AutoSamplingTheory.SALD.cycle139GeneralMovingTargetDiscreteEmWeakFpSourceLaplacianLowerObligation

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 cycle139GeneralMovingTargetDiscreteEmWeakFpSourceLaplacianLowerObligation :
    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.cycle139_em_weak_fp_source_laplacian_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 139 middle compiles SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField and SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hweakFpLaplacianDef premise left by SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula is no longer primitive; it is split into hweakFpSourceActionDef, identifying the weak-FP abstract Laplacian action with the source functional applied to a named source field, and hweakFpSourceFieldEqLaplacian, identifying that source field with Mathlib's Laplacian of the selected weak-test representative. The route keeps htestLaplacianStdBasisDef, density-Laplacian source-action/source-field facts, second-Green residual/divergence, box-divergence, signed-face trace, pointwise trace equality, pointwise zero trace, and diffusion leaves 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.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField
2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField
3. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula
5. Mathlib.Analysis.InnerProductSpace.Laplacian
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 the non-circular weak-FP source-Laplacian definition needed by the pointwise test-Laplacian route. It does not derive hweakFpLaplacianDef from hweakFpStdBasisDef or hweakFpDensityLaplacianAction, and it does not reintroduce htestLaplacianActionDef or htestLaplacianOperator. It does not close htestLaplacianStdBasisDef, density-Laplacian source facts, 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 cycle139GeneralMovingTargetDiscreteEmWeakFpSourceLaplacianLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle139_em_weak_fp_source_laplacian_lower"
  statement := "Cycle 139 middle compiles SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField and SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hweakFpLaplacianDef premise left by SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula is no longer primitive; it is split into hweakFpSourceActionDef, identifying the weak-FP abstract Laplacian action with the source functional applied to a named source field, and hweakFpSourceFieldEqLaplacian, identifying that source field with Mathlib's Laplacian of the selected weak-test representative. The route keeps htestLaplacianStdBasisDef, density-Laplacian source-action/source-field facts, second-Green residual/divergence, box-divergence, signed-face trace, pointwise trace equality, pointwise zero trace, and diffusion leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField",
    "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField",
    "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfTestStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:1379-1387",
    "appendix.tex:1392-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It narrows only the non-circular weak-FP source-Laplacian definition needed by the pointwise test-Laplacian route. It does not derive hweakFpLaplacianDef from hweakFpStdBasisDef or hweakFpDensityLaplacianAction, and it does not reintroduce htestLaplacianActionDef or htestLaplacianOperator. It does not close htestLaplacianStdBasisDef, density-Laplacian source facts, 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-139 lower_1 state-integral scout for `hweakFpSourceActionDef`. -/