", "title": "Constructive wire-profile restoration cost and exact gain boundary", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanWireProfileRestorationFormalized": true, "leanWireProfileRestorationAxiomAuditPassed": true, "leanWireProfileRestorationAuditedDeclarationCount": 19, "leanWireProfileRestorationQuotientAgreementTheorem": "PNP.DirectWire.WireProfileRestoration.quotientAgreement_iff", "leanWireProfileRestorationFullRestorationTheorem": "PNP.DirectWire.WireProfileRestoration.paidWitness_fullEquivalent", "leanWireProfileRestorationChargeBoundTheorem": "PNP.DirectWire.WireProfileRestoration.projectionDefect_le_charge", "leanWireProfileRestorationPaidOverheadTheorem": "PNP.DirectWire.WireProfileRestoration.paidWitness_exact_overhead", "leanWireProfileRestorationReclaimedBoundTheorem": "PNP.DirectWire.WireProfileRestoration.reclaimed_le_overhead", "leanWireProfileRestorationNormalizedOverheadTheorem": "PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_overhead", "leanWireProfileRestorationStrictGainTheorem": "PNP.DirectWire.WireProfileRestoration.normalizedWitness_smaller_iff", "leanWireProfileRestorationCheckedGainTheorem": "PNP.DirectWire.WireProfileRestoration.CheckedGain.checked", "leanWireProfileRestorationUnaryMinimumTheorem": "PNP.DirectWire.WireProfileRestoration.unary_fullMinimum", "leanWireProfileRestorationUnaryGainTheorem": "PNP.DirectWire.WireProfileRestoration.unary_smaller_iff_fullSlack_positive", "leanWireProfileRestorationArbitraryFiniteDimensionsCovered": true, "leanWireProfileRestorationOrdinaryOutputsAndActualFieldsPreserved": true, "leanWireProfileRestorationExistingSharedMaterializerReused": true, "leanWireProfileRestorationActualPhysicalChargeAndSavingsComputed": true, "leanWireProfileRestorationExactRemainingOverheadDerived": true, "leanWireProfileRestorationStrictOriginalSizeComparisonChecked": true, "leanWireProfileRestorationExistingUnaryMinimumCompatibilityProved": true, "leanWireProfileRestorationUnaryCompatibilityHasArbitraryOutputAndFieldWidths": true, "leanWireProfileRestorationPositiveSlackRefusalAndUnaryRecoveryKernelChecked": true, "leanWireProfileRestorationCallerSuppliedWitnessMinimumOrCorrectnessRequired": false, "leanWireProfileRestorationChargeEqualsProjectionDefectProved": false, "leanWireProfileRestorationNormalizerIsSemanticallyComplete": false, "leanWireProfileRestorationNoGainImpliesZeroSlack": false, "leanWireProfileRestorationUnaryCompletenessExtendedToArbitraryInputs": false, "leanWireProfileRestorationCompleteManuscriptProfileGrammarProved": false, "leanWireProfileRestorationTerminalFamiliesDerived": false, "leanWireProfileRestorationCompletePackageEOrGlobalRoutesProved": false, "leanWireProfileRestorationUnconditionalSaturatePositiveProved": false, "leanWireProfileRestorationUnconditionalBCELReadyProved": false, "leanWireProfileRestorationUnconditionalZeroSlackProved": false, "leanWireProfileRestorationExactPolynomialPCCMinProved": false, "leanWireProfileRestorationPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanWireProfileRestorationReferenceMinimizationIsExhaustive": true, "leanWireProfileRestorationRuntimeExecutionIsProofAuthority": false, "leanWireProfileRestorationScope": "arbitrary-finite-actual-wire-full-restoration-shared-materializer-charge-defect-upper-bound-paid-and-normalized-exact-overhead-checked-strict-gain-existing-one-input-minimum-compatibility-no-general-completeness-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.WireProfileRestoration.quotientAgreement_iff": "ac36df8e2914ca2ce3b3ac0d5194e7a44198896040c925ef6043ac2f22fb3aa8", "PNP.DirectWire.WireProfileRestoration.expanded_fullEquivalent": "152cc0a4a34040eefc769049f57dcc7aaf507acf0c24c01eec7bfa5ab6196db3", "PNP.DirectWire.WireProfileRestoration.paidWitness_fullEquivalent": "91fcd87a05266afd4d59445e508f39356e1e965d285ef0b60cc4f56c4a4dd9ed", "PNP.DirectWire.WireProfileRestoration.paidWitness_gateCount": "e65c828f6ba184573026592c22c615ae9f0fe922aff384f9f2f9fbc71ff11e2c", "PNP.DirectWire.WireProfileRestoration.fullMinimum_le_quotientMinimum_add_charge": "e2f252b82be65ebb18a0e0c5ace67f3caabe1dc7a5f05ea2c0764a2a140d3dc2", "PNP.DirectWire.WireProfileRestoration.projectionDefect_le_charge": "d13d80014d1eb15d43b0a481ec8410b545b7d5a4da81db03642497e4a9adc34a", "PNP.DirectWire.WireProfileRestoration.paidWitness_exact_overhead": "d6e074081f87063d2ad6b713ea09e5b94f40b36fc757d0e6f0380a845a181bc8", "PNP.DirectWire.WireProfileRestoration.paidWitness_smaller_iff": "2d72664e0872f27c3be711951c70a4bde84886e8d534ba832e6cb064fada4110", "PNP.DirectWire.WireProfileRestoration.paidWitness_optimal_iff": "604ebe08bd50792b3dbe74affbc0492bf2a02f32ed646c9516b750d6d4ab6f70", "PNP.DirectWire.WireProfileRestoration.normalizedWitness_fullEquivalent": "b37fe38d1f18d15b720080ce5e292b25c8e54a38828f1c680c79c8e2d61ca99c", "PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_accounting": "ccec14b81c029475f4a7caad3f9b3ba495fb09ca36775702d4136fe61f96802e", "PNP.DirectWire.WireProfileRestoration.reclaimed_le_overhead": "c3969ffe2a61b71d46de269c9fe5f133acd8e70ad4ce790bacc2c3ea0679bf30", "PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_overhead": "9bd7117014ca4004f05332c0799bb8e826688013cfc98ad10753be970beb3792", "PNP.DirectWire.WireProfileRestoration.normalizedWitness_smaller_iff": "e881bf24f9e1fbe5127979e5c6f5e5c2ec61332e3dbdcbf51a33073fd74e4139", "PNP.DirectWire.WireProfileRestoration.normalizedWitness_optimal_iff": "cbdfbb757e43dc5d2f937f0df5b89af7a810ec01e5959945386694abba9892ae", "PNP.DirectWire.WireProfileRestoration.checkedGain_isSome_iff": "04233de3e6c6d5992d8c268e06c05f122e8ec5be9f2b628eead4590c7e3f3c5d", "PNP.DirectWire.WireProfileRestoration.CheckedGain.checked": "f4d34bc65c13885b7f892e5ecaad086bb0d53ea2a7208656998c0f1754fc8b90", "PNP.DirectWire.WireProfileRestoration.unary_fullMinimum": "ac5222a3652828c7cffb92f14906304bb4e1d65b250e533093b217fea53bb4e4", "PNP.DirectWire.WireProfileRestoration.unary_smaller_iff_fullSlack_positive": "7533c99f91b3438644083adba00c92b4e89522c9e45b65e14b8f65f11bac5df3" }, "theoremAxioms": { "PNP.DirectWire.WireProfileRestoration.quotientAgreement_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.expanded_fullEquivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.paidWitness_fullEquivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.paidWitness_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