AutoSamplingTheory.SALD.cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralRawTermsMiddleObligation

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 cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralRawTermsMiddleObligation :
    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.cycle189_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_integral_raw_terms_middle

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 189 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hBrownianCoordinateGeneratorTaylorIntegralDef is no longer primitive once the source correspondence supplies hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, and hScalarLineTaylorCoeffDef. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs compiles the bridge by composing the cycle-183 source-integral congruence, the pointwise-to-a.e. adapter, the cycle-186 source-term pointwise bridge, the cycle-186 source-linear bridge, the cycle-187 source-quadratic bridge, and the cycle-188 raw selected-line Taylor split. Source anchors appendix.tex:958-970, appendix.tex:984-995, appendix.tex:1170-1176, 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: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar law/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, 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.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs
2. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralAndAE
3. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise
4. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
5. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
6. SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs
7. SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef
8. SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef
9. hBrownianCoordinateGeneratorTaylorIntegralDef
10. hBrownianCoordinateGeneratorSourceIntegralDef
11. hBrownianCoordinateGeneratorTaylorIntegrandAE
12. hSourceTaylorIntegrandPointwise
13. hSourceTaylorIntegrandRawDef
14. hSelectedLineTaylorRawSplitDef
15. hSourceLinearTermTaylorDef
16. hScalarLineFirstCoeffDef
17. hSourceQuadraticTermTaylorDef
18. hScalarLineTaylorCoeffDef
19. sourceTaylorIntegrand
20. sourceLinearTerm
21. sourceQuadraticTerm
22. normalizedRemainder
23. selectedTest
24. deriv
25. taylorCoeffWithin
26. Set.univ
27. stdOrthonormalBasis
28. ProbabilityTheory.gaussianReal
29. appendix.tex:958-970
30. appendix.tex:984-995
31. appendix.tex:1170-1176
32. appendix.tex:1379-1387
33. 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, or marked formalized. Mathlib use is limited to existing deriv/taylorCoeffWithin/Set.univ notation and the already imported Gaussian measure notation. This packet does not prove hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, scalar coefficient source fields, normalized-remainder domination fields, or selected weak-test Hessian fields.

def cycle189GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorIntegralRawTermsMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle189_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_integral_raw_terms_middle"
  statement := "Cycle 189 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hBrownianCoordinateGeneratorTaylorIntegralDef is no longer primitive once the source correspondence supplies hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, and hScalarLineTaylorCoeffDef. SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs compiles the bridge by composing the cycle-183 source-integral congruence, the pointwise-to-a.e. adapter, the cycle-186 source-term pointwise bridge, the cycle-186 source-linear bridge, the cycle-187 source-quadratic bridge, and the cycle-188 raw selected-line Taylor split. Source anchors appendix.tex:958-970, appendix.tex:984-995, appendix.tex:1170-1176, 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: hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar law/measurability fields, normalized-remainder pullback fields, hRemainderGeneratorLimitDef, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralRawTaylorAndTermDefs",
    "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegralDefOfSourceIntegralAndAE",
    "SALD.selectedWeakTestBrownianCoordinateGeneratorTaylorIntegrandAEOfPointwise",
    "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
    "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
    "SALD.selectedWeakTestSelectedLineTaylorSplitDefOfRawTaylorAndTermDefs",
    "SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef",
    "SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef",
    "hBrownianCoordinateGeneratorTaylorIntegralDef",
    "hBrownianCoordinateGeneratorSourceIntegralDef",
    "hBrownianCoordinateGeneratorTaylorIntegrandAE",
    "hSourceTaylorIntegrandPointwise",
    "hSourceTaylorIntegrandRawDef",
    "hSelectedLineTaylorRawSplitDef",
    "hSourceLinearTermTaylorDef",
    "hScalarLineFirstCoeffDef",
    "hSourceQuadraticTermTaylorDef",
    "hScalarLineTaylorCoeffDef",
    "sourceTaylorIntegrand",
    "sourceLinearTerm",
    "sourceQuadraticTerm",
    "normalizedRemainder",
    "selectedTest",
    "deriv",
    "taylorCoeffWithin",
    "Set.univ",
    "stdOrthonormalBasis",
    "ProbabilityTheory.gaussianReal",
    "appendix.tex:958-970",
    "appendix.tex:984-995",
    "appendix.tex:1170-1176",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No external SLT file was consulted, imported, ported, called, or marked formalized. Mathlib use is limited to existing deriv/taylorCoeffWithin/Set.univ notation and the already imported Gaussian measure notation. This packet does not prove hBrownianCoordinateGeneratorSourceIntegralDef, hSourceTaylorIntegrandRawDef, hSelectedLineTaylorRawSplitDef, scalar coefficient source fields, normalized-remainder domination fields, or selected weak-test Hessian fields."

/-- Cycle-189 proof-DAG pane for the raw-term coordinate Taylor integral bridge. -/