AutoSamplingTheory.SALD.cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation

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 cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation :
    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.cycle138_em_test_laplacian_pointwise_source_pullback_scout

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 138 lower_1 compiles SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct htestLaplacianPointwise leaf from SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity is derived from htestLaplacianActionDef and hweakFpLaplacianDef, the source-facing facts that the test-calculus action and weak-FP abstract Laplacian are both pullbacks of the same selected source-Laplacian action.

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.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback
2. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
3. SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity
4. appendix.tex:1379-1387
5. appendix.tex:1392-1427
6. 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 lower_1 proof-scout packet. It does not prove htestLaplacianActionDef or hweakFpLaplacianDef, nor their standard-basis refinements; it only removes the direct pointwise normalization as a primitive source theorem. It does not close the density-Laplacian source action, second-Green residual/divergence, box-divergence, trace, diffusion, KL differentiation, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content.

def cycle138GeneralMovingTargetDiscreteEmTestLaplacianPointwiseSourcePullbackScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle138_em_test_laplacian_pointwise_source_pullback_scout"
  statement := "Cycle 138 lower_1 compiles SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the direct htestLaplacianPointwise leaf from SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity is derived from htestLaplacianActionDef and hweakFpLaplacianDef, the source-facing facts that the test-calculus action and weak-FP abstract Laplacian are both pullbacks of the same selected source-Laplacian action."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfSourcePullback",
    "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
    "SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_1 proof-scout packet. It does not prove htestLaplacianActionDef or hweakFpLaplacianDef, nor their standard-basis refinements; it only removes the direct pointwise normalization as a primitive source theorem. It does not close the density-Laplacian source action, second-Green residual/divergence, box-divergence, trace, diffusion, KL differentiation, theorem closure, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, wrapper churn, non-EM fallback, or sald_version_2 content."

/-- Cycle-138 lower_2 bridge from the test-calculus standard-basis source
formula to the pointwise test-Laplacian normalization leaf. -/