.fullMinimum_le_quotientMinimum_add_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.projectionDefect_le_charge": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.paidWitness_exact_overhead": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.paidWitness_smaller_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.paidWitness_optimal_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.normalizedWitness_fullEquivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.reclaimed_le_overhead": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.normalizedWitness_exact_overhead": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.normalizedWitness_smaller_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.normalizedWitness_optimal_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.checkedGain_isSome_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.CheckedGain.checked": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.unary_fullMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileRestoration.unary_smaller_iff_fullSlack_positive": [ "Quot.sound", "propext" ] } }, { "number": 276, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-276", "id": "computed-wire-profile-exact-field-cost", "title": "Computed wire-profile models and exact independent-field cost", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanComputedWireProfileFormalized": true, "leanComputedWireProfileAxiomAuditPassed": true, "leanComputedWireProfileAuditedDeclarationCount": 72, "leanComputedWireProfileUniformSourceTheorem": "PNP.DirectWire.WireProfileAvailability.sourceMatches_iff", "leanComputedWireProfileFullMinimumBridgeTheorem": "PNP.DirectWire.WireProfileAvailability.full_minimum", "leanComputedWireProfileQuotientMinimumBridgeTheorem": "PNP.DirectWire.WireProfileAvailability.quotient_minimum", "leanComputedWireProfileAmbientCoherenceTheorem": "PNP.DirectWire.WireProfileAmbient.model_observe_coherent", "leanComputedWireProfileDerivedFieldSupportTheorem": "PNP.DirectWire.WireProfileFieldClosed.available", "leanComputedWireProfileSemanticRetractionTheorem": "PNP.DirectWire.SemanticGateRetraction.semantics", "leanComputedWireProfileIndependentFieldLowerBoundTheorem": "PNP.DirectWire.FreshNandCost.gateCount_lower_bound", "leanComputedWireProfileIndependentFieldMinimumTheorem": "PNP.DirectWire.FreshNandCost.referenceMinimum_extend", "leanComputedWireProfileCoupledFullMinimumTheorem": "PNP.DirectWire.ComputedWireProfileCost.full_minimum", "leanComputedWireProfileCoupledQuotientMinimumTheorem": "PNP.DirectWire.ComputedWireProfileCost.quotient_minimum", "leanComputedWireProfileCoupledMinimumGapTheorem": "PNP.DirectWire.ComputedWireProfileCost.minimum_gap", "leanComputedWireProfileArbitraryFiniteDimensionsCovered": true, "leanComputedWireProfileOneSourceUniformAcrossAllValuationsRequired": true, "leanComputedWireProfileModelAndFieldPreservingSupportComputed": true, "leanComputedWireProfileObserverPaddingAndRewordingCoherenceProved": true, "leanComputedWireProfileExactCostForArbitraryIndependentFreshFieldWidthsProved": true, "leanComputedWireProfileCallerSuppliedModelMinimumSupportOrCorrectnessRequired": false, "leanComputedWireProfileSemanticRetractionHasExplicitUniformConstantHypothesis": true, "leanComputedWireProfileRetractionHypothesisDischargedForIndependentFieldFamily": true, "leanComputedWireProfileExtractedSupportIsProperSmallerOrOptimalProved": false, "leanComputedWireProfileArbitraryManuscriptFieldAdditivityProved": false, "leanComputedWireProfileSharedMaterializerChargeEqualsProjectionDefectProved": false, "leanComputedWireProfileCompleteManuscriptProfileGrammarProved": false, "leanComputedWireProfileTerminalFamiliesDerived": false, "leanComputedWireProfileCompletePackageEOrGlobalRoutesProved": false, "leanComputedWireProfileUnconditionalSaturatePositiveProved": false, "leanComputedWireProfileUnconditionalBCELReadyProved": false, "leanComputedWireProfileUnconditionalZeroSlackProved": false, "leanComputedWireProfileExactPolynomialPCCMinProved": false, "leanComputedWireProfilePolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanComputedWireProfileAvailabilityAndReferenceMinimizationAreExhaustive": true, "leanComputedWireProfileRuntimeExecutionIsProofAuthority": false, "leanComputedWireProfileScope": "arbitrary-finite-computed-uniform-wire-availability-ambient-observer-coherence-source-derived-field-preserving-support-exact-independent-fresh-nand-cost-and-terminal-model-coupling-no-arbitrary-field-additivity-global-route-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.ComputedWireProfileCost.full_minimum": "b52b8497022d4804c1d52f1e43be42a3daf247fac6747a1e6372932478db8c8b", "PNP.DirectWire.ComputedWireProfileCost.minimum_gap": "8c138e3dc31739a19207aceca1da03cb668300e13a9f9af1e7d0d07e1d3173a2", "PNP.DirectWire.ComputedWireProfileCost.quotient_minimum": "200e81442a22988a98144c8f2f7cc4e6c97e031e7bd5967807ba9d7d6198ee65", "PNP.DirectWire.FreshNandCost.erased_constant": "c6a041cb0387b83ff67dfae4a5341fdf2a429defe1ec273c1b3e66d9c0452fb5", "PNP.DirectWire.FreshNandCost.erased_count_lower_bound": "acc7567090cd30e6f6c7e4eaf70c2dee8850238f39be11aa599f9d85ca79d076", "PNP.DirectWire.FreshNandCost.extend_gateCount": "7ba17ec951c7ac5ca2acace870cf5096cb00e45c2a05d674e3441f57eb986719", "PNP.DirectWire.FreshNandCost.extended_equivalent": "ed3cdf90bdfddc252781d110c336a93bd3740ae147d8b49168615544ca9c4bae", "PNP.DirectWire.FreshNandCost.extended_fresh": "a437a65c0fd94dd753eadb24ccddec958a40cc5314cb69eef5a78cac086728cc", "PNP.DirectWire.FreshNandCost.extended_old": "6564d883d285624b6a7ad574e689bffa1b2586b2a3ce547edfa3eba0781e7f0b", "PNP.DirectWire.FreshNandCost.freshCandidate_semantics": "2d4b2ce857b4598392b4f89e572d6f8db577cd84bdb15b58969eade200f8a017", "PNP.DirectWire.FreshNandCost.freshConditions": "b4a431b08524929fda03b7cd1c742e55fb012d34c21031ce1abc62260ca35ef2", "PNP.DirectWire.FreshNandCost.freshGate_injective": "3885732d9169cebcf904a42e0358653fc2d32963d06d5d08617bd2bd173896d8", "PNP.DirectWire.FreshNandCost.freshGate_selected": "5422faadf8e9bfe8c9df7ebbb6216422241bb6682c374f3597d58c6126975811", "PNP.DirectWire.FreshNandCost.freshGate_source": "8f0b27868cf4811abeab31661aa5b279bb58431f76eec65b9bafceee80157a38", "PNP.DirectWire.FreshNandCost.freshGate_value": "825e1cd37fb0d50c3ae1e87f1037a546b0654085453b0669498b3a75ca64885