AutoSamplingTheory.SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation

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 cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation :
    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_lower2

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 lower_2 illness-area Lean implementer packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the downstream hHessianOpNorm hypothesis under sald.general_moving_target_discrete.em_interpolation_fp is no longer primitive once the source correspondence supplies a Hessian representative sourceHessian with hSourceHasHessian : forall z, HasFDerivAt (fderiv Real sourceTest) (sourceHessian z) z and hSourceHessianBound : forall z, norm (sourceHessian z) <= C1. SALD.selectedWeakTestHessianOpNormOfSourceHessianField compiles the local Mathlib bridge by rewriting fderiv Real (fderiv Real sourceTest) z with (hSourceHasHessian z).fderiv and applying hSourceHessianBound z. This is not a testRegular wrapper and does not define or assume an unsourced SourceSelectedWeakTestC2bBoundedHessian predicate; the remaining source-contract boundary is exactly the pair hSourceHasHessian/hSourceHessianBound for the selected weak test from appendix.tex:984-995, appendix.tex:1026-1072, appendix.tex:1379-1387, and main_body.tex:273-305, with iteration_complexity.tex:309-321 still rejected as score-Hessian regularity rather than sourceTest regularity.

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.formalized — 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.selectedWeakTestHessianOpNormOfSourceHessianField
2. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
3. SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
4. HasFDerivAt.fderiv
5. hSourceHasHessian
6. hSourceHessianBound
7. sourceHessian
8. sourceTest
9. hHessianOpNorm
10. appendix.tex:984-995
11. appendix.tex:1026-1072
12. appendix.tex:1379-1387
13. main_body.tex:273-305
14. iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest
15. 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. The only new proof ingredient is Mathlib's HasFDerivAt.fderiv uniqueness lemma, used in the compiled theorem SALD.selectedWeakTestHessianOpNormOfSourceHessianField. The source-facing analytic work remains to justify hSourceHasHessian and hSourceHessianBound for the selected weak test.

def cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle173_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_hessian_source_lower2"
  statement := "Cycle 173 lower_2 illness-area Lean implementer packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the downstream hHessianOpNorm hypothesis under sald.general_moving_target_discrete.em_interpolation_fp is no longer primitive once the source correspondence supplies a Hessian representative sourceHessian with hSourceHasHessian : forall z, HasFDerivAt (fderiv Real sourceTest) (sourceHessian z) z and hSourceHessianBound : forall z, norm (sourceHessian z) <= C1. SALD.selectedWeakTestHessianOpNormOfSourceHessianField compiles the local Mathlib bridge by rewriting fderiv Real (fderiv Real sourceTest) z with (hSourceHasHessian z).fderiv and applying hSourceHessianBound z. This is not a testRegular wrapper and does not define or assume an unsourced SourceSelectedWeakTestC2bBoundedHessian predicate; the remaining source-contract boundary is exactly the pair hSourceHasHessian/hSourceHessianBound for the selected weak test from appendix.tex:984-995, appendix.tex:1026-1072, appendix.tex:1379-1387, and main_body.tex:273-305, with iteration_complexity.tex:309-321 still rejected as score-Hessian regularity rather than sourceTest regularity."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestHessianOpNormOfSourceHessianField",
    "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
    "SALD.cycle173GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
    "HasFDerivAt.fderiv",
    "hSourceHasHessian",
    "hSourceHessianBound",
    "sourceHessian",
    "sourceTest",
    "hHessianOpNorm",
    "appendix.tex:984-995",
    "appendix.tex:1026-1072",
    "appendix.tex:1379-1387",
    "main_body.tex:273-305",
    "iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No SLT theorem was consulted or imported. The only new proof ingredient is Mathlib's HasFDerivAt.fderiv uniqueness lemma, used in the compiled theorem SALD.selectedWeakTestHessianOpNormOfSourceHessianField. The source-facing analytic work remains to justify hSourceHasHessian and hSourceHessianBound for the selected weak test."

/-- Cycle-173 proof-DAG pane for the middle source-contract recovery packet. -/