AutoSamplingTheory.SALD.cycle162GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderDctLowerObligation

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 cycle162GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderDctLowerObligation :
    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_normalized_remainder_dct_lower

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 lower_2 packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes no longer needs to keep the dominated-convergence integral theorem open. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT compiles the Mathlib DCT step for the normalized scalar Taylor remainder integral under ProbabilityTheory.gaussianReal 0 v from eventual AEStronglyMeasurable, eventual a.e. domination by an integrable bound, and a.e. pointwise convergence to zero along nhdsWithin 0 (Set.Ioi 0). The remaining smaller source-cited theorem is the source Taylor pointwise limit for the concrete selected-test scalar path, plus the separate hFrozenScalarBrownianItoTaylorMomentDecomposition and hFrozenScalarBrownianItoQuadraticVariationNormalization hypotheses. The sibling hFrozenScalarBrownianItoEventFieldCoordinateSum remains explicit; sigma_eta^2/2 stays outside the event field.

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.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT
2. MeasureTheory.tendsto_integral_filter_of_dominated_convergence
3. MeasureTheory.AEStronglyMeasurable
4. MeasureTheory.Integrable
5. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
6. hFrozenScalarBrownianItoTaylorMomentDecomposition
7. hFrozenScalarBrownianItoQuadraticVariationNormalization
8. Real.taylor_tendsto
9. taylor_isLittleO
10. Mathlib.MeasureTheory.Integral.DominatedConvergence
11. Mathlib.Analysis.Calculus.Taylor
12. eq:general_moving_target_SALD_frozen_interp
13. appendix.tex:984-995
14. appendix.tex:1379-1387
15. 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 proof-producing packet inside the scalar Brownian/Ito illness area. Consulted Mathlib dominated convergence for the compiled integral-limit theorem; Mathlib Taylor remains cited for the next pointwise source step. The configured local SLT clone is absent, and no SLT theorem was imported or marked formalized.

def cycle162GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderDctLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle162_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_dct_lower"
  statement := "Cycle 162 lower_2 packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes no longer needs to keep the dominated-convergence integral theorem open. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT compiles the Mathlib DCT step for the normalized scalar Taylor remainder integral under ProbabilityTheory.gaussianReal 0 v from eventual AEStronglyMeasurable, eventual a.e. domination by an integrable bound, and a.e. pointwise convergence to zero along nhdsWithin 0 (Set.Ioi 0). The remaining smaller source-cited theorem is the source Taylor pointwise limit for the concrete selected-test scalar path, plus the separate hFrozenScalarBrownianItoTaylorMomentDecomposition and hFrozenScalarBrownianItoQuadraticVariationNormalization hypotheses. The sibling hFrozenScalarBrownianItoEventFieldCoordinateSum remains explicit; sigma_eta^2/2 stays outside the event field."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT",
    "MeasureTheory.tendsto_integral_filter_of_dominated_convergence",
    "MeasureTheory.AEStronglyMeasurable",
    "MeasureTheory.Integrable",
    "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
    "hFrozenScalarBrownianItoTaylorMomentDecomposition",
    "hFrozenScalarBrownianItoQuadraticVariationNormalization",
    "Real.taylor_tendsto",
    "taylor_isLittleO",
    "Mathlib.MeasureTheory.Integral.DominatedConvergence",
    "Mathlib.Analysis.Calculus.Taylor",
    "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 lower_2 proof-producing packet inside the scalar Brownian/Ito illness area. Consulted Mathlib dominated convergence for the compiled integral-limit theorem; Mathlib Taylor remains cited for the next pointwise source step. The configured local SLT clone is absent, and no SLT theorem was imported or marked formalized."

/-- Cycle-162 proof-DAG pane for the scalar Taylor remainder split. -/