AutoSamplingTheory.SALD.cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation

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 cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation :
    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_weak_fp_laplacian_std_basis_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 lower_2 compiles SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hweakFpLaplacianDef no longer targets an unspecified sourceLaplacianAction; when the selected weak test is represented in a finite-dimensional real inner-product source space, it follows from hweakFpStdBasisDef, the statement that the weak-FP abstract laplacian action is the standard-basis second-derivative source formula. The sibling htestLaplacianActionDef and all second-Green, box-divergence, trace, diffusion, and first-Green leaves 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.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula
2. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
3. Mathlib.Analysis.InnerProductSpace.Laplacian
4. InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis
5. appendix.tex:1379-1427
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 worker packet. It narrows only hweakFpLaplacianDef to the concrete hweakFpStdBasisDef source formula after instantiating the source Laplacian action by Mathlib's Laplacian passed through the source action functional. It does not claim htestLaplacianActionDef, second-Green, box-divergence, trace, diffusion, first-Green, KL differentiation, LSI, DV, Gronwall, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content.

def cycle134GeneralMovingTargetDiscreteEmWeakFpLaplacianStdBasisLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle134_em_weak_fp_laplacian_std_basis_lower"
  statement := "Cycle 134 lower_2 compiles SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hweakFpLaplacianDef no longer targets an unspecified sourceLaplacianAction; when the selected weak test is represented in a finite-dimensional real inner-product source space, it follows from hweakFpStdBasisDef, the statement that the weak-FP abstract laplacian action is the standard-basis second-derivative source formula. The sibling htestLaplacianActionDef and all second-Green, box-divergence, trace, diffusion, and first-Green leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis",
    "appendix.tex:1379-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It narrows only hweakFpLaplacianDef to the concrete hweakFpStdBasisDef source formula after instantiating the source Laplacian action by Mathlib's Laplacian passed through the source action functional. It does not claim htestLaplacianActionDef, second-Green, box-divergence, trace, diffusion, first-Green, KL differentiation, LSI, DV, Gronwall, theorem closure, SLT import, Lake/toolchain changes, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content."

/-- Cycle-134 proof-DAG pane for the source-pullback test-Laplacian boundary. -/