AutoSamplingTheory.SALD.cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefMiddleObligation

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 cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefMiddleObligation :
    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.cycle188_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_taylor_integrand_def_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 188 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hSourceTaylorIntegrandDef is no longer primitive once the source correspondence supplies hSourceTaylorIntegrandRawDef and hSelectedLineTaylorSplitDef. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit compiles the local two-rewrite bridge: rewrite sourceTaylorIntegrand as the selected weak-test increment along the normalized scalar Brownian coordinate line, then rewrite that selected-line increment as sourceLinearTerm plus sourceQuadraticTerm plus normalizedRemainder. Source anchors appendix.tex:958-970, appendix.tex:984-995, appendix.tex:1170-1176, and appendix.tex:1379-1387 keep the EM Brownian coordinate and the weak-FP sigma_eta^2/2 diffusion prefactor separate. Remaining exact Brownian/Ito backend: hSourceTaylorIntegrandRawDef, hSelectedLineTaylorSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar law/measurability fields, normalized-remainder pullback fields, 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.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit
2. SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs
3. SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef
4. SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef
5. hSourceTaylorIntegrandDef
6. hSourceTaylorIntegrandRawDef
7. hSelectedLineTaylorSplitDef
8. sourceTaylorIntegrand
9. sourceLinearTerm
10. sourceQuadraticTerm
11. normalizedRemainder
12. selectedTest
13. stdOrthonormalBasis
14. appendix.tex:958-970
15. appendix.tex:984-995
16. appendix.tex:1170-1176
17. appendix.tex:1379-1387
18. 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. The compiled proof is a local source-definition composition only; it does not prove hSourceTaylorIntegrandRawDef, hSelectedLineTaylorSplitDef, scalar coefficient source fields, normalized-remainder domination fields, or selected weak-test Hessian fields.

def cycle188GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceTaylorIntegrandDefMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle188_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_taylor_integrand_def_middle"
  statement := "Cycle 188 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hSourceTaylorIntegrandDef is no longer primitive once the source correspondence supplies hSourceTaylorIntegrandRawDef and hSelectedLineTaylorSplitDef. SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit compiles the local two-rewrite bridge: rewrite sourceTaylorIntegrand as the selected weak-test increment along the normalized scalar Brownian coordinate line, then rewrite that selected-line increment as sourceLinearTerm plus sourceQuadraticTerm plus normalizedRemainder. Source anchors appendix.tex:958-970, appendix.tex:984-995, appendix.tex:1170-1176, and appendix.tex:1379-1387 keep the EM Brownian coordinate and the weak-FP sigma_eta^2/2 diffusion prefactor separate. Remaining exact Brownian/Ito backend: hSourceTaylorIntegrandRawDef, hSelectedLineTaylorSplitDef, hSourceLinearTermTaylorDef, hScalarLineFirstCoeffDef, hSourceQuadraticTermTaylorDef, hScalarLineTaylorCoeffDef, scalar law/measurability fields, normalized-remainder pullback fields, and hRemainderMeas/hRemainderBound/hRemainderBoundInt. hSourceHasHessian/hSourceHessianBound remain documented source-contract gaps and are not active proof targets."
  source := saldGeneralMovingTargetDiscreteEmSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestSourceTaylorIntegrandDefOfRawAndLineTaylorSplit",
    "SALD.selectedWeakTestSourceTaylorIntegrandPointwiseOfLineTermDefs",
    "SALD.selectedWeakTestSourceLinearTermDefOfScalarLineFirstCoeffDef",
    "SALD.selectedWeakTestSourceQuadraticTermDefOfScalarLineTaylorCoeffDef",
    "hSourceTaylorIntegrandDef",
    "hSourceTaylorIntegrandRawDef",
    "hSelectedLineTaylorSplitDef",
    "sourceTaylorIntegrand",
    "sourceLinearTerm",
    "sourceQuadraticTerm",
    "normalizedRemainder",
    "selectedTest",
    "stdOrthonormalBasis",
    "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, or marked formalized. The compiled proof is a local source-definition composition only; it does not prove hSourceTaylorIntegrandRawDef, hSelectedLineTaylorSplitDef, scalar coefficient source fields, normalized-remainder domination fields, or selected weak-test Hessian fields."

/-- Cycle-188 proof-DAG pane for the source Taylor integrand definition bridge. -/