AutoSamplingTheory.SALD.cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Obligation

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 cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Obligation :
    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.cycle191_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_integral_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 191 middle dynamic-leaf worker packet. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hBrownianCoordinateGeneratorNormalizedLawDef is no longer primitive inside hBrownianCoordinateGeneratorSourceIntegralDef once the source supplies hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, and hVarianceDef. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw compiles the direct composition of the scalar-pushforward coordinate-generator bridge and the standard-Gaussian vector coordinate-law bridge. Source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 keep the normalized Brownian coordinate and weak-FP sigma_eta^2/2 diffusion prefactor separate. Remaining exact Brownian/Ito backend: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, hRemainderGeneratorLimitDef, hRemainderMeas, hRemainderBound, and 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.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw
2. SALD.selectedWeakTestBrownianCoordinateGeneratorNormalizedLawDefOfScalarPushforward
3. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfStdGaussianVectorLaw
4. hBrownianCoordinateGeneratorSourceIntegralDef
5. hBrownianCoordinateGeneratorNormalizedLawDef
6. hScalarMeas
7. hNormalizedCoordinateLawDef
8. hSourceTaylorIntegrandMeas
9. hGeneratorPullbackDef
10. hNormalizedVectorLaw
11. hCoordinateLawDef
12. hVarianceDef
13. normalizedCoordinateLaw
14. sourceTaylorIntegrand
15. brownianCoordinateGenerator
16. variance
17. ProbabilityTheory.stdGaussian
18. ProbabilityTheory.gaussianReal
19. MeasureTheory.integral_map
20. appendix.tex:958-970
21. appendix.tex:983-996
22. appendix.tex:1161-1170
23. appendix.tex:1379-1387
24. 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, called, queued, or marked formalized. Mathlib use is through the already compiled local SALD scalar pushforward, Gaussian coordinate-law, and variance bridges. This theorem does not prove hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, any scalar Taylor source fields, any dominated-remainder field, or the selected weak-test Hessian source-contract fields.

def cycle191GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceIntegralLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle191_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_integral_lower2"
  statement := "Cycle 191 middle dynamic-leaf worker packet. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hBrownianCoordinateGeneratorNormalizedLawDef is no longer primitive inside hBrownianCoordinateGeneratorSourceIntegralDef once the source supplies hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, and hVarianceDef. SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw compiles the direct composition of the scalar-pushforward coordinate-generator bridge and the standard-Gaussian vector coordinate-law bridge. Source anchors appendix.tex:958-970, appendix.tex:983-996, appendix.tex:1161-1170, and appendix.tex:1379-1387 keep the normalized Brownian coordinate and weak-FP sigma_eta^2/2 diffusion prefactor separate. Remaining exact Brownian/Ito backend: hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSourceTaylorIntegrandSelectedIncrementDef, hSelectedIncrementEndpointDef, hSelectedEndpointCoordinateLineDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, hRemainderGeneratorLimitDef, hRemainderMeas, hRemainderBound, and hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfScalarPushforwardAndStdGaussianVectorLaw",
    "SALD.selectedWeakTestBrownianCoordinateGeneratorNormalizedLawDefOfScalarPushforward",
    "SALD.selectedWeakTestBrownianCoordinateGeneratorSourceIntegralDefOfStdGaussianVectorLaw",
    "hBrownianCoordinateGeneratorSourceIntegralDef",
    "hBrownianCoordinateGeneratorNormalizedLawDef",
    "hScalarMeas",
    "hNormalizedCoordinateLawDef",
    "hSourceTaylorIntegrandMeas",
    "hGeneratorPullbackDef",
    "hNormalizedVectorLaw",
    "hCoordinateLawDef",
    "hVarianceDef",
    "normalizedCoordinateLaw",
    "sourceTaylorIntegrand",
    "brownianCoordinateGenerator",
    "variance",
    "ProbabilityTheory.stdGaussian",
    "ProbabilityTheory.gaussianReal",
    "MeasureTheory.integral_map",
    "appendix.tex:958-970",
    "appendix.tex:983-996",
    "appendix.tex:1161-1170",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No external SLT file was consulted, imported, ported, called, queued, or marked formalized. Mathlib use is through the already compiled local SALD scalar pushforward, Gaussian coordinate-law, and variance bridges. This theorem does not prove hScalarMeas, hNormalizedCoordinateLawDef, hSourceTaylorIntegrandMeas, hGeneratorPullbackDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, any scalar Taylor source fields, any dominated-remainder field, or the selected weak-test Hessian source-contract fields."

/-- Cycle-191 proof-DAG pane for the source-integral scalar-pushforward bridge. -/