AutoSamplingTheory.SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation

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 cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation :
    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_lower

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 lower compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction, SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff, and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff for appendix.tex:1379-1387. The handoffs remove the primitive hdriftSource premise from both the direct sample-split generator law-derivative route and the normalized weak-FP source-sign route. In its place they require two narrower source-cited facts: the frozen EM drift generator action equals the weak pairing of barB with the test gradient, and the barB weak pairing equals -(driftDiv phi) by the divergence/no-boundary theorem. Remaining exact analytic boundaries are the conditional-expectation generator action through condDistrib, the divergence/integration-by-parts theorem for hatRhoS*barB, diffusion source-action identification, sample-path parametric-integral differentiation, density/time regularity, admissible-test closure, and boundary hypotheses.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
3. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff
7. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
8. SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation
9. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
10. Mathlib.MeasureTheory.Integral.DivergenceTheorem
11. Mathlib.Analysis.Calculus.ParametricIntegral
12. appendix.tex:1379-1387
13. sald.general_moving_target_discrete.em_interpolation_fp
14. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Proof-producing local handoff plus remaining obligation. It narrows hdriftSource for the law-derivative and source-sign consumers but does not claim the barB conditional-drift generator theorem or the divergence/no-boundary theorem is formalized.

def cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle94_weak_fp_drift_action_lower"
  statement := "Cycle 94 lower compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction, SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff, and SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff for appendix.tex:1379-1387. The handoffs remove the primitive hdriftSource premise from both the direct sample-split generator law-derivative route and the normalized weak-FP source-sign route. In its place they require two narrower source-cited facts: the frozen EM drift generator action equals the weak pairing of barB with the test gradient, and the barB weak pairing equals -(driftDiv phi) by the divergence/no-boundary theorem. Remaining exact analytic boundaries are the conditional-expectation generator action through condDistrib, the divergence/integration-by-parts theorem for hatRhoS*barB, diffusion source-action identification, sample-path parametric-integral differentiation, density/time regularity, admissible-test closure, and boundary hypotheses."
  source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Proof-producing local handoff plus remaining obligation. It narrows hdriftSource for the law-derivative and source-sign consumers but does not claim the barB conditional-drift generator theorem or the divergence/no-boundary theorem is formalized."

/-- Cycle-94 proof-DAG pane for the conditional-drift weak action boundary. -/