b", "PNP.DirectWire.FreshNandCost.freshValue_joinInput": "77177bc59f0356e9d54bad1ae1891e4a6e469875be37ceb0a34fb60f812e5680", "PNP.DirectWire.FreshNandCost.freshValue_restricted": "95f5b81b6c8c3dbe8f70efb50f541172f5a0da6304bcdd24a8906d03f48e3c15", "PNP.DirectWire.FreshNandCost.gateCount_lower_bound": "f1ad49c531301e6a13cc796e8a481add4e7eec14de36c9d4cc048a621267245b", "PNP.DirectWire.FreshNandCost.inputNands_eval": "d26026dd26393870d4c796678a56872ca4b0b219d0010fe7548e317ad0a839c3", "PNP.DirectWire.FreshNandCost.oldCandidate_semantics": "2f3d44870d6c08335a5c9d775684c40561a1248d36f2d8656fffaa3dd63c686e", "PNP.DirectWire.FreshNandCost.padInputs_semantics": "1e461912370c3f90ab89397e2b88b66344cf540042a5e182311781a8af65d961", "PNP.DirectWire.FreshNandCost.profile_field": "ee6d3fd3233ad2bb36a097a9945e25b5c7dffd8bfc286d594b17b304be05d22e", "PNP.DirectWire.FreshNandCost.profile_fullMinimum": "cf93680e838511c7c078fbcaed9b6aeb53867039ab3acf5cda82b0a842f7a60b", "PNP.DirectWire.FreshNandCost.profile_fullSlack": "2f64766bc1ccd6954c573e65f1fa1b28e29668f20c5cbd22a3d09c91c714557b", "PNP.DirectWire.FreshNandCost.profile_gateCount": "d5f17e98292da1c70e7ddfa2b578981790f1f7072475fbfd59e5bc386e5e3b5b", "PNP.DirectWire.FreshNandCost.profile_materializer_charge_lower_bound": "bb29f4c44b6ce0ec8e53aa1e460788124c7f593bdbdca8a3c4f658430f6c5488", "PNP.DirectWire.FreshNandCost.profile_output": "36c60f9c2f31a5e5375fd200422b46f3c061362bcc257066fba059eac4d1cd9f", "PNP.DirectWire.FreshNandCost.profile_projectionDefect": "847b187796ec9c30984ff6782e76539de6f0319fda9b41c8fd9261fa82c6e8ef", "PNP.DirectWire.FreshNandCost.profile_quotientMinimum": "0c1f3918b7d381d81cc731ea46df8613b55f41dc240348d08d08babb3789881a", "PNP.DirectWire.FreshNandCost.referenceMinimum_extend": "b78d74a197672a827d9aa75ba4849a03d75446ca4dec8d2b636180521019062a", "PNP.DirectWire.FreshNandCost.referenceMinimum_padInputs": "9170275bafb42cbf8fa6cf58d5af8281dfb8dff62abe7f0eb4c1542083759b7b", "PNP.DirectWire.FreshNandCost.restricted_oldInput": "6780d73f9bef82748611d3da261775a79b2fa52da0c2dc0a6d60fa5032d3662b", "PNP.DirectWire.SemanticGateRetraction.gateCount_eq_sub": "d27131884b06c36cc340d8a11790af2452b24403b4d022561459ffd7d0565ff0", "PNP.DirectWire.SemanticGateRetraction.gateCount_partition": "f450b43aa37fdd27917199c8cefdd3b199d05771d054d0b243a51061788f923b", "PNP.DirectWire.SemanticGateRetraction.kept_gate_value": "4db4c08736e999203d9bf231ba6c14687f0ac66872c9e604e16d1c295105feb8", "PNP.DirectWire.SemanticGateRetraction.reboundSource_value": "105fbd89ff70d73deabe3a55a25c4aef5637aced180bd1621882f33f9dcbfe86", "PNP.DirectWire.SemanticGateRetraction.semantics": "ac67118b00ec5fd47e5c8227fc79e48ec31e4e986eb50156a580101e39d7ae18", "PNP.DirectWire.WireProfileAmbient.available_iff_exists": "d7929c5ff6dceb114bbfe3bbdc5f999266bd6853b33b6e94d85f682a25d31956", "PNP.DirectWire.WireProfileAmbient.available_pad": "58c4f4bdde950973886711ec919effbb063002d9d6222f7e1bfb20aceb9edbfc", "PNP.DirectWire.WireProfileAmbient.available_pad_iff": "a3408729098856e173a1671061cb59eb83e1830e6ed827161d51e70e80fc81c7", "PNP.DirectWire.WireProfileAmbient.available_reword": "563a3a7d05874992b7a41cbd28944917374ae7839971bb407d6ca705779c73c4", "PNP.DirectWire.WireProfileAmbient.eval_paddedSource": "44f649f15ec7a89400d24a6aeed4a7bc90808823a335fc18e8486e2b0d08d3b4", "PNP.DirectWire.WireProfileAmbient.eval_retractSource": "958eded91369714457e24411bc582cb52985fa788254b86e5a42b8f6d153e02b", "PNP.DirectWire.WireProfileAmbient.model_observe_coherent": "e883989b1a9ca0205c799b45d8e3f2e9b0d0d2a6ecb15a10800f03aab54fab6d", "PNP.DirectWire.WireProfileAmbient.pad_fieldValue": "b352f9b13086e15bed18b4f3ec9104e6464263f6ddb96b4d07ec7f556aebdbd9", "PNP.DirectWire.WireProfileAmbient.pad_gateCount": "619b844fbb3db3b8537685ffb48aae8db008be9c7935de3609135f83b08bb5be", "PNP.DirectWire.WireProfileAvailability.available_of_source": "0156c31ae5c2b88e8c4c8995d72ca868aaf49a331cf275b3ac29c6c0c9994567", "PNP.DirectWire.WireProfileAvailability.bind_fieldValue": "fc1d8de8f433323969a63570fabaddad9f6a07e8f3c38ef5c6be32e11c0764ba", "PNP.DirectWire.WireProfileAvailability.bind_full": "6222d9745db83ae95ce24b279cd9c75d0e4334e761e7c26b56ebcef736dd94c0", "PNP.DirectWire.WireProfileAvailability.bind_gateCount": "adeca6dea6897cc8c24815ce7b0a6c2f5d49253f2ecfb523782225a21f033db1", "PNP.DirectWire.WireProfileAvailability.bind_implementation": "5aec5074d1ae9811ef406ebfe65b5a16892a5e737b9eae31117fc02e7a171f25", "PNP.DirectWire.WireProfileAvailability.bind_quotient": "d9ecb9e8cd6967f4fcdd709207dff17cb28e7a855fe1498a82b50cab110066bd", "PNP.DirectWire.WireProfileAvailability.current_available": "d17af8c16c7f6acc4f185c06197389a9a215166db468fc8e092a360ffe53aebb", "PNP.DirectWire.WireProfileAvailability.findSource_congr": "3ad9d76c26034ee6b7416ec578b7d45afb327ce51f309259489b0a7d049ed1a8", "PNP.DirectWire.WireProfileAvailability.findSource_sound": "8ef5fa5509b46d2b451056e9e5e23f2cfcd11443525951036590bd42fa3007cf", "PNP.DirectWire.WireProfileAvailability.full_match_iff": "2e2ed497ad51ae1af9bf68269e7e5d82ce263e2b9458d7fe88ff162f04e48e98", "PNP.DirectWire.WireProfileAvailability.full_minimum": "d894275b1596e32a841b9edca7a8366d66398516aebf4fa80fa2ff386139c2ee", "PNP.DirectWire.WireProfileAvailability.quotient_match_iff": "ff9e227eb1f99143430fd9829e206ba69202827ea06c08d9a88580def849acf4", "PNP.DirectWire.WireProfileAvailability.quotient_minimum": "2e659a60e2ebf934d5384f8a3ad9ef26c350f92840ee3d8bcb1f67d9578af987", "PNP.DirectWire.WireProfileAvailability.sourceMatches_congr": "407014c882536a90f49d4c5db0b639e9ec7f974bc02229590f3ce54d2aabd351", "PNP.DirectWire.WireProfileAvailability.sourceMatches_iff": "03c35ad97050635551a840a885ac918212a922973ce35989b79c95f8e86bb1ca", "PNP.DirectWire.WireProfileAvailability.system_congr": "d13fbc9331e548e2a1bda401ebd6984de3b395f3a20765457de589213ffdfd2c", "PNP.DirectWire.WireProfileAvailability.system_fullEquivalent": "c16848517baf9ededf5937d54cbbcf052de7ac48452a6b4e4c44bb35b0937132", "PNP.DirectWire.WireProfileFieldClosed.ambient_fieldValue": "10b95b00b6ab4c76b23c8f165b8891130dfb7f4ed2613e9d0bb282f5f61f8c80", "PNP.DirectWire.WireProfileFieldClosed.available": "c57a279b278e284dc9a085e7f8ba378dfb8e625812e0c2c8e326f4c84448dfab", "PNP.DirectWire.WireProfileFieldClosed.boundary_isInput": "e5d7b3065a5612cf1f2ad4130f23cdc2d65ca2262dd4cf3e0bf2c8b1acc7fb84", "PNP.DirectWire.WireProfileFieldClosed.gate_value": "45bf7c61525b1b7f5a5c8ce2fffbdfc6e97aec8dacfbf019c962a2a80052e8e9", "PNP.DirectWire.WireProfileFieldClosed.source_selected": "fa08a70951298605688abe6dcf162fb1c87e75586092326d5597acc82a922c99", "PNP.DirectWire.extractTerminalSupport_gate_evaluation": "67afb92512e21b56382fc07e40361c3343368d68cff986f44d108aa370cb416c", "PNP.DirectWire.extractTerminalSupport_gate_induced": "e7585986519237a1ab0fa177facb398a2492d97957998f328089123c6da72e5a", "PNP.DirectWire.terminalPhysicalComplementRecords_gateCount_partition": "a07ed66527b70b6c939c62e98dbc4779df2062a11b006d376f354ae5ed60257a", "PNP.DirectWire.terminalPhysicalComplementRecords_selected": "a70e440b1ba6a74878e4d7de1ca00b2b3fedcf55c49853f1b9586bf01dfc84b2" }, "theoremAxioms": { "PNP.DirectWire.ComputedWireProfileCost.full_minimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.ComputedWireProfileCost.minimum_gap": [ "Quot.sound", "propext" ], "PNP.DirectWire.ComputedWireProfileCost.quotient_minimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.erased_constant": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.erased_count_lower_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.extend_gateCount": [], "PNP.DirectWire.FreshNandCost.extended_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.extended_fresh": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.extended_old": [], "PNP.DirectWire.FreshNandCost.freshCandidate_semantics": [], "PNP.DirectWire.FreshNandCost.freshConditions": [], "PNP.DirectWire.FreshNandCost.freshGate_injective": [], "PNP.DirectWire.FreshNandCost.freshGate_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.freshGate_source": [], "PNP.DirectWire.FreshNandCost.freshGate_value": [], "PNP.DirectWire.FreshNandCost.freshValue_joinInput": [], "PNP.DirectWire.FreshNandCost.freshValue_restricted": [], "PNP.DirectWire.FreshNandCost.gateCount_lower_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.inputNands_eval": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.oldCandidate_semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.padInputs_semantics": [], "PNP.DirectWire.FreshNandCost.profile_field": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.profile_fullMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.profile_fullSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.profile_gateCount": [], "PNP.DirectWire.FreshNandCost.profile_materializer_charge_lower_bound": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.profile_output": [], "PNP.DirectWire.FreshNandCost.profile_projectionDefect": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.profile_quotientMinimum": [ "Quot.sound" ], "PNP.DirectWire.FreshNandCost.referenceMinimum_extend": [ "Quot.sound", "propext" ], "PNP.DirectWire.FreshNandCost.referenceMinimum_padInputs": [ "Quot.sound" ], "PNP.DirectWire.FreshNandCost.restricted_oldInput": [], "PNP.DirectWire.SemanticGateRetraction.gateCount_eq_sub": [ "Quot.sound", "propext" ], "PNP.DirectWire.SemanticGateRetraction.gateCount_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.SemanticGateRetraction.kept_gate_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.SemanticGateRetraction.reboundSource_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.SemanticGateRetraction.semantics": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAmbient.available_iff_exists": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAmbient.available_pad": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAmbient.available_pad_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAmbient.available_reword": [], "PNP.DirectWire.WireProfileAmbient.eval_paddedSource": [], "PNP.DirectWire.WireProfileAmbient.eval_retractSource": [ "propext" ], "PNP.DirectWire.WireProfileAmbient.model_observe_coherent": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAmbient.pad_fieldValue": [], "PNP.DirectWire.WireProfileAmbient.pad_gateCount": [], "PNP.DirectWire.WireProfileAvailability.available_of_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.bind_fieldValue": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.bind_full": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.bind_gateCount": [], "PNP.DirectWire.WireProfileAvailability.bind_implementation": [], "PNP.DirectWire.WireProfileAvailability.bind_quotient": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.current_available": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.findSource_congr": [ "Quot.sound" ], "PNP.DirectWire.WireProfileAvailability.findSource_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.full_match_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.full_minimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.quotient_match_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.quotient_minimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileAvailability.sourceMatches_congr": [ "Quot.sound" ], "PNP.DirectWire.WireProfileAvailability.sourceMatches_iff": [ "Quot.sound" ], "PNP.DirectWire.WireProfileAvailability.system_congr": [ "Quot.sound" ], "PNP.DirectWire.WireProfileAvailability.system_fullEquivalent": [ "Quot.sound" ], "PNP.DirectWire.WireProfileFieldClosed.ambient_fieldValue": [], "PNP.DirectWire.WireProfileFieldClosed.available": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileFieldClosed.boundary_isInput": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileFieldClosed.gate_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.WireProfileFieldClosed.source_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.extractTerminalSupport_gate_evaluation": [ "Quot.sound", "propext" ], "PNP.DirectWire.extractTerminalSupport_gate_induced": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalPhysicalComplementRecords_gateCount_partition": [ "Quot.sound", "propext" ], "PNP.DirectWire.terminalPhysicalComplementRecords_selected": [ "Quot.sound", "propext" ] } }, { "number": 277, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-277", "id": "computed-closed-support-profile-squares", "title": "Computed closed-support observations and profile-compatible squares", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanClosedSupportProfileFormalized": true, "leanClosedSupportProfileAxiomAuditPassed": true, "leanClosedSupportProfileAuditedDeclarationCount": 