AutoSamplingTheory.SALD.cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderQuadraticBoundIntLowerObligation

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 cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderQuadraticBoundIntLowerObligation :
    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.cycle164_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_quadratic_bound_int

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 164 lower_2 dynamic-leaf worker packet. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: the hBoundInt input to SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero for the quadratic Gaussian domination bound fun z => C * z ^ 2. SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable compiles MeasureTheory.Integrable (fun z : Real => C * z ^ 2) (ProbabilityTheory.gaussianReal 0 v) from ProbabilityTheory.integrable_exp_mul_gaussianReal and ProbabilityTheory.integrable_pow_of_integrable_exp_mul. The remaining source-cited DCT input is hBound, namely the pointwise domination of the concrete selected-test normalized remainder by that quadratic bound; Taylor moment decomposition, quadratic-variation normalization, and coordinate-sum leaves remain separate. 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.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable
2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero
3. ProbabilityTheory.integrable_exp_mul_gaussianReal
4. ProbabilityTheory.integrable_pow_of_integrable_exp_mul
5. MeasureTheory.Integrable.const_mul
6. hBound
7. hBoundInt
8. hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes
9. hFrozenScalarBrownianItoTaylorMomentDecomposition
10. hFrozenScalarBrownianItoQuadraticVariationNormalization
11. hFrozenScalarBrownianItoEventFieldCoordinateSum
12. Mathlib.Probability.Distributions.Gaussian.Real
13. Mathlib.Probability.Moments.IntegrableExpMul
14. eq:general_moving_target_SALD_frozen_interp
15. appendix.tex:984-995
16. appendix.tex:1379-1387
17. 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 worker packet inside the scalar Brownian/Ito illness area. It proves only Gaussian quadratic-bound integrability for the DCT hBoundInt input after the intended bound has the source shape C * z^2. The configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized.

def cycle164GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderQuadraticBoundIntLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle164_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_normalized_remainder_quadratic_bound_int"
  statement := "Cycle 164 lower_2 dynamic-leaf worker packet. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: the hBoundInt input to SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero for the quadratic Gaussian domination bound fun z => C * z ^ 2. SALD.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable compiles MeasureTheory.Integrable (fun z : Real => C * z ^ 2) (ProbabilityTheory.gaussianReal 0 v) from ProbabilityTheory.integrable_exp_mul_gaussianReal and ProbabilityTheory.integrable_pow_of_integrable_exp_mul. The remaining source-cited DCT input is hBound, namely the pointwise domination of the concrete selected-test normalized remainder by that quadratic bound; Taylor moment decomposition, quadratic-variation normalization, and coordinate-sum leaves remain separate. 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.gaussianRealSelectedTestLineSecondOrderQuadraticBoundIntegrable",
    "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderIntegralTendstoZero",
    "ProbabilityTheory.integrable_exp_mul_gaussianReal",
    "ProbabilityTheory.integrable_pow_of_integrable_exp_mul",
    "MeasureTheory.Integrable.const_mul",
    "hBound",
    "hBoundInt",
    "hFrozenScalarBrownianItoNormalizedTaylorRemainderVanishes",
    "hFrozenScalarBrownianItoTaylorMomentDecomposition",
    "hFrozenScalarBrownianItoQuadraticVariationNormalization",
    "hFrozenScalarBrownianItoEventFieldCoordinateSum",
    "Mathlib.Probability.Distributions.Gaussian.Real",
    "Mathlib.Probability.Moments.IntegrableExpMul",
    "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 worker packet inside the scalar Brownian/Ito illness area. It proves only Gaussian quadratic-bound integrability for the DCT hBoundInt input after the intended bound has the source shape C * z^2. The configured local SLT clone is absent, and no SLT theorem was imported, ported, or marked formalized."

/-- Cycle-164 proof-DAG pane for the concrete normalized-remainder measurability leaf. -/