AutoSamplingTheory.SALD.cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation

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 cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation :
    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.cycle180_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_moment_middle

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 180 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoTaylorMomentDecomposition under SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder is no longer primitive once the source supplies hBrownianCoordinateGeneratorTaylorIntegralDef, hLinearInt, hQuadraticInt, hRemainderInt, and hRemainderGeneratorLimitDef. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefs compiles the integral-linearity bridge: rewrite the source Taylor integral for brownianCoordinateGenerator, split the integral of linearCoeff*z + quadraticCoeff*z^2 + normalizedRemainder by MeasureTheory.integral_add using explicit Integrable fields, pull out scalar coefficients by MeasureTheory.integral_const_mul, and rewrite the remainder integral by hRemainderGeneratorLimitDef. Remaining exact source boundary is the frozen scalar Brownian Taylor integral definition plus summand integrability and the normalized remainder definition from appendix.tex:984-995, appendix.tex:1170-1176, and appendix.tex:1379-1387. hSourceHasHessian/hSourceHessianBound remain separate source-contract gaps; hScalarLineTaylorCoeffDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSecondCoeff, normalized-remainder domination/DCT data, and coordinate-sum 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

SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefs
SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder
SALD.gaussianRealZeroOneDimTaylorMomentContribution
hFrozenScalarBrownianItoTaylorMomentDecomposition
hBrownianCoordinateGeneratorTaylorIntegralDef
hLinearInt
hQuadraticInt
hRemainderInt
hRemainderGeneratorLimitDef
normalizedRemainder
brownianCoordinateGenerator
linearCoeff
quadraticCoeff
remainderGeneratorLimit
MeasureTheory.integral_add
MeasureTheory.integral_const_mul
hScalarLineTaylorCoeffDef
hNormalizedVectorLaw
hCoordinateLawDef
hVarianceDef
hSecondCoeff
hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
hFrozenScalarBrownianItoEventFieldCoordinateSum
hSourceHasHessian
hSourceHessianBound
eq:general_moving_target_SALD_frozen_interp
appendix.tex:984-995
appendix.tex:1170-1176
appendix.tex:1379-1387
source-contract-gap for selected weak-test Hessian fields
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. Mathlib consultation was limited to the already imported Bochner integral linearity declarations MeasureTheory.integral_add and MeasureTheory.integral_const_mul plus the existing local Gaussian/Taylor chain. This packet rejects Hessian wrapper churn, VP score-Hessian substitution, sigma_eta^2/2 event-field moves, and sald_version_2.tex use.

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 cycle180GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorMomentMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle180_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_moment_middle"
  statement := "Cycle 180 middle dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: hFrozenScalarBrownianItoTaylorMomentDecomposition under SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder is no longer primitive once the source supplies hBrownianCoordinateGeneratorTaylorIntegralDef, hLinearInt, hQuadraticInt, hRemainderInt, and hRemainderGeneratorLimitDef. SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefs compiles the integral-linearity bridge: rewrite the source Taylor integral for brownianCoordinateGenerator, split the integral of linearCoeff*z + quadraticCoeff*z^2 + normalizedRemainder by MeasureTheory.integral_add using explicit Integrable fields, pull out scalar coefficients by MeasureTheory.integral_const_mul, and rewrite the remainder integral by hRemainderGeneratorLimitDef. Remaining exact source boundary is the frozen scalar Brownian Taylor integral definition plus summand integrability and the normalized remainder definition from appendix.tex:984-995, appendix.tex:1170-1176, and appendix.tex:1379-1387. hSourceHasHessian/hSourceHessianBound remain separate source-contract gaps; hScalarLineTaylorCoeffDef, hNormalizedVectorLaw, hCoordinateLawDef, hVarianceDef, hSecondCoeff, normalized-remainder domination/DCT data, and coordinate-sum remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.formalized
  dependsOn := [
    "SALD.selectedWeakTestFrozenScalarBrownianItoTaylorMomentDecompositionOfIntegralDefs",
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoOneDimTaylorOfGaussianMomentRemainder",
    "SALD.gaussianRealZeroOneDimTaylorMomentContribution",
    "hFrozenScalarBrownianItoTaylorMomentDecomposition",
    "hBrownianCoordinateGeneratorTaylorIntegralDef",
    "hLinearInt",
    "hQuadraticInt",
    "hRemainderInt",
    "hRemainderGeneratorLimitDef",
    "normalizedRemainder",
    "brownianCoordinateGenerator",
    "linearCoeff",
    "quadraticCoeff",
    "remainderGeneratorLimit",
    "MeasureTheory.integral_add",
    "MeasureTheory.integral_const_mul",
    "hScalarLineTaylorCoeffDef",
    "hNormalizedVectorLaw",
    "hCoordinateLawDef",
    "hVarianceDef",
    "hSecondCoeff",
    "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
    "hFrozenScalarBrownianItoEventFieldCoordinateSum",
    "hSourceHasHessian",
    "hSourceHessianBound",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:984-995",
    "appendix.tex:1170-1176",
    "appendix.tex:1379-1387",
    "source-contract-gap for selected weak-test Hessian fields",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "No local SLT file was consulted or imported. Mathlib consultation was limited to the already imported Bochner integral linearity declarations MeasureTheory.integral_add and MeasureTheory.integral_const_mul plus the existing local Gaussian/Taylor chain. This packet rejects Hessian wrapper churn, VP score-Hessian substitution, sigma_eta^2/2 event-field moves, and sald_version_2.tex use."

/-- Cycle-180 lower_1 compiled polynomial-integrability bridge.

This proof-scout packet discharges the linear and quadratic Gaussian summand
integrability inputs in the Taylor moment split.  The remaining source-facing
Taylor-integral boundary is the coordinate-generator Taylor integral
definition, normalized-remainder integrability, and the remainder-integral
definition.
-/

Existing module entry · Audited data-reader index · All teaching coverage