AutoSamplingTheory.SALD.cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation

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 cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation :
    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_scalar

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_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hemGeneratorLaplacianEventFieldEqLaplacian is no longer primitive; it follows from the smaller statewise source display hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = Laplacian.laplacian (selectedTest phi) x. The remaining analytic source boundary is precisely that scalar display, cited to the frozen EM interpolation and Fokker--Planck Laplacian lines at appendix.tex:984-995 and appendix.tex:1379-1387.

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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar
2. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
3. hemGeneratorLaplacianEventFieldEqLaplacian
4. appendix.tex:984-995
5. appendix.tex:1379-1387
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.

Lower_2 illness-area refiner for the EM conditional-law/state-event backend. It narrows the exact pointwise Delta identity to a statewise scalar display and explicitly rejects the older cycle-151/152 weak-FP source-field route, trace-field route, downstream total-event/source-functional wrapper, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, non-EM fallback, or sald_version_2.tex content.

def cycle157GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseScalarLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle157_em_generator_laplacian_event_field_pointwise_scalar"
  statement := "Cycle 157 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hemGeneratorLaplacianEventFieldEqLaplacian is no longer primitive; it follows from the smaller statewise source display hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = Laplacian.laplacian (selectedTest phi) x. The remaining analytic source boundary is precisely that scalar display, cited to the frozen EM interpolation and Fokker--Planck Laplacian lines at appendix.tex:984-995 and appendix.tex:1379-1387."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfPointwiseScalar",
    "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
    "hemGeneratorLaplacianEventFieldEqLaplacian",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Lower_2 illness-area refiner for the EM conditional-law/state-event backend. It narrows the exact pointwise Delta identity to a statewise scalar display and explicitly rejects the older cycle-151/152 weak-FP source-field route, trace-field route, downstream total-event/source-functional wrapper, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, non-EM fallback, or sald_version_2.tex content."

/-- Cycle-157 proof-DAG pane for the event-field pointwise standard-basis split. -/