AutoSamplingTheory.SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower2Obligation

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 cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower2Obligation :
    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.cycle174_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_quadratic_variation_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 174 lower_2 dynamic-leaf Lean implementer packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoQuadraticVariationNormalization under SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder is no longer primitive once the source correspondence supplies hQuadraticCoeffDef : testRegular -> forall phi x i, quadraticCoeff phi x i = SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator (selectedTest phi) x ((stdOrthonormalBasis Real E) i) and hVarianceOne : testRegular -> forall phi x i, (variance phi x i : Real) = 1. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne compiles the local algebraic bridge by rewriting the quadratic coefficient and normalized variance, then simplifying multiplication by one. The remaining source-facing gap is exactly the pair hQuadraticCoeffDef/hVarianceOne from appendix.tex:984-995 and appendix.tex:1379-1387, with sigma_eta^2/2 kept outside the Brownian event field. The sibling leaves hFrozenScalarBrownianItoTaylorMomentDecomposition, hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes, and hFrozenScalarBrownianItoEventFieldCoordinateSum remain explicit.

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.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne
2. SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower1Obligation
3. SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
5. SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator
6. hFrozenScalarBrownianItoQuadraticVariationNormalization
7. hQuadraticCoeffDef
8. hVarianceOne
9. hFrozenScalarBrownianItoTaylorMomentDecomposition
10. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
11. hFrozenScalarBrownianItoEventFieldCoordinateSum
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.

No local SLT file was consulted or imported. The compiled proof uses only local rewriting by hQuadraticCoeffDef and hVarianceOne plus Real multiplication by one; it does not promote either source field, move sigma_eta^2/2 into the event field, or return to selected weak-test Hessian wrapper churn.

def cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle174_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_quadratic_variation_lower2"
  statement := "Cycle 174 lower_2 dynamic-leaf Lean implementer packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoQuadraticVariationNormalization under SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder is no longer primitive once the source correspondence supplies hQuadraticCoeffDef : testRegular -> forall phi x i, quadraticCoeff phi x i = SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator (selectedTest phi) x ((stdOrthonormalBasis Real E) i) and hVarianceOne : testRegular -> forall phi x i, (variance phi x i : Real) = 1. SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne compiles the local algebraic bridge by rewriting the quadratic coefficient and normalized variance, then simplifying multiplication by one. The remaining source-facing gap is exactly the pair hQuadraticCoeffDef/hVarianceOne from appendix.tex:984-995 and appendix.tex:1379-1387, with sigma_eta^2/2 kept outside the Brownian event field. The sibling leaves hFrozenScalarBrownianItoTaylorMomentDecomposition, hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes, and hFrozenScalarBrownianItoEventFieldCoordinateSum remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestQuadraticVariationNormalizationOfCoeffDefAndVarianceOne",
    "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationLower1Obligation",
    "SALD.cycle174GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticVariationMiddleObligation",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
    "SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator",
    "hFrozenScalarBrownianItoQuadraticVariationNormalization",
    "hQuadraticCoeffDef",
    "hVarianceOne",
    "hFrozenScalarBrownianItoTaylorMomentDecomposition",
    "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
    "hFrozenScalarBrownianItoEventFieldCoordinateSum",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No local SLT file was consulted or imported. The compiled proof uses only local rewriting by hQuadraticCoeffDef and hVarianceOne plus Real multiplication by one; it does not promote either source field, move sigma_eta^2/2 into the event field, or return to selected weak-test Hessian wrapper churn."

/-- Cycle-174 proof-DAG pane for the Brownian quadratic-variation leaf. -/