AutoSamplingTheory.SALD.cycle165GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorQuotientSplitLower2Obligation

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 cycle165GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorQuotientSplitLower2Obligation :
    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.cycle165_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_quotient_split

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 165 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the deterministic hTaylorQuotientBound input to SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderQuadraticBoundOfTaylorQuotientBound is no longer primitive once a first-order quadratic Taylor-remainder estimate hFirst, a second Taylor coefficient bound hSecondCoeff, and constant bookkeeping 0 <= C and C1 + C2 <= C are supplied. SALD.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff compiles this deterministic algebraic split using taylorWithinEval_succ, taylorCoeffWithin, division by r^2 off r = 0, and the triangle inequality. Remaining source-cited work is to prove the smaller first-order quadratic remainder/second-coefficient estimates from the selected-test regularity route, plus hFrozenScalarBrownianItoTaylorMomentDecomposition, hFrozenScalarBrownianItoQuadraticVariationNormalization, and 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.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff
2. SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderQuadraticBoundOfTaylorQuotientBound
3. hTaylorQuotientBound
4. hFirst
5. hSecondCoeff
6. taylorWithinEval_succ
7. taylorCoeffWithin
8. taylorWithinEval_self
9. norm_sub_le
10. field_simp
11. Mathlib.Analysis.Calculus.Taylor
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.

Dynamic-leaf worker packet in the selected scalar Brownian/Ito normalized-remainder branch. Local Mathlib consulted only through Analysis.Calculus.Taylor and basic norm/field arithmetic already available in the project. The configured local SLT clone is absent, and no SLT theorem was consulted, imported, ported, or marked formalized.

def cycle165GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorQuotientSplitLower2Obligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle165_em_generator_laplacian_event_field_frozen_scalar_brownian_ito_taylor_quotient_split"
  statement := "Cycle 165 lower_2 dynamic-leaf worker packet. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the deterministic hTaylorQuotientBound input to SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderQuadraticBoundOfTaylorQuotientBound is no longer primitive once a first-order quadratic Taylor-remainder estimate hFirst, a second Taylor coefficient bound hSecondCoeff, and constant bookkeeping 0 <= C and C1 + C2 <= C are supplied. SALD.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff compiles this deterministic algebraic split using taylorWithinEval_succ, taylorCoeffWithin, division by r^2 off r = 0, and the triangle inequality. Remaining source-cited work is to prove the smaller first-order quadratic remainder/second-coefficient estimates from the selected-test regularity route, plus hFrozenScalarBrownianItoTaylorMomentDecomposition, hFrozenScalarBrownianItoQuadraticVariationNormalization, and 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.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff",
    "SALD.gaussianRealSelectedTestLineSecondOrderNormalizedRemainderQuadraticBoundOfTaylorQuotientBound",
    "hTaylorQuotientBound",
    "hFirst",
    "hSecondCoeff",
    "taylorWithinEval_succ",
    "taylorCoeffWithin",
    "taylorWithinEval_self",
    "norm_sub_le",
    "field_simp",
    "Mathlib.Analysis.Calculus.Taylor",
    "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 in the selected scalar Brownian/Ito normalized-remainder branch. Local Mathlib consulted only through Analysis.Calculus.Taylor and basic norm/field arithmetic already available in the project. The configured local SLT clone is absent, and no SLT theorem was consulted, imported, ported, or marked formalized."

/-- Cycle-165 proof-DAG pane for the concrete normalized-remainder domination leaf. -/