24, "leanClosedSupportProfileRetainedSourceTheorem": "PNP.DirectWire.ClosedSupportObservation.available_iff_retained_source", "leanClosedSupportProfileComputedTableTheorem": "PNP.DirectWire.ClosedSupportObservation.available_eq_tableAvailable", "leanClosedSupportProfileSeedUnionTheorem": "PNP.DirectWire.ClosedSupportUnion.available_append", "leanClosedSupportProfileFiniteFamilyTheorem": "PNP.DirectWire.ClosedSupportUnion.available_flatten", "leanClosedSupportProfileRequestedFieldsTheorem": "PNP.DirectWire.ClosedSupportProfile.projected_fieldValue", "leanClosedSupportProfileActualCornerTheorem": "PNP.DirectWire.ClosedSupportSquare.corner_fieldValue", "leanClosedSupportProfileCornerAgreementTheorem": "PNP.DirectWire.ClosedSupportSquare.corners_fieldValue_equal", "leanClosedSupportProfileArbitraryFiniteDimensionsCovered": true, "leanClosedSupportProfileComputedSupportAndMatchingTable": true, "leanClosedSupportProfileUniformFieldValuesAtActualCornersProved": true, "leanClosedSupportProfileCallerSuppliedClosureOrCorrectnessRequired": false, "leanClosedSupportProfileOrdinaryOutputEquivalenceProved": false, "leanClosedSupportProfileCompleteManuscriptProjectionSquareProved": false, "leanClosedSupportProfileProperPositiveSupportProved": false, "leanClosedSupportProfileDuplicateIsNormalizedTerminalCounterexample": false, "leanClosedSupportProfileCompletePackageEOrGlobalRoutesProved": false, "leanClosedSupportProfileUnconditionalSaturatePositiveProved": false, "leanClosedSupportProfileUnconditionalBCELReadyProved": false, "leanClosedSupportProfileUnconditionalZeroSlackProved": false, "leanClosedSupportProfileExactPolynomialPCCMinProved": false, "leanClosedSupportProfilePolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanClosedSupportProfileSourceMatchingAndInfluenceAreExhaustive": true, "leanClosedSupportProfileRuntimeExecutionIsProofAuthority": false, "leanClosedSupportProfileScope": "arbitrary-finite-computed-closed-support-observations-source-alternatives-union-and-profile-seeded-actual-square-corner-compatibility-no-ordinary-output-proper-positive-full-profile-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.ClosedSupportObservation.available_eq_tableAvailable": "36284860f3182440dcc3da9997bd6ed38ead391b387a68fadc80ed25afac84d0", "PNP.DirectWire.ClosedSupportObservation.available_iff_retained_source": "fb3cb40786c80fcf013c7f3b416afde3aa2387726e22d9e9493e31e029509a9e", "PNP.DirectWire.ClosedSupportObservation.available_of_retained_source": "f313f1f1d7ee09299706e95e0f60c23bbb7ef276e2eb5258128d2ed374e08d66", "PNP.DirectWire.ClosedSupportObservation.boundary_isInput": "e5d2bdf2e64b60135b2d4e6252234b5243512f5cd8e53856081b30ee9569e790", "PNP.DirectWire.ClosedSupportObservation.gate_value": "950413f4c8ad24ce9d900ad8e199be263bc32bc12bf90cbdd9d59baa82503ad0", "PNP.DirectWire.ClosedSupportObservation.lift_retained_source": "c4e8768c53b537b640523e5c1d0611fb537c87246605a8c092c02e964abe9f4b", "PNP.DirectWire.ClosedSupportObservation.mem_matchingSources": "2b64c44c843b773cc956648fcd42c136cf5ee3bf16145ca09ca5d996fbbdba15", "PNP.DirectWire.ClosedSupportObservation.retract_support_source": "13d83a42f5ffa140fff436423e6c8f6970d29f3edfb0a19934e6817f96475210", "PNP.DirectWire.ClosedSupportObservation.tableAvailable_iff": "70a629b8bf4422a67cc1d98a7439d27894a786f3aa7d27f6f5c12d7de06a3e1f", "PNP.DirectWire.ClosedSupportProfile.profile_available": "0c747b559a85a56a1bec444232dce9fa606376204c01ea1e7fc95942017c6ce2", "PNP.DirectWire.ClosedSupportProfile.projected_available": "9c9c8563bcb49b2ec9d6b9ab3adeacd1c7cd478a192a667b65f33ed5ee74cfb9", "PNP.DirectWire.ClosedSupportProfile.projected_fieldValue": "d4667a897c89db1f6be34087132d22ee064e589dddfce16ee9c2e3a9958051d6", "PNP.DirectWire.ClosedSupportProfile.projected_tableAvailable": "86a59577ff0afb9bd2fa697503a95050a44b2b898886d539749522c129c92e89", "PNP.DirectWire.ClosedSupportSquare.corner_available": "be838c5b6f99217989f84aa11a754ed1d1525ee873c4849d805bf4859f886d8e", "PNP.DirectWire.ClosedSupportSquare.corner_fieldValue": "4f09121aaf481d01c80e32facf4824f2b9da76e056e472f264157ecd313934a0", "PNP.DirectWire.ClosedSupportSquare.corner_profileMember": "ef29c2d6dbf0afbd1fcb21f82f2fa23afd42478e9240a817813932c0aaf1cad4", "PNP.DirectWire.ClosedSupportSquare.corners_fieldValue_equal": "c4b49f95b5d857ed5a1b166c77ce9b7cb072cfaab7ce97b0651f002ec90855b8", "PNP.DirectWire.ClosedSupportUnion.available_append": "cf59906f789c5a7c18e811d8dd05fd878ea337c3f934b17f4237df8ee8063488", "PNP.DirectWire.ClosedSupportUnion.available_flatten": "826ace2bec3532d1c43ed0f33596c8c873a0c7b86c93607936066eb2ba39a15b", "PNP.DirectWire.ClosedSupportUnion.available_mono": "43c2830b54c41efa14a24e72c51d53c9d3e0683c48aa8b16e7daba77164fdba7", "PNP.DirectWire.ClosedSupportUnion.mem_records_append": "85c496b68303cc018de0098c6cf542f56d757ad95079bc9730e33f06853cb5bc", "PNP.DirectWire.ClosedSupportUnion.records_mono": "365f866fe74f2f178e8beadce47d4efbdd5d34d4f1207118081c8a47ddcc1b58", "PNP.DirectWire.ClosedSupportUnion.retained_append": "88acde589597fc8632407c9035e7d569998125775d3e4860e9bff33687720c18", "PNP.DirectWire.ClosedSupportUnion.tableAvailable_append": "d97244bbc85ab3df8ac32c368da9c1fc1eb61d943845c974a74a02ed320f96ef" }, "theoremAxioms": { "PNP.DirectWire.ClosedSupportObservation.available_eq_tableAvailable": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.available_iff_retained_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.available_of_retained_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.boundary_isInput": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.gate_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.lift_retained_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.mem_matchingSources": [ "propext" ], "PNP.DirectWire.ClosedSupportObservation.retract_support_source": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportObservation.tableAvailable_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportProfile.profile_available": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportProfile.projected_available": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportProfile.projected_fieldValue": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportProfile.projected_tableAvailable": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportSquare.corner_available": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportSquare.corner_fieldValue": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportSquare.corner_profileMember": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportSquare.corners_fieldValue_equal": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.available_append": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.available_flatten": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.available_mono": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.mem_records_append": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.records_mono": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.retained_append": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportUnion.tableAvailable_append": [ "Quot.sound", "propext" ] } }, { "number": 278, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-19-278", "id": "computed-closed-support-full-profile-gain", "title": "Computed closed-support full-profile physical gain", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanClosedSupportFullGainFormalized": true, "leanClosedSupportFullGainAxiomAuditPassed": true, "leanClosedSupportFullGainAuditedDeclarationCount": 27, "leanClosedSupportFullGainPrimaryInputSpecializationTheorem": "PNP.DirectWire.ClosedSupportFullGain.prefixSource_value", "leanClosedSupportFullGainRetainedFieldTheorem": "PNP.DirectWire.ClosedSupportFullGain.prefixField_value", "leanClosedSupportFullGainWholeCarrierTheorem": "PNP.DirectWire.ClosedSupportFullGain.result_fullEquivalent", "leanClosedSupportFullGainExactGateBalanceTheorem": "PNP.DirectWire.ClosedSupportFullGain.result_exact_accounting", "leanClosedSupportFullGainWholeFullSlackBalanceTheorem": "PNP.DirectWire.ClosedSupportFullGain.result_fullSlack_balance", "leanClosedSupportFullGainLocalSlackBoundTheorem": "PNP.DirectWire.ClosedSupportFullGain.localFullSlack_le_global", "leanClosedSupportFullGainCheckedRouteTheorem": "PNP.DirectWire.ClosedSupportFullGain.improvement?_sound", "leanClosedSupportFullGainStrictGainTheorem": "PNP.DirectWire.ClosedSupportFullGain.improvement?_strictGain", "leanClosedSupportFullGainArbitraryFiniteDimensionsCovered": true, "leanClosedSupportFullGainComputedClosedSupportAndFullMinimum": true, "leanClosedSupportFullGainComplementAndReconnectionDerived": true, "leanClosedSupportFullGainUniformOutputsAndComputationalFieldsPreserved": true, "leanClosedSupportFullGainCallerSuppliedObserverReplacementOrCorrectnessRequired": false, "leanClosedSupportFullGainLocalFullSlackExactlyRetiredFromWhole": true, "leanClosedSupportFullGainProperPositiveSupportDiscoveryProved": false, "leanClosedSupportFullGainWholeSpanIsProperLocalVerifyDW": false, "leanClosedSupportFullGainCompleteManuscriptProfileGrammarProved": false, "leanClosedSupportFullGainGlobalRouteCoverageProved": false, "leanClosedSupportFullGainUnconditionalSaturatePositiveProved": false, "leanClosedSupportFullGainUnconditionalBCELReadyProved": false, "leanClosedSupportFullGainUnconditionalZeroSlackProved": false, "leanClosedSupportFullGainExactPolynomialPCCMinProved": false, "leanClosedSupportFullGainPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanClosedSupportFullGainReferenceMinimumMatchingAndInfluenceAreExhaustive": true, "leanClosedSupportFullGainRuntimeExecutionIsProofAuthority": false, "leanClosedSupportFullGainScope": "arbitrary-finite-computed-closed-support-full-minimum-derived-physical-complement-uniform-whole-output-and-computational-field-equivalence-exact-gate-and-full-slack-balance-checked-strict-descent-no-proper-positive-discovery-complete-profile-global-route-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.ClosedSupportFullGain.ambient_output": "ee568f70b67653b08b7e6a446f41c4a7afc669fb8d9f64079e17d002ab07f1b9", "PNP.DirectWire.ClosedSupportFullGain.boundarySource_value": "af26c3fb2de1f7a161d1070d037d3695e8f6e159af40f5c1345ee2060b3c95d9", "PNP.DirectWire.ClosedSupportFullGain.complement_gate_value": "99ad4452989a8e4bbcb7d257dda6e12acd5b6578148579454b6538e78d1b7383", "PNP.DirectWire.ClosedSupportFullGain.fieldSource_value": "508f7a818cf914e93b5103db786c749b9e130d90a4e10f6e4b2e860b18fac54c", "PNP.DirectWire.ClosedSupportFullGain.improvement?_none_iff": "5f98a2587f19fc9154dc010f322dd6880f46e2a09f4f9e33d87f7bf9e0f9d267", "PNP.DirectWire.ClosedSupportFullGain.improvement?_sound": "045804cce1560f746fb655689b7401cae42ba6ffad0359460eba57d6a7daeb6d", "PNP.DirectWire.ClosedSupportFullGain.improvement?_strictGain": "26465ff5e8043e1b8348f741c564d7884bf5ea445c2e4f536dafbad61c241a5a", "PNP.DirectWire.ClosedSupportFullGain.inputBinding_eval": "100a65ba4f3e2e05637bf7d309187d39d9053ba58768734bcd9c490ab7bac731", "PNP.DirectWire.ClosedSupportFullGain.interface_index_exists": "1130fec13c73b0fbc27ee4fb97afebe8c6c3f876372d9a1b4d1714d92c42e249", "PNP.DirectWire.ClosedSupportFullGain.interface_index_sound": "832e7b0043849d0b3081e92856e5e41b05b769c241f1f95764e87d88d007d6ae", "PNP.DirectWire.ClosedSupportFullGain.localFullSlack_le_global": "77dbb9280db83b5315c6d398f73631b6dacdc79ce42d857d6ef8dc9b111be4a2", "PNP.DirectWire.ClosedSupportFullGain.offered_available": "99765be4b85467b2acf1b8fedd80f3a32872e920ba434c1b53e90c0bfac064f8", "PNP.DirectWire.ClosedSupportFullGain.offered_gateCount": "7b9303daa49c71db11745cbd8ff49e35e4d2de20de1468f7d6255f3800cb0d51", "PNP.DirectWire.ClosedSupportFullGain.offered_gateCount_le": "4dfcc8b90d10ac3201fd9a039a2032b72a88f870d1077bae8527744d782da679", "PNP.DirectWire.ClosedSupportFullGain.outputSource_value": "77978caf94fad2d86adb034eeb4127ab697a626979820544a37dba23e6cf48ca", "PNP.DirectWire.ClosedSupportFullGain.prefixField_value": "1d426e2e2a43cf3f41d9512c0d60fc8e9a51fe0a70aeffa41460422b34815752", "PNP.DirectWire.ClosedSupportFullGain.prefixOutput_value": "66253f4a759423d4beda0ea2524e815ebf052e75ea63565f528e6be1a22c2749", "PNP.DirectWire.ClosedSupportFullGain.prefixSource_value": "ab53152242651971b218aafc87ad3538303263b7d4071f89765480452874632e", "PNP.DirectWire.ClosedSupportFullGain.restrict_extendZero": "a5894a9fea644ddaf89e902ee96209795e92b627ca1b49834b9e1241d37a6076", "PNP.DirectWire.ClosedSupportFullGain.result_exact_accounting": "45f5d0e572e15769050735209c56e9826a8d0bbbb79dfeeab872478bb8e5f6b0", "PNP.DirectWire.ClosedSupportFullGain.result_fullEquivalent": "c4ce482c3195b7eaf840eb6f6e02ed14fa79e93f15aa0e2774fb8354f53ef095", "PNP.DirectWire.ClosedSupportFullGain.result_fullMinimum": "6cf8caaca12504a4ab9a09ba24a02e445a996626500f2fab69034ff6b2f