AutoSamplingTheory.SALD.cycle137GeneralMovingTargetDiscreteEmWeakFpDensityLaplacianActionLowerObligation

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 cycle137GeneralMovingTargetDiscreteEmWeakFpDensityLaplacianActionLowerObligation :
    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.cycle137_em_weak_fp_density_laplacian_action_lower

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 137 compiles SALD.generalMovingTargetDiscreteWeakFpDensityLaplacianActionOfPointwiseWeakLaplacianIbP and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseWeakLaplacianIbP for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the remaining hweakFpDensityLaplacianAction function-equality input from cycle 136 is no longer primitive; it follows from the pointwise weak Laplacian integration-by-parts identity densityLaplacianAction phi = laplacian phi for each selected weak test. The downstream standard-basis consumer can now use that pointwise IBP equality plus hdensityLaplacianStdBasisDef, while hdensityLaplacianActionDef, hsourceDensityLaplacianEqLaplacian, htestLaplacianStdBasisDef, and all second-Green, box-divergence, trace, diffusion, and first-Green leaves remain explicit.

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.generalMovingTargetDiscreteWeakFpDensityLaplacianActionOfPointwiseWeakLaplacianIbP
2. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseWeakLaplacianIbP
3. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfSourceDensityLaplacianFormula
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfStdBasisSourceFormula
6. appendix.tex:1379-1387
7. appendix.tex:1392-1427
8. 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.

Dynamic-leaf worker packet. It narrows only hweakFpDensityLaplacianAction to a pointwise weak Laplacian IBP theorem boundary and feeds that smaller boundary into the cycle-136 weak-FP standard-basis source formula. It does not prove the underlying Green identity, density-Laplacian source action definition, source-field Laplacian equality, htestLaplacianStdBasisDef, second-Green, box-divergence, trace, diffusion, first-Green, KL differentiation, LSI, DV, Gronwall, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle137GeneralMovingTargetDiscreteEmWeakFpDensityLaplacianActionLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle137_em_weak_fp_density_laplacian_action_lower"
  statement := "Cycle 137 compiles SALD.generalMovingTargetDiscreteWeakFpDensityLaplacianActionOfPointwiseWeakLaplacianIbP and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseWeakLaplacianIbP for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the remaining hweakFpDensityLaplacianAction function-equality input from cycle 136 is no longer primitive; it follows from the pointwise weak Laplacian integration-by-parts identity densityLaplacianAction phi = laplacian phi for each selected weak test. The downstream standard-basis consumer can now use that pointwise IBP equality plus hdensityLaplacianStdBasisDef, while hdensityLaplacianActionDef, hsourceDensityLaplacianEqLaplacian, htestLaplacianStdBasisDef, and all second-Green, box-divergence, trace, diffusion, and first-Green leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpDensityLaplacianActionOfPointwiseWeakLaplacianIbP",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseWeakLaplacianIbP",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfSourceDensityLaplacianFormula",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfStdBasisSourceFormula",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It narrows only hweakFpDensityLaplacianAction to a pointwise weak Laplacian IBP theorem boundary and feeds that smaller boundary into the cycle-136 weak-FP standard-basis source formula. It does not prove the underlying Green identity, density-Laplacian source action definition, source-field Laplacian equality, htestLaplacianStdBasisDef, second-Green, box-divergence, trace, diffusion, first-Green, KL differentiation, LSI, DV, Gronwall, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-137 lower_1 scout obligation splitting pointwise weak Laplacian IBP
into the three Green/test-calculus identities from the source proof. -/