AutoSamplingTheory.SALD.cycle134GeneralMovingTargetDiscreteEmSourceLaplacianStdBasisScoutObligation

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 cycle134GeneralMovingTargetDiscreteEmSourceLaplacianStdBasisScoutObligation :
    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_source_laplacian_std_basis_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 134 lower_1 compiles SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the remaining source-definition facts htestLaplacianActionDef and hweakFpLaplacianDef should no longer target an unspecified sourceLaplacianAction; the lower_2-ready route is to instantiate the selected source test as a smooth real-valued function on a finite-dimensional real inner-product space and identify both abstract actions with Mathlib's Laplacian, whose standard-basis iterated-derivative formula is now a compiled local theorem.

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.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
2. SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback
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 proof-scout packet. It produces a compiled Mathlib-backed local theorem for the selected weak-test Laplacian formula, but does not claim the remaining source definitions are proved. The next implementation step is one of htestLaplacianActionDef or hweakFpLaplacianDef by showing the corresponding abstract action is the Mathlib Laplacian/standard-basis second-derivative action on the selected source test. No SLT import, non-EM fallback, source-index rebaseline, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content is introduced.

def cycle134GeneralMovingTargetDiscreteEmSourceLaplacianStdBasisScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle134_em_source_laplacian_std_basis_scout"
  statement := "Cycle 134 lower_1 compiles SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv for appendix.tex:1379-1427. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the remaining source-definition facts htestLaplacianActionDef and hweakFpLaplacianDef should no longer target an unspecified sourceLaplacianAction; the lower_2-ready route is to instantiate the selected source test as a smooth real-valued function on a finite-dimensional real inner-product space and identify both abstract actions with Mathlib's Laplacian, whose standard-basis iterated-derivative formula is now a compiled local theorem."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "SALD.generalMovingTargetDiscreteTestLaplacianOperatorNormalizationOfSourcePullback",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis",
    "appendix.tex:1379-1427",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf proof-scout packet. It produces a compiled Mathlib-backed local theorem for the selected weak-test Laplacian formula, but does not claim the remaining source definitions are proved. The next implementation step is one of htestLaplacianActionDef or hweakFpLaplacianDef by showing the corresponding abstract action is the Mathlib Laplacian/standard-basis second-derivative action on the selected source test. No SLT import, non-EM fallback, source-index rebaseline, theorem-status promotion, fake closure, broad audit, wrapper churn, or sald_version_2 content is introduced."

/-- Cycle-134 lower_2 obligation narrowing the weak-FP Laplacian definition
leaf to the standard-basis source formula. -/