0a93d", "PNP.DirectWire.ClosedSupportFullGain.result_fullSlack_balance": "8cb443818ba57aec70181da2ebe015424f9426e5f6e719db8310006b50bb2d2d", "PNP.DirectWire.ClosedSupportFullGain.result_gain_balance": "35e9be6bf27970a14e331de0c92c3e90a515d0ad55fbc156442cec161630d939", "PNP.DirectWire.ClosedSupportFullGain.result_output": "c670cc9864366a7e5fde03c6f61c76ffd01923ca4e3e9efad64bbd4c1f1621cb", "PNP.DirectWire.ClosedSupportFullGain.result_strict_iff": "8fb91b09da8cba2f59fe0dd0bf5aabba01532f870f028ce872dff432683f0f7c", "PNP.DirectWire.ClosedSupportFullGain.retained_source_value": "b4eb6842f1eddc3c45a6f04d54cee302893708e9d293279d745e7f367abc2c84" }, "theoremAxioms": { "PNP.DirectWire.ClosedSupportFullGain.ambient_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.boundarySource_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.complement_gate_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.fieldSource_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.improvement?_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.improvement?_sound": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.improvement?_strictGain": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.inputBinding_eval": [ "propext" ], "PNP.DirectWire.ClosedSupportFullGain.interface_index_exists": [ "propext" ], "PNP.DirectWire.ClosedSupportFullGain.interface_index_sound": [ "propext" ], "PNP.DirectWire.ClosedSupportFullGain.localFullSlack_le_global": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.offered_available": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.offered_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.offered_gateCount_le": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.outputSource_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.prefixField_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.prefixOutput_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.prefixSource_value": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.restrict_extendZero": [ "Quot.sound" ], "PNP.DirectWire.ClosedSupportFullGain.result_exact_accounting": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.result_fullEquivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.result_fullMinimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.result_fullSlack_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.result_gain_balance": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.result_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.result_strict_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedSupportFullGain.retained_source_value": [ "Quot.sound", "propext" ] } }, { "number": 279, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-279", "id": "computed-whole-support-minimum-bridge", "title": "Computed whole-support minimum bridge", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanClosedWholeMinimumFormalized": true, "leanClosedWholeMinimumAxiomAuditPassed": true, "leanClosedWholeMinimumAuditedDeclarationCount": 22, "leanClosedWholeMinimumDerivedWholeSeedTheorem": "PNP.DirectWire.ClosedWholeMinimum.support_gateCount", "leanClosedWholeMinimumExactOrdinaryInterfaceTheorem": "PNP.DirectWire.ClosedWholeMinimum.interface_iff_output", "leanClosedWholeMinimumComputedFieldAvailabilityTheorem": "PNP.DirectWire.ClosedWholeMinimum.available_all", "leanClosedWholeMinimumSizePreservingComparisonTheorem": "PNP.DirectWire.ClosedWholeMinimum.forward_gateCount", "leanClosedWholeMinimumExactMinimumTheorem": "PNP.DirectWire.ClosedWholeMinimum.full_minimum", "leanClosedWholeMinimumAttainedMinimumTheorem": "PNP.DirectWire.ClosedWholeMinimum.result_optimal", "leanClosedWholeMinimumExactFullSlackTheorem": "PNP.DirectWire.ClosedWholeMinimum.fullSlack_eq", "leanClosedWholeMinimumPostReferenceSlackTheorem": "PNP.DirectWire.ClosedWholeMinimum.result_zero_fullSlack", "leanClosedWholeMinimumCheckedNoImprovementTheorem": "PNP.DirectWire.ClosedWholeMinimum.improvement_none_iff", "leanClosedWholeMinimumArbitraryFiniteDimensionsCovered": true, "leanClosedWholeMinimumSeedInterfaceAndObserverDerived": true, "leanClosedWholeMinimumIndependentFullReferenceMinimaEqual": true, "leanClosedWholeMinimumComputedResultAttainsFullReferenceMinimum": true, "leanClosedWholeMinimumCallerSuppliedEqualityMinimumOrCorrectnessRequired": false, "leanClosedWholeMinimumWholeSpanIsProperLocalVerifyDW": false, "leanClosedWholeMinimumProperPositiveSupportDiscoveryProved": false, "leanClosedWholeMinimumCompleteManuscriptProfileGrammarProved": false, "leanClosedWholeMinimumGlobalRouteCoverageProved": false, "leanClosedWholeMinimumUnconditionalSaturatePositiveProved": false, "leanClosedWholeMinimumUnconditionalBCELReadyProved": false, "leanClosedWholeMinimumUnconditionalZeroSlackProved": false, "leanClosedWholeMinimumExactPolynomialPCCMinProved": false, "leanClosedWholeMinimumPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanClosedWholeMinimumReferenceSearchRemainsExhaustive": true, "leanClosedWholeMinimumRuntimeExecutionIsProofAuthority": false, "leanClosedWholeMinimumScope": "arbitrary-finite-derived-whole-gate-seed-computed-ordinary-interface-full-field-availability-size-preserving-two-way-reference-minimum-equality-attained-whole-full-minimum-no-proper-local-manuscript-zeroslack-global-route-or-polynomial-claim" }, "theoremKernelTypeSha256": { "PNP.DirectWire.ClosedWholeMinimum.ambient_output_absent": "de1f2f9477952316157534c5abccc9eb177defc5ca4c63f3d3813b47b56d6f63", "PNP.DirectWire.ClosedWholeMinimum.available_all": "abda5f4e8f992398218a6715a299cd2040fa7484a95c40e6427e8aaedcf6d4c7", "PNP.DirectWire.ClosedWholeMinimum.forward_available": "d2bc1aa0bc4e5b2485adb2b925a9ea19d3ad2165fcf5cb85f68da57bb8adb7b2", "PNP.DirectWire.ClosedWholeMinimum.forward_equivalent": "1b55ee408cd4b476c52987bc53616ce1a0b26e6e9fa904db928fe37c086fe516", "PNP.DirectWire.ClosedWholeMinimum.forward_gateCount": "0a6b23e44cbdda91623811bde32b30c4afed5f39a27cfd30ae18de3677825803", "PNP.DirectWire.ClosedWholeMinimum.forward_output_none": "717987c2cf6cee2ee80ce3e80336f92d6327a475483976348f1acbc9bd245ae0", "PNP.DirectWire.ClosedWholeMinimum.forward_output_some": "8f107d84399f072c2dea4fc67e348da169a3cb6bb716b8965eba34cdfd6ca22f", "PNP.DirectWire.ClosedWholeMinimum.fullSlack_eq": "b87bc9c3743641fe8d6481244fb1fcfe4a3bd090a75fd1563505eb98c2ace03d", "PNP.DirectWire.ClosedWholeMinimum.full_minimum": "1130