AutoSamplingTheory.SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation

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 cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation :
    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.cycle94_weak_fp_drift_action_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 94 middle records the active backend judgment: cycle 93 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 selected supplied hypothesis is hdriftSource behind the weak conditional Fokker-Planck source-sign and direct law-derivative handoffs. Replace it by the smaller conditional-drift weak-action boundary: driftAction phi is the weak test-gradient pairing of the named conditional drift barB with phi, and that pairing equals -(driftDiv phi) by the source-cited divergence/no-boundary theorem. Classification: narrows-source-cited-boundary.

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.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation
2. SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation
3. SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
8. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
9. Mathlib.MeasureTheory.Integral.DivergenceTheorem
10. appendix.tex:1368-1377
11. appendix.tex:1379-1387
12. 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. It does not prove the conditional-expectation generator identity, divergence/integration-by-parts theorem, diffusion source action, weak Fokker-Planck equation, KL derivative, theorem closure, SLT result, or any Lake dependency.

def cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle94_weak_fp_drift_action_middle"
  statement := "Cycle 94 middle records the active backend judgment: cycle 93 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 selected supplied hypothesis is hdriftSource behind the weak conditional Fokker-Planck source-sign and direct law-derivative handoffs. Replace it by the smaller conditional-drift weak-action boundary: driftAction phi is the weak test-gradient pairing of the named conditional drift barB with phi, and that pairing equals -(driftDiv phi) by the source-cited divergence/no-boundary theorem. Classification: narrows-source-cited-boundary."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation",
    "SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation",
    "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle source-to-Lean synchronization only. It does not prove the conditional-expectation generator identity, divergence/integration-by-parts theorem, diffusion source action, weak Fokker-Planck equation, KL derivative, theorem closure, SLT result, or any Lake dependency."

/-- Cycle-94 lower obligation for the compiled `barB` drift-action handoff. -/