AutoSamplingTheory.SALD.cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation

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 cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation :
    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.cycle133_em_test_laplacian_normalization_lower_1

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 133 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the broad htestLaplacian premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero is replaced by the test-local premise htestLaplacianLocal : ∀ φ, Admissible φ → testRegular → testLaplacianAction φ = laplacian φ. The theorem ignores commonSpace, conditionalKernel, driftRegular, densityRegular, and boundaryBehavior when reconstructing the old htestLaplacian shape, and 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero
3. appendix.tex:1379-1387
4. appendix.tex:1392-1427
5. 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.

Natural-language proof-scout packet plus compiled local composition. It does not prove the analytic source theorem that the chosen test-Laplacian action equals the abstract laplacian for admissible regular tests; that is the remaining test-local boundary. It does not prove 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 cycle133GeneralMovingTargetDiscreteEmTestLaplacianNormalizationScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle133_em_test_laplacian_normalization_lower_1"
  statement := "Cycle 133 lower_1 compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the broad htestLaplacian premise from SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero is replaced by the test-local premise htestLaplacianLocal : ∀ φ, Admissible φ → testRegular → testLaplacianAction φ = laplacian φ. The theorem ignores commonSpace, conditionalKernel, driftRegular, densityRegular, and boundaryBehavior when reconstructing the old htestLaplacian shape, and 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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZeroOfTestLaplacianNormalization",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqPointwiseTestTraceZero",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Natural-language proof-scout packet plus compiled local composition. It does not prove the analytic source theorem that the chosen test-Laplacian action equals the abstract laplacian for admissible regular tests; that is the remaining test-local boundary. It does not prove 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-133 lower_2 packet narrowing the test-local Laplacian normalization
to an operator-level source identity for the regular test calculus. -/