AutoSamplingTheory.SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation

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 cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation :
    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.cycle173_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 173 middle illness-area refiner packet after python3 tools/astis.py blueprint-refresh ASTIS-SALD-001. Classification: rejected-wrapper-churn. The refreshed blueprint still points to the selected-test second-Frechet-derivative operator-norm and Brownian coordinate unit region, but the local Lean state has already discharged the Brownian coordinate unit direction by SALD.gaussianRealStdOrthonormalBasisUnit and the hHessianOpNorm-to-hSecondFDerivOpNorm bridge by SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm. Therefore the exact lower-ready boundary remains hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 under sald.general_moving_target_discrete.em_interpolation_fp. Middle rechecked appendix.tex:984-995, appendix.tex:1026-1072, appendix.tex:1379-1387, main_body.tex:273-305, iteration_complexity.tex:309-321, and the original SALD TeX search excluding sald_version_2.tex for smooth/test/Hessian/bounded regularity terms. These sources provide the frozen EM Brownian interpolation, weak Fokker-Planck Laplacian display, drift/score Lipschitz and integrability assumptions, and a VP score Hessian bound, but they do not provide a selected weak-test global bounded-Hessian field for sourceTest. This packet therefore rejects testRegular -> hHessianOpNorm, testRegular -> hSecondFDerivOpNorm, SourceSelectedWeakTestC2bBoundedHessian, or VP score-Hessian substitutions unless the source correspondence first supplies an independent selected weak-test C2_b/bounded-Hessian field.

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.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
2. SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag
3. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
4. SALD.gaussianRealStdOrthonormalBasisUnit
5. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
6. hHessianOpNorm
7. hSecondFDerivOpNorm
8. sourceTest
9. testRegular
10. SourceSelectedWeakTestC2bBoundedHessian proposed only as source-backed field
11. SelectedWeakTestC2bBoundedHessian projection rejected without source backing
12. iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest
13. appendix.tex:984-995
14. appendix.tex:1026-1072
15. appendix.tex:1379-1387
16. main_body.tex:273-305
17. paper-wide original-source search excluding sald_version_2.tex
18. source-contract-gap
19. 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.

No SLT theorem was consulted or imported. This is a source-contract recovery packet: the configured local SLT clone is absent, and the local/Mathlib work needed after hHessianOpNorm is already compiled. Lower should only attempt a theorem if it consumes a source-backed selected weak-test bounded-Hessian field; otherwise this boundary remains a faithful source-contract gap.

def cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle173_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_middle"
  statement := "Cycle 173 middle illness-area refiner packet after python3 tools/astis.py blueprint-refresh ASTIS-SALD-001. Classification: rejected-wrapper-churn. The refreshed blueprint still points to the selected-test second-Frechet-derivative operator-norm and Brownian coordinate unit region, but the local Lean state has already discharged the Brownian coordinate unit direction by SALD.gaussianRealStdOrthonormalBasisUnit and the hHessianOpNorm-to-hSecondFDerivOpNorm bridge by SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm. Therefore the exact lower-ready boundary remains hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 under sald.general_moving_target_discrete.em_interpolation_fp. Middle rechecked appendix.tex:984-995, appendix.tex:1026-1072, appendix.tex:1379-1387, main_body.tex:273-305, iteration_complexity.tex:309-321, and the original SALD TeX search excluding sald_version_2.tex for smooth/test/Hessian/bounded regularity terms. These sources provide the frozen EM Brownian interpolation, weak Fokker-Planck Laplacian display, drift/score Lipschitz and integrability assumptions, and a VP score Hessian bound, but they do not provide a selected weak-test global bounded-Hessian field for sourceTest. This packet therefore rejects testRegular -> hHessianOpNorm, testRegular -> hSecondFDerivOpNorm, SourceSelectedWeakTestC2bBoundedHessian, or VP score-Hessian substitutions unless the source correspondence first supplies an independent selected weak-test C2_b/bounded-Hessian field."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
    "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag",
    "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
    "SALD.gaussianRealStdOrthonormalBasisUnit",
    "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
    "hHessianOpNorm",
    "hSecondFDerivOpNorm",
    "sourceTest",
    "testRegular",
    "SourceSelectedWeakTestC2bBoundedHessian proposed only as source-backed field",
    "SelectedWeakTestC2bBoundedHessian projection rejected without source backing",
    "iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest",
    "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",
    "source-contract-gap",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No SLT theorem was consulted or imported. This is a source-contract recovery packet: the configured local SLT clone is absent, and the local/Mathlib work needed after hHessianOpNorm is already compiled. Lower should only attempt a theorem if it consumes a source-backed selected weak-test bounded-Hessian field; otherwise this boundary remains a faithful source-contract gap."

/-- Cycle-173 lower_1 proof-scout route for the remaining selected-test
Hessian source contract. -/