AutoSamplingTheory.SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

id : String (explicit)

Stable obligation identifier.

sald.general_moving_target_discrete.cycle172_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_middle

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 172 middle illness-area refiner packet after python3 tools/astis.py blueprint-refresh ASTIS-SALD-001. Classification: rejected-wrapper-churn. The refreshed dynamic leaf still points to the selected-test second-Frechet-derivative operator-norm/Brownian coordinate unit region, and the illness area refines it to the exact source-contract boundary hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 under sald.general_moving_target_discrete.em_interpolation_fp. The Brownian coordinate unit direction and the hHessianOpNorm-to-hSecondFDerivOpNorm bridge are already compiled by SALD.gaussianRealStdOrthonormalBasisUnit and SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm. This packet rejects another testRegular -> hHessianOpNorm, testRegular -> hSecondFDerivOpNorm, or SelectedWeakTestC2bBoundedHessian projection unless the source correspondence first supplies a non-opaque selected weak-test C2_b/bounded-Hessian field. Targeted source recheck of appendix.tex:984-995, appendix.tex:1026-1072, appendix.tex:1379-1387, main_body.tex:273-305, and the original SALD TeX search excluding sald_version_2.tex found EM Brownian/Laplacian usage and drift/score Lipschitz/integrability assumptions, but no selected weak-test global bounded-Hessian field. Therefore the exact remaining dependency is a source-contract gap, not a Mathlib, SLT, or wrapper gap.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
2. SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag
3. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
4. SALD.gaussianRealStdOrthonormalBasisUnit
5. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
6. hHessianOpNorm
7. sourceTest
8. testRegular
9. selected weak-test C2_b/bounded-Hessian source interface
10. SelectedWeakTestC2bBoundedHessian projection rejected without source backing
11. appendix.tex:984-995
12. appendix.tex:1026-1072
13. appendix.tex:1379-1387
14. main_body.tex:273-305
15. paper-wide original-source search excluding sald_version_2.tex
16. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Middle packet for the refreshed illness area. No local SLT file was consulted because the blocker is source-contract recovery: the configured SLT clone is absent and the already compiled local/Mathlib facts cover only the Brownian unit direction and the Hessian-to-iterated-Frechet bridge. Lower should either find a genuine source-backed selected weak-test bounded-Hessian field or keep hHessianOpNorm as the exact source-contract gap.

def cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle172_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_middle"
  statement := "Cycle 172 middle illness-area refiner packet after python3 tools/astis.py blueprint-refresh ASTIS-SALD-001. Classification: rejected-wrapper-churn. The refreshed dynamic leaf still points to the selected-test second-Frechet-derivative operator-norm/Brownian coordinate unit region, and the illness area refines it to the exact source-contract boundary hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 under sald.general_moving_target_discrete.em_interpolation_fp. The Brownian coordinate unit direction and the hHessianOpNorm-to-hSecondFDerivOpNorm bridge are already compiled by SALD.gaussianRealStdOrthonormalBasisUnit and SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm. This packet rejects another testRegular -> hHessianOpNorm, testRegular -> hSecondFDerivOpNorm, or SelectedWeakTestC2bBoundedHessian projection unless the source correspondence first supplies a non-opaque selected weak-test C2_b/bounded-Hessian field. Targeted source recheck of appendix.tex:984-995, appendix.tex:1026-1072, appendix.tex:1379-1387, main_body.tex:273-305, and the original SALD TeX search excluding sald_version_2.tex found EM Brownian/Laplacian usage and drift/score Lipschitz/integrability assumptions, but no selected weak-test global bounded-Hessian field. Therefore the exact remaining dependency is a source-contract gap, not a Mathlib, SLT, or wrapper gap."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
    "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag",
    "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
    "SALD.gaussianRealStdOrthonormalBasisUnit",
    "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
    "hHessianOpNorm",
    "sourceTest",
    "testRegular",
    "selected weak-test C2_b/bounded-Hessian source interface",
    "SelectedWeakTestC2bBoundedHessian projection rejected without source backing",
    "appendix.tex:984-995",
    "appendix.tex:1026-1072",
    "appendix.tex:1379-1387",
    "main_body.tex:273-305",
    "paper-wide original-source search excluding sald_version_2.tex",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle packet for the refreshed illness area. No local SLT file was consulted because the blocker is source-contract recovery: the configured SLT clone is absent and the already compiled local/Mathlib facts cover only the Brownian unit direction and the Hessian-to-iterated-Frechet bridge. Lower should either find a genuine source-backed selected weak-test bounded-Hessian field or keep hHessianOpNorm as the exact source-contract gap."

/-- Cycle-172 proof-DAG pane for the refreshed Hessian source-contract
illness area. -/