AutoSamplingTheory.SALD.cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation

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 cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation :
    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.cycle134_em_test_laplacian_source_pullback_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 134 middle compiles SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback and SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct htestLaplacianOperator premise left by SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization is replaced by two source-definition facts against one shared selected weak-test Laplacian action: htestLaplacianActionDef and hweakFpLaplacianDef. The theorem keeps hsecondGreenTestTracePointwiseEq, htestTracePointwiseZero, box-divergence regularity/face-trace facts, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, and hdiffusionLaplacianTerm 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.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback
3. SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
5. appendix.tex:1379-1387
6. appendix.tex:1392-1427
7. 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 does not introduce a theorem equivalent to htestLaplacianOperator under a pointwise or funext name; instead it records the smaller source-calculus definition boundary that the selected test-Laplacian action and weak-FP Laplacian action are pullbacks of the same source Laplacian. It does not prove those source definitions, compact support/decay, pointwise second-Green trace identification, weighted-field regularity, divergence integrability, face-to-trace identification, second-Green residual/divergence facts, Brownian diffusion construction, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content.

def cycle134GeneralMovingTargetDiscreteEmTestLaplacianSourcePullbackLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle134_em_test_laplacian_source_pullback_lower"
  statement := "Cycle 134 middle compiles SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback and SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct htestLaplacianOperator premise left by SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization is replaced by two source-definition facts against one shared selected weak-test Laplacian action: htestLaplacianActionDef and hweakFpLaplacianDef. The theorem keeps hsecondGreenTestTracePointwiseEq, htestTracePointwiseZero, box-divergence regularity/face-trace facts, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, and hdiffusionLaplacianTerm explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfSourceLaplacianPullback",
    "SALD.generalMovingTargetDiscreteTestLaplacianLocalOfOperatorNormalization",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It does not introduce a theorem equivalent to htestLaplacianOperator under a pointwise or funext name; instead it records the smaller source-calculus definition boundary that the selected test-Laplacian action and weak-FP Laplacian action are pullbacks of the same source Laplacian. It does not prove those source definitions, compact support/decay, pointwise second-Green trace identification, weighted-field regularity, divergence integrability, face-to-trace identification, second-Green residual/divergence facts, Brownian diffusion construction, full weak FP, KL differentiation, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content."

/-- Cycle-134 lower_1 proof-scout obligation for the Mathlib source formula
below the shared source-pullback Laplacian boundary. -/