AutoSamplingTheory.SALD.cycle185GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Obligation

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 cycle185GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Obligation :
    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.cycle185_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_remainder_limit_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 185 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hRemainderGeneratorLimitDef is no longer primitive once the source supplies hRemainderGeneratorNormalizedLawDef together with hNormalizedVectorLaw, hCoordinateLawDef, and hVarianceDef. SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw compiles the bridge: rewrite the normalized-remainder integral from normalizedCoordinateLaw to gaussianReal 0 1 using SALD.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw, then rewrite variance phi x i to 1 using SALD.selectedWeakTestNormalizedVarianceDefOfGaussianRealUnitLaw to recover gaussianReal 0 (variance phi x i). Remaining exact Brownian/Ito backend: hRemainderGeneratorNormalizedLawDef, hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hSourceTaylorIntegrandPointwise, and 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.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw
2. SALD.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw
3. SALD.selectedWeakTestNormalizedVarianceDefOfGaussianRealUnitLaw
4. hRemainderGeneratorLimitDef
5. hRemainderGeneratorNormalizedLawDef
6. hNormalizedVectorLaw
7. hCoordinateLawDef
8. hVarianceDef
9. normalizedVectorLaw
10. normalizedCoordinateLaw
11. normalizedRemainder
12. remainderGeneratorLimit
13. variance
14. ProbabilityTheory.stdGaussian
15. ProbabilityTheory.gaussianReal
16. eq:SALD_general_EM
17. eq:general_moving_target_SALD_frozen_interp
18. appendix.tex:984-995
19. appendix.tex:1170-1176
20. appendix.tex:1379-1387
21. runs/20260612-012747-657607-ASTIS-SALD-001-cycle185/lower_1_remainder_generator_limit_route.md
22. 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.

No external SLT file was consulted, imported, ported, or marked formalized. Mathlib support is only through the already compiled local SALD Gaussian coordinate-law and variance bridges. This theorem does not prove hRemainderGeneratorNormalizedLawDef, hSourceTaylorIntegrandPointwise, scalar pushforward/measurability fields, the DCT remainder package, or selected weak-test Hessian fields.

def cycle185GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoRemainderLimitLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle185_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_remainder_limit_lower2"
  statement := "Cycle 185 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hRemainderGeneratorLimitDef is no longer primitive once the source supplies hRemainderGeneratorNormalizedLawDef together with hNormalizedVectorLaw, hCoordinateLawDef, and hVarianceDef. SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw compiles the bridge: rewrite the normalized-remainder integral from normalizedCoordinateLaw to gaussianReal 0 1 using SALD.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw, then rewrite variance phi x i to 1 using SALD.selectedWeakTestNormalizedVarianceDefOfGaussianRealUnitLaw to recover gaussianReal 0 (variance phi x i). Remaining exact Brownian/Ito backend: hRemainderGeneratorNormalizedLawDef, hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hSourceTaylorIntegrandPointwise, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestRemainderGeneratorLimitDefOfStdGaussianVectorLaw",
    "SALD.selectedWeakTestNormalizedCoordinateLawOfStdGaussianVectorLaw",
    "SALD.selectedWeakTestNormalizedVarianceDefOfGaussianRealUnitLaw",
    "hRemainderGeneratorLimitDef",
    "hRemainderGeneratorNormalizedLawDef",
    "hNormalizedVectorLaw",
    "hCoordinateLawDef",
    "hVarianceDef",
    "normalizedVectorLaw",
    "normalizedCoordinateLaw",
    "normalizedRemainder",
    "remainderGeneratorLimit",
    "variance",
    "ProbabilityTheory.stdGaussian",
    "ProbabilityTheory.gaussianReal",
    "eq:SALD_general_EM",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1170-1176",
    "appendix.tex:1379-1387",
    "runs/20260612-012747-657607-ASTIS-SALD-001-cycle185/lower_1_remainder_generator_limit_route.md",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No external SLT file was consulted, imported, ported, or marked formalized. Mathlib support is only through the already compiled local SALD Gaussian coordinate-law and variance bridges. This theorem does not prove hRemainderGeneratorNormalizedLawDef, hSourceTaylorIntegrandPointwise, scalar pushforward/measurability fields, the DCT remainder package, or selected weak-test Hessian fields."

/-- Cycle-185 proof-DAG pane for the remainder-generator law split. -/