AutoSamplingTheory.SALD.cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation

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 cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation :
    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.cycle158_em_generator_laplacian_event_field_brownian_def_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 158 lower_2 narrows hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian to hEmGeneratorLaplacianEventFieldBrownianDef, the source-facing definition that the named frozen EM Laplacian event field is SALD.emFrozenBrownianLaplacianEventField selectedTest. The compiled theorem SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef unfolds that definition to recover the scalar statewise Delta display. The remaining source-cited boundary is to prove the Brownian-generator event-field definition from eq:general_moving_target_SALD_frozen_interp and the Fokker--Planck diffusion term at appendix.tex:1379-1387, without weak-FP source-field, trace-field, total-event/source-functional, or non-EM fallbacks.

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.emFrozenBrownianLaplacianEventField
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef
3. hEmGeneratorLaplacianEventFieldBrownianDef
4. hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian
5. eq:general_moving_target_SALD_frozen_interp
6. appendix.tex:984-995
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.

Lower_2 dynamic-leaf/illness-area refiner. Local SLT files were not consulted because the narrowed boundary is the paper-internal Brownian-generator event-field definition, not a probability/concentration reuse theorem.

def cycle158GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle158_em_generator_laplacian_event_field_brownian_def_lower"
  statement := "Cycle 158 lower_2 narrows hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian to hEmGeneratorLaplacianEventFieldBrownianDef, the source-facing definition that the named frozen EM Laplacian event field is SALD.emFrozenBrownianLaplacianEventField selectedTest. The compiled theorem SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef unfolds that definition to recover the scalar statewise Delta display. The remaining source-cited boundary is to prove the Brownian-generator event-field definition from eq:general_moving_target_SALD_frozen_interp and the Fokker--Planck diffusion term at appendix.tex:1379-1387, without weak-FP source-field, trace-field, total-event/source-functional, or non-EM fallbacks."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.emFrozenBrownianLaplacianEventField",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldPointwiseEqLaplacianOfBrownianDef",
    "hEmGeneratorLaplacianEventFieldBrownianDef",
    "hEmGeneratorLaplacianEventFieldPointwiseEqLaplacian",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Lower_2 dynamic-leaf/illness-area refiner. Local SLT files were not consulted because the narrowed boundary is the paper-internal Brownian-generator event-field definition, not a probability/concentration reuse theorem."

/-- Cycle-158 proof-DAG pane for the scalar event-field Delta blocker. -/