AutoSamplingTheory.SALD.cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoLineContDiffLower2Obligation

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 cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoLineContDiffLower2Obligation :
    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.cycle167_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_line_contdiff_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 167 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hNonnegCont, hNegCont, hNonnegBaseDiff, and hNegBaseDiff below SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorBaseDiff are no longer primitive once the selected scalar line has global ContDiffOn Real 2 regularity on Set.univ. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff compiles the all-r first-order quadratic remainder from one global selected-line ContDiffOn hypothesis plus the two signed interval second-derivative domination hypotheses. The reflected negative-line regularity is supplied by composing the global line with q |-> -q, using Mathlib ContDiff.comp, contDiff_neg, and contDiff_id; base differentiability at 0 is supplied by ContDiffOn.contDiffAt and ContDiffAt.differentiableAt. Remaining source-cited boundary: prove the global selected-line ContDiffOn Real 2 fact and the signed interval second-derivative domination 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.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff
2. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorBaseDiff
3. hLine
4. hNonnegSecond
5. hNegSecond
6. hNonnegCont
7. hNegCont
8. hNonnegBaseDiff
9. hNegBaseDiff
10. ContDiffOn.mono
11. contDiffOn_univ
12. ContDiff.comp
13. contDiff_neg
14. contDiff_id
15. ContDiffOn.contDiffAt
16. ContDiffAt.differentiableAt
17. appendix.tex:984-995
18. appendix.tex:1379-1387
19. 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 lower_2 packet inside the scalar Brownian/Ito illness area. Consulted local Mathlib ContDiff composition/basic operations and Taylor-adjacent APIs already imported by this file; the configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized. This rejects wrapper churn by removing four interval/base regularity hypotheses and exposing global line ContDiff plus second-derivative domination as the smaller source-facing boundary.

def cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoLineContDiffLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle167_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_line_contdiff_lower2"
  statement := "Cycle 167 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hNonnegCont, hNegCont, hNonnegBaseDiff, and hNegBaseDiff below SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorBaseDiff are no longer primitive once the selected scalar line has global ContDiffOn Real 2 regularity on Set.univ. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff compiles the all-r first-order quadratic remainder from one global selected-line ContDiffOn hypothesis plus the two signed interval second-derivative domination hypotheses. The reflected negative-line regularity is supplied by composing the global line with q |-> -q, using Mathlib ContDiff.comp, contDiff_neg, and contDiff_id; base differentiability at 0 is supplied by ContDiffOn.contDiffAt and ContDiffAt.differentiableAt. Remaining source-cited boundary: prove the global selected-line ContDiffOn Real 2 fact and the signed interval second-derivative domination 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.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfGlobalLineContDiff",
    "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorBaseDiff",
    "hLine",
    "hNonnegSecond",
    "hNegSecond",
    "hNonnegCont",
    "hNegCont",
    "hNonnegBaseDiff",
    "hNegBaseDiff",
    "ContDiffOn.mono",
    "contDiffOn_univ",
    "ContDiff.comp",
    "contDiff_neg",
    "contDiff_id",
    "ContDiffOn.contDiffAt",
    "ContDiffAt.differentiableAt",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_2 packet inside the scalar Brownian/Ito illness area. Consulted local Mathlib ContDiff composition/basic operations and Taylor-adjacent APIs already imported by this file; the configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized. This rejects wrapper churn by removing four interval/base regularity hypotheses and exposing global line ContDiff plus second-derivative domination as the smaller source-facing boundary."

/-- Cycle-168 ambient selected-test regularity narrowing packet. -/