AutoSamplingTheory.SALD.cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation

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 cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation :
    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.cycle159_em_generator_laplacian_event_field_brownian_pointwise

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 159 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldBrownianDef is no longer primitive; it follows from the smaller pointwise Brownian-generator event-field source display hEmGeneratorLaplacianEventFieldBrownianPointwiseDef : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = SALD.emFrozenBrownianLaplacianEventField selectedTest phi x. The remaining source-cited boundary is to prove that pointwise definition directly from eq:general_moving_target_SALD_frozen_interp and the Fokker--Planck diffusion display at appendix.tex:1379-1387, without weak-FP source-field, trace-field, downstream 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise
2. SALD.emFrozenBrownianLaplacianEventField
3. hEmGeneratorLaplacianEventFieldBrownianPointwiseDef
4. hEmGeneratorLaplacianEventFieldBrownianDef
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.

Dynamic-leaf middle worker packet inside the EM conditional-law/state-event backend. Local SLT files were not consulted because this is a paper-internal Brownian-generator event-field definition; the bridge uses only function extensionality and the local Brownian event-field definition. It rejects wrapper churn through weak-FP source fields, trace fields, total-event/source-functional consumers, theorem-status promotion, fake closure, Lake/toolchain changes, non-EM fallback, or sald_version_2.tex.

def cycle159GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianPointwiseLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle159_em_generator_laplacian_event_field_brownian_pointwise"
  statement := "Cycle 159 middle compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hEmGeneratorLaplacianEventFieldBrownianDef is no longer primitive; it follows from the smaller pointwise Brownian-generator event-field source display hEmGeneratorLaplacianEventFieldBrownianPointwiseDef : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = SALD.emFrozenBrownianLaplacianEventField selectedTest phi x. The remaining source-cited boundary is to prove that pointwise definition directly from eq:general_moving_target_SALD_frozen_interp and the Fokker--Planck diffusion display at appendix.tex:1379-1387, without weak-FP source-field, trace-field, downstream total-event/source-functional, or non-EM fallbacks."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldBrownianDefOfPointwise",
    "SALD.emFrozenBrownianLaplacianEventField",
    "hEmGeneratorLaplacianEventFieldBrownianPointwiseDef",
    "hEmGeneratorLaplacianEventFieldBrownianDef",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf middle worker packet inside the EM conditional-law/state-event backend. Local SLT files were not consulted because this is a paper-internal Brownian-generator event-field definition; the bridge uses only function extensionality and the local Brownian event-field definition. It rejects wrapper churn through weak-FP source fields, trace fields, total-event/source-functional consumers, theorem-status promotion, fake closure, Lake/toolchain changes, non-EM fallback, or sald_version_2.tex."

/-- Cycle-159 lower_2 standard-basis split of the Brownian pointwise boundary. -/