AutoSamplingTheory.SALD.cycle183GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegrandLower2Obligation

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 cycle183GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegrandLower2Obligation :
    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.cycle183_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_integrand_lower2

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 183 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hBrownianCoordinateGeneratorTaylorIntegrandAE is no longer primitive once the source supplies hSourceTaylorIntegrandPointwise. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise compiles the pointwise-to-a.e. bridge using Filter.Eventually.of_forall under ProbabilityTheory.gaussianReal 0 (variance phi x i). Remaining exact source boundary is hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandPointwise, hRemainderGeneratorLimitDef, and the concrete normalized-remainder measurability/domination package hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — 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.formalized — 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.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise
2. Filter.Eventually.of_forall
3. hBrownianCoordinateGeneratorTaylorIntegrandAE
4. hSourceTaylorIntegrandPointwise
5. sourceTaylorIntegrand
6. linearCoeff
7. quadraticCoeff
8. normalizedRemainder
9. variance
10. ProbabilityTheory.gaussianReal
11. hScalarLineTaylorCoeffDef
12. eq:general_moving_target_SALD_frozen_interp
13. appendix.tex:984-995
14. appendix.tex:1170-1176
15. appendix.tex:1379-1387

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

No external SLT file was consulted, imported, or marked formalized. Mathlib use is exactly Filter.Eventually.of_forall. This narrows only the a.e. integrand equality to a pointwise source Taylor identity; it does not reopen selected weak-test Hessian regularity, move sigma_eta^2/2 into the event field, or prove the source Taylor expansion.

def cycle183GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegrandLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle183_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_integrand_lower2"
  statement := "Cycle 183 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hBrownianCoordinateGeneratorTaylorIntegrandAE is no longer primitive once the source supplies hSourceTaylorIntegrandPointwise. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise compiles the pointwise-to-a.e. bridge using Filter.Eventually.of_forall under ProbabilityTheory.gaussianReal 0 (variance phi x i). Remaining exact source boundary is hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandPointwise, hRemainderGeneratorLimitDef, and the concrete normalized-remainder measurability/domination package hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise",
    "Filter.Eventually.of_forall",
    "hBrownianCoordinateGeneratorTaylorIntegrandAE",
    "hSourceTaylorIntegrandPointwise",
    "sourceTaylorIntegrand",
    "linearCoeff",
    "quadraticCoeff",
    "normalizedRemainder",
    "variance",
    "ProbabilityTheory.gaussianReal",
    "hScalarLineTaylorCoeffDef",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1170-1176",
    "appendix.tex:1379-1387"
  ]
  note := "No external SLT file was consulted, imported, or marked formalized. Mathlib use is exactly Filter.Eventually.of_forall. This narrows only the a.e. integrand equality to a pointwise source Taylor identity; it does not reopen selected weak-test Hessian regularity, move sigma_eta^2/2 into the event field, or prove the source Taylor expansion."

/-- Cycle-183 proof-DAG pane for the Brownian coordinate source-integral leaf. -/