AutoSamplingTheory.SALD.cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseScoutObligation

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 cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseScoutObligation :
    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.cycle160_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_pointwise_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 160 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoGeneratorDefOfPointwise. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoGeneratorEventFieldDef is no longer primitive; it follows from the pointwise stochastic-generator display hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = SALD.emFrozenScalarBrownianItoGeneratorEventField selectedTest phi x. The remaining source-cited boundary is to prove that pointwise equality directly from the scalar Brownian increment in eq:general_moving_target_SALD_frozen_interp, the Ito/Taylor generator formula, and the positive FP diffusion display at appendix.tex:1379-1387, with sigma_eta^2/2 kept outside the event field and without weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM, wrapper, broad-audit, fake-closure, theorem-status-promotion, Lake/toolchain, SLT-import, or sald_version_2 routes.

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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoGeneratorDefOfPointwise
2. SALD.emFrozenScalarBrownianItoGeneratorEventField
3. hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef
4. hFrozenScalarBrownianItoGeneratorEventFieldDef
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 lower_1 proof scout inside the EM conditional-law/state-event backend. Consulted appendix.tex:984-995 and appendix.tex:1379-1387 plus the existing Mathlib Laplacian bridge and local Gaussian/covariance inventory. The configured local SLT project path is absent, and no SLT theorem was imported; the remaining dependency is an internal-paper stochastic-generator theorem.

def cycle160GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoPointwiseScoutObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle160_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_pointwise_scout"
  statement := "Cycle 160 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoGeneratorDefOfPointwise. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoGeneratorEventFieldDef is no longer primitive; it follows from the pointwise stochastic-generator display hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef : testRegular -> forall phi x, emGeneratorLaplacianEventField phi x = SALD.emFrozenScalarBrownianItoGeneratorEventField selectedTest phi x. The remaining source-cited boundary is to prove that pointwise equality directly from the scalar Brownian increment in eq:general_moving_target_SALD_frozen_interp, the Ito/Taylor generator formula, and the positive FP diffusion display at appendix.tex:1379-1387, with sigma_eta^2/2 kept outside the event field and without weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM, wrapper, broad-audit, fake-closure, theorem-status-promotion, Lake/toolchain, SLT-import, or sald_version_2 routes."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoGeneratorDefOfPointwise",
    "SALD.emFrozenScalarBrownianItoGeneratorEventField",
    "hFrozenScalarBrownianItoGeneratorEventFieldPointwiseDef",
    "hFrozenScalarBrownianItoGeneratorEventFieldDef",
    "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 lower_1 proof scout inside the EM conditional-law/state-event backend. Consulted appendix.tex:984-995 and appendix.tex:1379-1387 plus the existing Mathlib Laplacian bridge and local Gaussian/covariance inventory. The configured local SLT project path is absent, and no SLT theorem was imported; the remaining dependency is an internal-paper stochastic-generator theorem."

/-- Cycle-160 lower_2 coordinate-generator split of the pointwise frozen scalar
Ito generator boundary. -/