AutoSamplingTheory.SALD.cycle135GeneralMovingTargetDiscreteEmTestLaplacianStdBasisLowerObligation

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 cycle135GeneralMovingTargetDiscreteEmTestLaplacianStdBasisLowerObligation :
    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.cycle135_em_test_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 135 compiles SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: htestLaplacianActionDef 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 htestLaplacianStdBasisDef, the statement that the test-calculus abstract laplacian action is the standard-basis second-derivative source formula. The operator leaf can now be derived directly from htestLaplacianStdBasisDef plus hweakFpStdBasisDef. 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.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula
2. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis
7. appendix.tex:1379-1427
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 htestLaplacianActionDef to the concrete htestLaplacianStdBasisDef source formula after instantiating the source Laplacian action by Mathlib's Laplacian passed through the source action functional. The lower_1 operator scout theorem also composes htestLaplacianStdBasisDef with hweakFpStdBasisDef to derive the old htestLaplacianOperator boundary. It does not claim the source-facing htestLaplacianStdBasisDef or hweakFpStdBasisDef, 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 cycle135GeneralMovingTargetDiscreteEmTestLaplacianStdBasisLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle135_em_test_laplacian_std_basis_lower"
  statement := "Cycle 135 compiles SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula and SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfStdBasisSourceFormula for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: htestLaplacianActionDef 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 htestLaplacianStdBasisDef, the statement that the test-calculus abstract laplacian action is the standard-basis second-derivative source formula. The operator leaf can now be derived directly from htestLaplacianStdBasisDef plus hweakFpStdBasisDef. All second-Green, box-divergence, trace, diffusion, and first-Green leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteTestLaplacianActionDefOfStdBasisSourceFormula",
    "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfStdBasisSourceFormula",
    "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 htestLaplacianActionDef to the concrete htestLaplacianStdBasisDef source formula after instantiating the source Laplacian action by Mathlib's Laplacian passed through the source action functional. The lower_1 operator scout theorem also composes htestLaplacianStdBasisDef with hweakFpStdBasisDef to derive the old htestLaplacianOperator boundary. It does not claim the source-facing htestLaplacianStdBasisDef or hweakFpStdBasisDef, 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-135 lower_2 downstream consumer for the standard-basis
test-Laplacian source formulas. -/