AutoSamplingTheory.SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation

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 cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation :
    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_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 92 lower compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff for appendix.tex:1379-1387. The first theorem removes the supplied hgeneratorSplit premise from SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff by setting generatorAction phi definitionally to driftAction phi + diffusionAction phi. The second theorem removes the separate hlawDerivative input for the direct weak-test derivative route: it transports the sample-space split-generator HasDerivAt result through AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample and rewrites the derivative value to the source signs. Classification: discharges-supplied-hypothesis for hgeneratorSplit and narrows-source-cited-boundary for hlawDerivative. Remaining exact analytic boundaries are sample-path/parametric-integral differentiation of the split generator sum, drift source-action identification through bar b_{k,s}, diffusion source-action identification with coefficient sigma_eta^2/2, density/time regularity, admissible-test closure, and boundary hypotheses.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource — 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.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
5. AutoSamplingTheory.lawMapIntegral
6. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
7. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
8. SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation
9. appendix.tex:1379-1387
10. 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.

Proof-producing local theorems plus remaining obligation. They reduce supplied generator-split/law-derivative inputs but do not prove the EM generator theorem, parametric integral differentiation, source-action identifications, conditional law compatibility, KL derivative, LSI, DV, Gronwall, theorem closure, or any SLT result.

def cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle92_weak_fp_split_generator_lower"
  statement := "Cycle 92 lower compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff and SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff for appendix.tex:1379-1387. The first theorem removes the supplied hgeneratorSplit premise from SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff by setting generatorAction phi definitionally to driftAction phi + diffusionAction phi. The second theorem removes the separate hlawDerivative input for the direct weak-test derivative route: it transports the sample-space split-generator HasDerivAt result through AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample and rewrites the derivative value to the source signs. Classification: discharges-supplied-hypothesis for hgeneratorSplit and narrows-source-cited-boundary for hlawDerivative. Remaining exact analytic boundaries are sample-path/parametric-integral differentiation of the split generator sum, drift source-action identification through bar b_{k,s}, diffusion source-action identification with coefficient sigma_eta^2/2, density/time regularity, admissible-test closure, and boundary hypotheses."
  source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitMiddleObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing local theorems plus remaining obligation. They reduce supplied generator-split/law-derivative inputs but do not prove the EM generator theorem, parametric integral differentiation, source-action identifications, conditional law compatibility, KL derivative, LSI, DV, Gronwall, theorem closure, or any SLT result."

/-- Cycle-92 proof-DAG pane for the split-generator weak-FP boundary. -/