AutoSamplingTheory.SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation

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 cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation :
    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.cycle119_canonical_barB_weak_fp_consumer_lower_ready

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 119 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated for appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. The theorem consumes SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface, fixes barB to the canonical condDistrib guide-plus-score field, derives Integrable canonicalBarB (hatRhoS s0) locally, feeds SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBInnerGradientBound, and then applies SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff. The supplied canonical-barB integrability input is no longer part of the weak-FP consumer. Remaining exact boundary: ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions, namely the EM sample-path HasDerivAt/local-domination package, derivative-value split, canonical drift weak-action identity, no-boundary divergence identity for hatRhoS * canonicalBarB, diffusion source-action identity, and law-derivative/partialS uniqueness if the normalized source-sign consumer is used.

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.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated
3. SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBInnerGradientBound
5. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
8. SALD.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorLowerObligation
9. SALD.cycle118GeneralMovingTargetDiscreteCanonicalBarBDownstreamLowerObligation
10. ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions
11. appendix.tex:1368-1377
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 lower packet. It consumes the cycle-118 canonical barB witness and removes a supplied integrability input from the weak-FP consumer path. It does not prove the EM path derivative, no-boundary theorem, diffusion source action, KL derivative, LSI, DV, Gronwall, source-index rebaseline, SLT reuse, Lake dependency, theorem status, or sald_version_2 content.

def cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle119_canonical_barB_weak_fp_consumer_lower_ready"
  statement := "Cycle 119 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated for appendix.tex:1368-1387. Classification: narrows-source-cited-boundary. The theorem consumes SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface, fixes barB to the canonical condDistrib guide-plus-score field, derives Integrable canonicalBarB (hatRhoS s0) locally, feeds SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBInnerGradientBound, and then applies SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff. The supplied canonical-barB integrability input is no longer part of the weak-FP consumer. Remaining exact boundary: ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions, namely the EM sample-path HasDerivAt/local-domination package, derivative-value split, canonical drift weak-action identity, no-boundary divergence identity for hatRhoS * canonicalBarB, diffusion source-action identity, and law-derivative/partialS uniqueness if the normalized source-sign consumer is used."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle119GeneralMovingTargetDiscreteCanonicalBarBWeakFpConsumerMiddleObligation",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBEmStateEventInterface",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBInnerGradientBound",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfDominatedSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.cycle110GeneralMovingTargetDiscreteWeakFpDominatedGeneratorLowerObligation",
    "SALD.cycle118GeneralMovingTargetDiscreteCanonicalBarBDownstreamLowerObligation",
    "ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Proof-producing lower packet. It consumes the cycle-118 canonical barB witness and removes a supplied integrability input from the weak-FP consumer path. It does not prove the EM path derivative, no-boundary theorem, diffusion source action, KL derivative, LSI, DV, Gronwall, source-index rebaseline, SLT reuse, Lake dependency, theorem status, or sald_version_2 content."

/-- Cycle-119 proof-DAG pane for the canonical `barB` weak-FP consumer. -/