eabcdce4e914eb1b975ba1a71cbc5aaba01c275c589522d419190f180577", "PNP.DirectWire.ClosedWholeMinimum.gate_selected": "4941ffa61289594b072955d12bdf1d4b745dc4044652d9802b32f811b45321ce", "PNP.DirectWire.ClosedWholeMinimum.global_minimum_le": "620f470f41a44eed9fcc3b80b1d0ed4bff3eb078430433dbc5f1b30c1aa0051f", "PNP.DirectWire.ClosedWholeMinimum.improvement_none_iff": "d31e874330121a7b2919784e382cc5c0956e819d4a9415e68773d2fb2de9695e", "PNP.DirectWire.ClosedWholeMinimum.interface_iff_output": "958fd1e723c83dd5071f3a5dffcffc38bdf66fab22357ad6da44d0b249d64179", "PNP.DirectWire.ClosedWholeMinimum.outputIndex_exists": "bc950d30ff11863f52698c243a1668d7b015a945377de5571996238d2671533c", "PNP.DirectWire.ClosedWholeMinimum.outputIndex_none_not_interface": "d6e35fa2b4b3d2dfd9a1de80fb8f2d4b2bd6166f7edd192867f7d89920b979f6", "PNP.DirectWire.ClosedWholeMinimum.outputIndex_sound": "949c3138997ab5f60be81748a37eb85c64823d87d61c4cf8abe303c8180d49d8", "PNP.DirectWire.ClosedWholeMinimum.result_gateCount": "10ad0ca84393a31831a39e1a0db9c8f0068e672d9d5d8075328d2dbdc9a25014", "PNP.DirectWire.ClosedWholeMinimum.result_optimal": "98b401fb9516b8b8e1a9525bb49d69be4cc0318e11cf9f8a5f1aa7f47e02696b", "PNP.DirectWire.ClosedWholeMinimum.result_zero_fullSlack": "848cab843f093d0b0ecb0c5d8f966843bee0079620bae28bb8dda4d3afd4d6e5", "PNP.DirectWire.ClosedWholeMinimum.source_retained": "00955517186813221b3a6ce2d1dceacfbfd4d6edcaefbe348be0d8c0ebf086d6", "PNP.DirectWire.ClosedWholeMinimum.support_gateCount": "cbdc7da1e90b9748c70d67cd45d0c4e2cd54b7d79b68b9fe0d7379c6b7068d0d", "PNP.DirectWire.ClosedWholeMinimum.support_minimum_le": "200e284d486b2a3494379785431d126117cc77f4956c42ef5d24d9341109c925" }, "theoremAxioms": { "PNP.DirectWire.ClosedWholeMinimum.ambient_output_absent": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.available_all": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.forward_available": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.forward_equivalent": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.forward_gateCount": [], "PNP.DirectWire.ClosedWholeMinimum.forward_output_none": [], "PNP.DirectWire.ClosedWholeMinimum.forward_output_some": [], "PNP.DirectWire.ClosedWholeMinimum.fullSlack_eq": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.full_minimum": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.gate_selected": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.global_minimum_le": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.improvement_none_iff": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.interface_iff_output": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.outputIndex_exists": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.outputIndex_none_not_interface": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.outputIndex_sound": [ "propext" ], "PNP.DirectWire.ClosedWholeMinimum.result_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.result_optimal": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.result_zero_fullSlack": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.source_retained": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.support_gateCount": [ "Quot.sound", "propext" ], "PNP.DirectWire.ClosedWholeMinimum.support_minimum_le": [ "Quot.sound", "propext" ] } }, { "number": 280, "coordinate": "PNP-FORMAL-RECONSTRUCTION-STATUS-2026-09-20-280", "id": "computed-closed-support-nested-positivity", "title": "Computed nested-support cost and positivity transport", "classification": "formalized-foundation-only", "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.", "nonClaim": "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.", "fields": { "leanClosedSupportNestedGainFormalized": true, "leanClosedSupportNestedGainAxiomAuditPassed": true, "leanClosedSupportNestedGainAuditedDeclarationCount": 36, "leanClosedSupportNestedGainPhysicalDifferenceTheorem": "PNP.DirectWire.ClosedSupportNestedGain.support_count_decomposition", "leanClosedSupportNestedGainExactOrdinaryInterfaceTheorem": "PNP.DirectWire.ClosedSupportNestedGain.outputSource_value", "leanClosedSupportNestedGainExactFieldObservationTheorem": "PNP.DirectWire.ClosedSupportNestedGain.extended_available", "leanClosedSupportNestedGainFullMinimumCostBoundTheorem": "PNP.DirectWire.ClosedSupportNestedGain.full_minimum_cost_balance", "leanClosedSupportNestedGainQuotientMinimumCostBoundTheorem": "PNP.DirectWire.ClosedSupportNestedGain.quotient_minimum_cost_balance", "leanClosedSupportNestedGainFullSlackMonotonicityTheorem": "PNP.DirectWire.ClosedSupportNestedGain.full_slack_le", "leanClosedSupportNestedGainQuotientSlackMonotonicityTheorem": "PNP.DirectWire.ClosedSupportNestedGain.quotient_slack_le", "leanClosedSupportNestedGainPhysicalInclusionPositivityTheorem": "PNP.DirectWire.ClosedSupportNestedGain.positive_mono", "leanClosedSupportNestedGainRawSeedInclusionTheorem": "PNP.DirectWire.ClosedSupportNestedGain.included_of_seed_subset", "leanClosedSupportNestedGainRawSeedPositivityTheorem": "PNP.DirectWire.ClosedSupportNestedGain.seed_positive", "leanClosedSupportNestedGainArbitraryFiniteDimensionsCovered": true, "leanClosedSupportNestedGainSupportsDifferenceAndBindingsDerived": true, "leanClosedSupportNestedGainAmbientInputsRetained": true, "leanClosedSupportNestedGainExactFalseAndTrueFieldObservationsPreserved": true, "leanClosedSupportNestedGainFullAndQuotientComparisonsDerived": true, "leanClosedSupportNestedGainCallerSuppliedCostOrFieldEqualityRequired": false, "leanClosedSupportNestedGainInitialRawWitnessPositivityPreservationProved": false, "leanClosedSupportNestedGainProperPositiveSupportDiscoveryProved": false, "leanClosedSupportNestedGainCompleteManuscriptProfileGrammarProved": false, "leanClosedSupportNestedGainGlobalRouteCoverageProved": false, "leanClosedSupportNestedGainUnconditionalSaturatePositiveProved": false, "leanClosedSupportNestedGainUnconditionalBCELReadyProved": false, "leanClosedSupportNestedGainUnconditionalZeroSlackProved": false, "leanClosedSupportNestedGainExactPolynomialPCCMinProved": false, "leanClosedSupportNestedGainPolynomialRuntimeOutputAndCertificateBoundsProved": false, "leanClosedSupportNestedGainReferenceSearchRemainsExhaustive": true, "leanClosedSupportNestedGainRuntimeExecutionIsProofAuthority": false, "leanClosedSupportNestedGainScope": 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