AutoSamplingTheory.SALD.cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation

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 cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation :
    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.cycle163_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_source_eq

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 163 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hSourceEq input below SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq is no longer open for the concrete selected-test scalar Taylor normalizedRemainder. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder defines the source-shaped expression, SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq proves the eventual Gaussian-a.e. source equality by definitional equality, and SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero derives the DCT integral limit without an hSourceEq premise. Remaining source-cited inputs are hMeas, hBound, and hBoundInt for this concrete remainder, plus hFrozenScalarBrownianItoTaylorMomentDecomposition, hFrozenScalarBrownianItoQuadraticVariationNormalization, and the sibling hFrozenScalarBrownianItoEventFieldCoordinateSum. 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.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.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder
2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq
3. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
4. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq
5. SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE
6. SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT
7. taylorWithinEval
8. Filter.Eventually.of_forall
9. hMeas
10. hBound
11. hBoundInt
12. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
13. hFrozenScalarBrownianItoTaylorMomentDecomposition
14. hFrozenScalarBrownianItoQuadraticVariationNormalization
15. hFrozenScalarBrownianItoEventFieldCoordinateSum
16. Mathlib.Analysis.Calculus.Taylor
17. Mathlib.MeasureTheory.Integral.DominatedConvergence
18. eq:general_moving_target_SALD_frozen_interp
19. appendix.tex:984-995
20. appendix.tex:1379-1387
21. 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. It discharges the source-equality bridge for the source-shaped selected-test normalized remainder and leaves only concrete DCT regularity/domination plus the separate moment, quadratic-variation, and coordinate-sum source leaves. Local Mathlib Taylor/DCT APIs were already imported; the configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized.

def cycle163GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderSourceEqLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle163_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_source_eq"
  statement := "Cycle 163 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hSourceEq input below SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq is no longer open for the concrete selected-test scalar Taylor normalizedRemainder. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder defines the source-shaped expression, SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq proves the eventual Gaussian-a.e. source equality by definitional equality, and SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero derives the DCT integral limit without an hSourceEq premise. Remaining source-cited inputs are hMeas, hBound, and hBoundInt for this concrete remainder, plus hFrozenScalarBrownianItoTaylorMomentDecomposition, hFrozenScalarBrownianItoQuadraticVariationNormalization, and the sibling hFrozenScalarBrownianItoEventFieldCoordinateSum. 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.formalized
  dependsOn := [
    "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainder",
    "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderSourceEq",
    "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
    "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfSelectedTestLineEq",
    "SALD.gaussianRealSelectedTestLineSecondOrderTaylorRemainderPointwiseAE",
    "SALD.gaussianRealNormalizedTaylorRemainderIntegralTendstoZeroOfDCT",
    "taylorWithinEval",
    "Filter.Eventually.of_forall",
    "hMeas",
    "hBound",
    "hBoundInt",
    "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
    "hFrozenScalarBrownianItoTaylorMomentDecomposition",
    "hFrozenScalarBrownianItoQuadraticVariationNormalization",
    "hFrozenScalarBrownianItoEventFieldCoordinateSum",
    "Mathlib.Analysis.Calculus.Taylor",
    "Mathlib.MeasureTheory.Integral.DominatedConvergence",
    "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 packet inside the scalar Brownian/Ito illness area. It discharges the source-equality bridge for the source-shaped selected-test normalized remainder and leaves only concrete DCT regularity/domination plus the separate moment, quadratic-variation, and coordinate-sum source leaves. Local Mathlib Taylor/DCT APIs were already imported; the configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized."

/-- Cycle-163 proof-DAG pane for the source Taylor pointwise limit. -/