AutoSamplingTheory.SALD.cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectMiddleObligation

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 cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectMiddleObligation :
    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_taylor_reflect

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 middle dynamic-leaf worker packet. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hNegTaylorReflect in SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylor is no longer primitive. SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv compiles the reflected Set.univ first-order Taylor-polynomial compatibility for q |-> sourceTest (x + q • (-e)) at -r from the domain reflection q |-> -q and Mathlib deriv_comp_neg. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect then supplies the all-r first-order quadratic remainder from signed interval ContDiffOn, signed second-derivative domination, and interval-to-Set.univ Taylor compatibility alone. Remaining source-cited boundary: derive hNonnegCont, hNonnegSecond, hNonnegTaylorCompat, hNegCont, hNegSecond, and hNegTaylorCompat from the paper's selected-test bounded-Hessian/regularity hypotheses. 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.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv
2. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect
3. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylor
4. hNegTaylorReflect
5. deriv_comp_neg
6. taylorWithinEval_succ
7. Set.univ
8. hNonnegCont
9. hNonnegSecond
10. hNonnegTaylorCompat
11. hNegCont
12. hNegSecond
13. hNegTaylorCompat
14. selected-test second-derivative or bounded-Hessian source hypothesis
15. eq:general_moving_target_SALD_frozen_interp
16. appendix.tex:984-995
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.

Dynamic-leaf middle packet inside the scalar Brownian/Ito illness area. Consulted local Mathlib Taylor and Deriv.Shift through the imported Taylor stack; no local SLT clone is present and no SLT theorem was imported or marked formalized. This discharges one explicit reflected Taylor compatibility hypothesis and leaves the signed interval regularity/second-derivative/interval-compatibility data as the smaller source-facing boundary.

def cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle167_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_reflect"
  statement := "Cycle 167 middle dynamic-leaf worker packet. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hNegTaylorReflect in SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylor is no longer primitive. SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv compiles the reflected Set.univ first-order Taylor-polynomial compatibility for q |-> sourceTest (x + q • (-e)) at -r from the domain reflection q |-> -q and Mathlib deriv_comp_neg. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect then supplies the all-r first-order quadratic remainder from signed interval ContDiffOn, signed second-derivative domination, and interval-to-Set.univ Taylor compatibility alone. Remaining source-cited boundary: derive hNonnegCont, hNonnegSecond, hNonnegTaylorCompat, hNegCont, hNegSecond, and hNegTaylorCompat from the paper's selected-test bounded-Hessian/regularity hypotheses. hSecondCoeff, Taylor moment decomposition, quadratic-variation normalization, and coordinate-sum leaves remain separate."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv",
    "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect",
    "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylor",
    "hNegTaylorReflect",
    "deriv_comp_neg",
    "taylorWithinEval_succ",
    "Set.univ",
    "hNonnegCont",
    "hNonnegSecond",
    "hNonnegTaylorCompat",
    "hNegCont",
    "hNegSecond",
    "hNegTaylorCompat",
    "selected-test second-derivative or bounded-Hessian source hypothesis",
    "eq:general_moving_target_SALD_frozen_interp",
    "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 Taylor and Deriv.Shift through the imported Taylor stack; no local SLT clone is present and no SLT theorem was imported or marked formalized. This discharges one explicit reflected Taylor compatibility hypothesis and leaves the signed interval regularity/second-derivative/interval-compatibility data as the smaller source-facing boundary."

/-- Cycle-167 proof-DAG pane for the reflected Taylor compatibility discharge. -/