AutoSamplingTheory.SALD.cycle175GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticCoeffLower2Obligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle175GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticCoeffLower2Obligation :
    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.cycle175_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_quadratic_coeff_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 175 lower_2 dynamic-leaf Lean implementer packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hQuadraticCoeffDef is no longer primitive once the source correspondence supplies hSecondTaylorCoeffDef : testRegular -> forall phi x i, quadraticCoeff phi x i = iteratedFDeriv Real 2 (selectedTest phi) x ![(stdOrthonormalBasis Real E) i, (stdOrthonormalBasis Real E) i]. SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef compiles the definitional bridge by unfolding SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator. The remaining source-facing gap is exactly hSecondTaylorCoeffDef from appendix.tex:984-995 and appendix.tex:1379-1387; hVarianceOne, hSecondCoeff, hSourceHasHessian/hSourceHessianBound, Taylor moment decomposition, normalized-remainder DCT data, and coordinate-sum remain separate. The theorem does not derive the coefficient from unexpanded testRegular, does not define sourceHessian from the desired conclusion, does not move sigma_eta^2/2 inside the event field, and does not use sald_version_2.tex.

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

SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef
SALD.cycle175GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticCoeffLower1Obligation
SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator
hSecondTaylorCoeffDef
hQuadraticCoeffDef
hVarianceOne
hSecondCoeff
hSourceHasHessian
hSourceHessianBound
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 : 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 is local definitional unfolding of SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator against hSecondTaylorCoeffDef; it keeps hSecondTaylorCoeffDef as the source-cited analytic boundary.

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle175GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticCoeffLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle175_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_quadratic_coeff_lower2"
  statement := "Cycle 175 lower_2 dynamic-leaf Lean implementer packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hQuadraticCoeffDef is no longer primitive once the source correspondence supplies hSecondTaylorCoeffDef : testRegular -> forall phi x i, quadraticCoeff phi x i = iteratedFDeriv Real 2 (selectedTest phi) x ![(stdOrthonormalBasis Real E) i, (stdOrthonormalBasis Real E) i]. SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef compiles the definitional bridge by unfolding SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator. The remaining source-facing gap is exactly hSecondTaylorCoeffDef from appendix.tex:984-995 and appendix.tex:1379-1387; hVarianceOne, hSecondCoeff, hSourceHasHessian/hSourceHessianBound, Taylor moment decomposition, normalized-remainder DCT data, and coordinate-sum remain separate. The theorem does not derive the coefficient from unexpanded testRegular, does not define sourceHessian from the desired conclusion, does not move sigma_eta^2/2 inside the event field, and does not use sald_version_2.tex."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestQuadraticCoeffDefOfSecondTaylorCoeffDef",
    "SALD.cycle175GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoQuadraticCoeffLower1Obligation",
    "SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator",
    "hSecondTaylorCoeffDef",
    "hQuadraticCoeffDef",
    "hVarianceOne",
    "hSecondCoeff",
    "hSourceHasHessian",
    "hSourceHessianBound",
    "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 is local definitional unfolding of SALD.emFrozenScalarBrownianItoOneDimTaylorGenerator against hSecondTaylorCoeffDef; it keeps hSecondTaylorCoeffDef as the source-cited analytic boundary."

/-- Cycle-175 proof-DAG pane for the selected-line Taylor-domination bridge. -/

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