AutoSamplingTheory.SALD.cycle137GeneralMovingTargetDiscreteEmPointwiseGreenIbPScoutObligation

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 cycle137GeneralMovingTargetDiscreteEmPointwiseGreenIbPScoutObligation :
    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_pointwise_green_ibp_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 137 lower_1 compiles SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the pointwise weak Laplacian IBP theorem densityLaplacianAction phi = laplacian phi is no longer a single supplied theorem boundary; it follows from three pointwise source-facing leaves: first-Green densityLaplacianAction phi = negativeGradientPairAction phi, second-Green negativeGradientPairAction phi = testLaplacianAction phi, and test-Laplacian normalization testLaplacianAction phi = laplacian phi. The density-Laplacian source-action definition, source-field Laplacian equality, htestLaplacianStdBasisDef, box-divergence, trace, diffusion, and first/second Green analytic instantiations 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.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity
2. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity
3. SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseWeakLaplacianIbP
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity
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 lower_1 proof-scout packet. It gives lower_2 a one-theorem implementation target: prove the three pointwise Green/test-calculus leaves for the selected weak tests, then feed them through SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity. It does not prove the analytic Green identities, source density-Laplacian definitions, htestLaplacianStdBasisDef, box-divergence, trace, diffusion, 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 cycle137GeneralMovingTargetDiscreteEmPointwiseGreenIbPScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle137_em_pointwise_green_ibp_scout"
  statement := "Cycle 137 lower_1 compiles SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity and SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the pointwise weak Laplacian IBP theorem densityLaplacianAction phi = laplacian phi is no longer a single supplied theorem boundary; it follows from three pointwise source-facing leaves: first-Green densityLaplacianAction phi = negativeGradientPairAction phi, second-Green negativeGradientPairAction phi = testLaplacianAction phi, and test-Laplacian normalization testLaplacianAction phi = laplacian phi. The density-Laplacian source-action definition, source-field Laplacian equality, htestLaplacianStdBasisDef, box-divergence, trace, diffusion, and first/second Green analytic instantiations remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscretePointwiseWeakLaplacianIbPOfGreenIdentity",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity",
    "SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseWeakLaplacianIbP",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity",
    "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 gives lower_2 a one-theorem implementation target: prove the three pointwise Green/test-calculus leaves for the selected weak tests, then feed them through SALD.generalMovingTargetDiscreteWeakFpStdBasisDefOfPointwiseGreenIdentity. It does not prove the analytic Green identities, source density-Laplacian definitions, htestLaplacianStdBasisDef, box-divergence, trace, diffusion, 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_2 narrowing of the second-Green pointwise leaf to the
box-divergence and pointwise-trace boundary. -/