AutoSamplingTheory.SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitMiddleObligation

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 cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitMiddleObligation :
    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.cycle92_weak_fp_split_generator_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 92 middle records the active backend judgment: cycle 91 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387. The lower target is the generator-to-law weak Fokker-Planck boundary consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff. To avoid wrapper churn, the selected proof-producing refinement must remove one supplied input; this cycle targets hgeneratorSplit by using a definitionally split generator action driftAction + diffusionAction while keeping sample-path HasDerivAt, law weak derivative, drift source action, and diffusion source action as explicit remaining analytic boundaries.

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.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff
3. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
4. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
5. SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation
6. Mathlib.Analysis.Calculus.ParametricIntegral
7. Mathlib.MeasureTheory.Integral.Bochner.Basic
8. appendix.tex:1379-1387
9. 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 synchronization only. The source signs and sigma_eta^2/2 coefficient are fixed; no weak Fokker-Planck theorem, KL derivative, theorem closure, SLT result, or Lake dependency is promoted.

def cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle92_weak_fp_split_generator_middle"
  statement := "Cycle 92 middle records the active backend judgment: cycle 91 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387. The lower target is the generator-to-law weak Fokker-Planck boundary consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff. To avoid wrapper churn, the selected proof-producing refinement must remove one supplied input; this cycle targets hgeneratorSplit by using a definitionally split generator action driftAction + diffusionAction while keeping sample-path HasDerivAt, law weak derivative, drift source action, and diffusion source action as explicit remaining analytic boundaries."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
    "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle source-to-Lean synchronization only. The source signs and sigma_eta^2/2 coefficient are fixed; no weak Fokker-Planck theorem, KL derivative, theorem closure, SLT result, or Lake dependency is promoted."

/-- Cycle-92 lower obligation for the split-generator law-transport handoff. -/