AutoSamplingTheory.SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseLaplacianScoutObligation

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 cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseLaplacianScoutObligation :
    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.cycle157_em_generator_laplacian_event_field_pointwise_laplacian_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 157 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef is no longer primitive; it follows from the smaller source-facing pointwise Delta identity hemGeneratorLaplacianEventFieldEqLaplacian together with SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. Lower_2 should prove hemGeneratorLaplacianEventFieldEqLaplacian directly from the frozen EM interpolation and Fokker--Planck Laplacian display at appendix.tex:984-995 and appendix.tex:1379-1387, not by reusing the cycle-151/152 source-field or trace-field consumers.

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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian
2. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
3. hemGeneratorLaplacianEventFieldEqLaplacian
4. hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef
5. appendix.tex:984-995
6. appendix.tex:1368-1387
7. appendix.tex:1379-1387
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.

Natural-language proof scout plus compiled local Mathlib bridge. This narrows only the pointwise standard-basis display to the source Delta identity for the named frozen EM event field. It does not prove the conditional-drift Fokker--Planck theorem, weak-FP source-field equality, event/trace equality, state-event integral formula, SLT import, downstream consumer wrapper, broad audit, theorem-status promotion, fake closure, or sald_version_2.tex content.

def cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseLaplacianScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle157_em_generator_laplacian_event_field_pointwise_laplacian_scout"
  statement := "Cycle 157 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef is no longer primitive; it follows from the smaller source-facing pointwise Delta identity hemGeneratorLaplacianEventFieldEqLaplacian together with SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. Lower_2 should prove hemGeneratorLaplacianEventFieldEqLaplacian directly from the frozen EM interpolation and Fokker--Planck Laplacian display at appendix.tex:984-995 and appendix.tex:1379-1387, not by reusing the cycle-151/152 source-field or trace-field consumers."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseStdBasisDefOfPointwiseLaplacian",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "hemGeneratorLaplacianEventFieldEqLaplacian",
    "hEmGeneratorLaplacianEventFieldPointwiseStdBasisDef",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Natural-language proof scout plus compiled local Mathlib bridge. This narrows only the pointwise standard-basis display to the source Delta identity for the named frozen EM event field. It does not prove the conditional-drift Fokker--Planck theorem, weak-FP source-field equality, event/trace equality, state-event integral formula, SLT import, downstream consumer wrapper, broad audit, theorem-status promotion, fake closure, or sald_version_2.tex content."

/-- Cycle-157 lower_2 narrowing of the pointwise event-field Laplacian leaf. -/