AutoSamplingTheory.SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation

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 cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation :
    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.cycle86_weak_fp_generator_boundary_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 86 middle translates appendix.tex lines 1379-1387 into the lower-ready generator-to-law theorem boundary. For every admissible weak test phi and interior time s, the desired local theorem should start from the sample-space EM interpolation hatX_s, prove or assume the sample-path/parametric-integral derivative HasDerivAt (fun s => integral omega, phi (hatX_s omega) dP) of the frozen EM generator action, transport that derivative across hatRhoS = Law(hatX_s) using AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, and only then feed the resulting partialS phi = generatorAction phi into the existing source-sign wrappers. The lower packet is classified narrows-source-cited-boundary unless it actually removes the supplied generator/time-derivative hypothesis. The remaining named subtheorems are sample-path generator differentiation, Bochner/parametric integral interchange for the time-dependent interpolation, drift source-action identification through the cycle-85 conditional-field regularity, diffusion/quadratic-variation source-action identification with coefficient sigma_eta^2/2, and admissible-test density/boundary hypotheses.

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.obligation — 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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation
2. AutoSamplingTheory.lawMapIntegral
3. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
4. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
5. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
8. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
9. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
10. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
11. Mathlib.Analysis.Calculus.ParametricIntegral
12. Mathlib.MeasureTheory.Integral.Bochner.Basic
13. 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.

Middle source-to-Lean boundary, classified narrows-source-cited-boundary. It does not add a theorem wrapper, discharge the generator/time-derivative hypothesis, prove weak FP/KL differentiation, or promote any theorem, SLT, or Lake status.

def cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle86_weak_fp_generator_boundary_middle"
  statement := "Cycle 86 middle translates appendix.tex lines 1379-1387 into the lower-ready generator-to-law theorem boundary. For every admissible weak test phi and interior time s, the desired local theorem should start from the sample-space EM interpolation hatX_s, prove or assume the sample-path/parametric-integral derivative HasDerivAt (fun s => integral omega, phi (hatX_s omega) dP) of the frozen EM generator action, transport that derivative across hatRhoS = Law(hatX_s) using AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, and only then feed the resulting partialS phi = generatorAction phi into the existing source-sign wrappers. The lower packet is classified narrows-source-cited-boundary unless it actually removes the supplied generator/time-derivative hypothesis. The remaining named subtheorems are sample-path generator differentiation, Bochner/parametric integral interchange for the time-dependent interpolation, drift source-action identification through the cycle-85 conditional-field regularity, diffusion/quadratic-variation source-action identification with coefficient sigma_eta^2/2, and admissible-test density/boundary hypotheses."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation",
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
    "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle source-to-Lean boundary, classified narrows-source-cited-boundary. It does not add a theorem wrapper, discharge the generator/time-derivative hypothesis, prove weak FP/KL differentiation, or promote any theorem, SLT, or Lake status."

/-- Cycle-86 lower obligation for the sample-space derivative to law weak-FP
generator handoff. -/