AutoSamplingTheory.SALD.cycle162GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorRemainderLowerObligation

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 cycle162GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorRemainderLowerObligation :
    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.cycle162_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_remainder

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 162 middle packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoTaylorRemainderGeneratorLimit should no longer be an opaque one-dimensional Brownian/Ito generator theorem. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder compiles the algebraic handoff from a source Taylor moment decomposition, Brownian quadratic-variation normalization, and vanishing normalized Taylor remainder to hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor, using SALD.gaussianRealZeroOneDimTaylorMomentContribution. The remaining smaller source-cited theorem is hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes together with its exact Taylor moment decomposition and quadratic-variation normalization hypotheses under selected-test C^2/integrability assumptions. The sibling hFrozenScalarBrownianItoEventFieldCoordinateSum remains explicit; sigma_eta^2/2 stays outside the event field. Weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM fallback, wrapper churn, broad audit, theorem-status promotion, fake closure, Lake/toolchain change, SLT import, and sald_version_2.tex routes are rejected.

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.obligation — 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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
2. SALD.gaussianRealZeroOneDimTaylorMomentContribution
3. SALD.gaussianRealZeroSecondMoment
4. hFrozenScalarBrownianItoTaylorMomentDecomposition
5. hFrozenScalarBrownianItoQuadraticVariationNormalization
6. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
7. hFrozenScalarBrownianItoTaylorRemainderGeneratorLimit
8. hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor
9. hFrozenScalarBrownianItoEventFieldCoordinateSum
10. SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator
11. ProbabilityTheory.integral_id_gaussianReal
12. eq:general_moving_target_SALD_frozen_interp
13. appendix.tex:984-995
14. appendix.tex:1379-1387
15. Mathlib.Probability.Distributions.Gaussian.Real
16. Mathlib.Analysis.Calculus.Taylor
17. Mathlib.MeasureTheory.Integral.Bochner.Basic
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 worker packet inside the scalar Brownian/Ito illness area. Consulted Mathlib Gaussian.Real for the moment inputs already imported locally; inspected Mathlib Taylor/FDeriv file availability for the remaining analytic remainder boundary. The local SLT clone is absent and no SLT theorem was imported or marked formalized.

def cycle162GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorRemainderLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle162_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_remainder"
  statement := "Cycle 162 middle packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoTaylorRemainderGeneratorLimit should no longer be an opaque one-dimensional Brownian/Ito generator theorem. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder compiles the algebraic handoff from a source Taylor moment decomposition, Brownian quadratic-variation normalization, and vanishing normalized Taylor remainder to hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor, using SALD.gaussianRealZeroOneDimTaylorMomentContribution. The remaining smaller source-cited theorem is hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes together with its exact Taylor moment decomposition and quadratic-variation normalization hypotheses under selected-test C^2/integrability assumptions. The sibling hFrozenScalarBrownianItoEventFieldCoordinateSum remains explicit; sigma_eta^2/2 stays outside the event field. Weak-FP source-field, trace-field, downstream total-event/source-functional, non-EM fallback, wrapper churn, broad audit, theorem-status promotion, fake closure, Lake/toolchain change, SLT import, and sald_version_2.tex routes are rejected."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
    "SALD.gaussianRealZeroOneDimTaylorMomentContribution",
    "SALD.gaussianRealZeroSecondMoment",
    "hFrozenScalarBrownianItoTaylorMomentDecomposition",
    "hFrozenScalarBrownianItoQuadraticVariationNormalization",
    "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
    "hFrozenScalarBrownianItoTaylorRemainderGeneratorLimit",
    "hFrozenScalarBrownianItoCoordinateGeneratorOneDimTaylor",
    "hFrozenScalarBrownianItoEventFieldCoordinateSum",
    "SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator",
    "ProbabilityTheory.integral_id_gaussianReal",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "Mathlib.Probability.Distributions.Gaussian.Real",
    "Mathlib.Analysis.Calculus.Taylor",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet inside the scalar Brownian/Ito illness area. Consulted Mathlib Gaussian.Real for the moment inputs already imported locally; inspected Mathlib Taylor/FDeriv file availability for the remaining analytic remainder boundary. The local SLT clone is absent and no SLT theorem was imported or marked formalized."

/-- Cycle-162 lower_1 scout route for the normalized scalar Taylor remainder. -/