AutoSamplingTheory.SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation

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 cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation :
    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.cycle171_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 171 middle illness-area refiner packet. Classification: rejected-wrapper-churn. Exact wrapper churn rejected: do not add an opaque testRegular -> hHessianOpNorm or testRegular -> hSecondFDerivOpNorm theorem for the selected weak test unless testRegular is expanded to a source-backed C2_b/bounded-Hessian field. The live remaining boundary is hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 under sald.general_moving_target_discrete.em_interpolation_fp. The source anchors appendix.tex:984-995 and appendix.tex:1379-1387 justify the Brownian generator/Laplacian weak-test use, while appendix.tex:1026-1072 and main_body.tex:273-305 state Lipschitz and integrability assumptions rather than a global selected-test bounded-Hessian field. Brownian coordinate unit direction is already discharged by SALD.gaussianRealStdOrthonormalBasisUnit, and hHessianOpNorm-to-hSecondFDerivOpNorm is already compiled by SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm.

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.cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormLower2Obligation
2. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
3. SALD.gaussianRealStdOrthonormalBasisUnit
4. SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis
5. hHessianOpNorm
6. testRegular
7. selected weak-test C2_b/bounded-Hessian source interface
8. appendix.tex:984-995
9. appendix.tex:1026-1072
10. appendix.tex:1379-1387
11. main_body.tex:273-305
12. 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 keeps the active boundary as a source-contract gap, not a Mathlib or SLT gap. No SLT theorem was needed or imported; the local SLT clone is absent. Lower should only proceed if the paper/testRegular correspondence exposes the bounded-Hessian field itself, not a renamed copy of the missing operator-norm bound.

def cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle171_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_middle"
  statement := "Cycle 171 middle illness-area refiner packet. Classification: rejected-wrapper-churn. Exact wrapper churn rejected: do not add an opaque testRegular -> hHessianOpNorm or testRegular -> hSecondFDerivOpNorm theorem for the selected weak test unless testRegular is expanded to a source-backed C2_b/bounded-Hessian field. The live remaining boundary is hHessianOpNorm : forall z : E, norm (fderiv Real (fderiv Real sourceTest) z) <= C1 under sald.general_moving_target_discrete.em_interpolation_fp. The source anchors appendix.tex:984-995 and appendix.tex:1379-1387 justify the Brownian generator/Laplacian weak-test use, while appendix.tex:1026-1072 and main_body.tex:273-305 state Lipschitz and integrability assumptions rather than a global selected-test bounded-Hessian field. Brownian coordinate unit direction is already discharged by SALD.gaussianRealStdOrthonormalBasisUnit, and hHessianOpNorm-to-hSecondFDerivOpNorm is already compiled by SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle170GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianOpNormLower2Obligation",
    "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
    "SALD.gaussianRealStdOrthonormalBasisUnit",
    "SALD.gaussianRealSelectedTestDirectionalSecondBoundOfSecondFDerivOpNormStdOrthonormalBasis",
    "hHessianOpNorm",
    "testRegular",
    "selected weak-test C2_b/bounded-Hessian source interface",
    "appendix.tex:984-995",
    "appendix.tex:1026-1072",
    "appendix.tex:1379-1387",
    "main_body.tex:273-305",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle keeps the active boundary as a source-contract gap, not a Mathlib or SLT gap. No SLT theorem was needed or imported; the local SLT clone is absent. Lower should only proceed if the paper/testRegular correspondence exposes the bounded-Hessian field itself, not a renamed copy of the missing operator-norm bound."

/-- Cycle-171 proof-DAG pane for the rejected wrapper and remaining source
contract. -/