AutoSamplingTheory.SALD.cycle168GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceContDiffMiddleObligation

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 cycle168GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceContDiffMiddleObligation :
    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.cycle168_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_contdiff_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 168 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hLine below SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff is no longer primitive once the selected source test has ambient global ContDiffOn Real 2 regularity on Set.univ. SALD.gaussianRealSelectedTestLineContDiffOnOfSourceContDiffOn compiles the affine-line composition q |-> sourceTest (x + q • e), and SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSourceContDiffOn feeds that line regularity into the cycle-167 global-line Taylor bridge. Remaining source-cited boundary: prove ambient selected-test ContDiffOn Real 2 and the two signed interval second-derivative domination hypotheses from the paper's selected-test bounded-Hessian/regularity assumptions. hSecondCoeff, Taylor moment decomposition, quadratic-variation normalization, and coordinate-sum leaves remain separate.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.gaussianRealSelectedTestLineContDiffOnOfSourceContDiffOn
2. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSourceContDiffOn
3. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff
4. hSource
5. hLine
6. hNonnegSecond
7. hNegSecond
8. contDiffOn_univ
9. ContDiff.comp
10. ContDiff.add
11. ContDiff.smul_const
12. contDiff_const
13. contDiff_id
14. appendix.tex:984-995
15. appendix.tex:1379-1387
16. 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.

Dynamic-leaf middle packet inside the scalar Brownian/Ito illness area. Consulted local Mathlib ContDiff Basic/Operations/Comp APIs; the configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized. This rejects wrapper churn by only supplying hLine from ambient selected-test C^2 regularity while preserving the signed second-derivative domination leaves.

def cycle168GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoSourceContDiffMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle168_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_source_contdiff_middle"
  statement := "Cycle 168 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hLine below SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff is no longer primitive once the selected source test has ambient global ContDiffOn Real 2 regularity on Set.univ. SALD.gaussianRealSelectedTestLineContDiffOnOfSourceContDiffOn compiles the affine-line composition q |-> sourceTest (x + q • e), and SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSourceContDiffOn feeds that line regularity into the cycle-167 global-line Taylor bridge. Remaining source-cited boundary: prove ambient selected-test ContDiffOn Real 2 and the two signed interval second-derivative domination hypotheses from the paper's selected-test bounded-Hessian/regularity assumptions. hSecondCoeff, Taylor moment decomposition, quadratic-variation normalization, and coordinate-sum leaves remain separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.gaussianRealSelectedTestLineContDiffOnOfSourceContDiffOn",
    "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSourceContDiffOn",
    "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff",
    "hSource",
    "hLine",
    "hNonnegSecond",
    "hNegSecond",
    "contDiffOn_univ",
    "ContDiff.comp",
    "ContDiff.add",
    "ContDiff.smul_const",
    "contDiff_const",
    "contDiff_id",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf middle packet inside the scalar Brownian/Ito illness area. Consulted local Mathlib ContDiff Basic/Operations/Comp APIs; the configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized. This rejects wrapper churn by only supplying hLine from ambient selected-test C^2 regularity while preserving the signed second-derivative domination leaves."

/-- Cycle-168 lower_2 global line-second-derivative narrowing packet. -/