AutoSamplingTheory.SALD.cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation

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 cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation :
    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.cycle127_em_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 127 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated for appendix.tex:1368-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: the canonical hdriftBarBAction continuation from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated. The theorem derives driftAction phi equals the weak test-gradient pairing against canonicalBarB from the guideAction/scoreAction component split, the two canonical condDistrib component pairings, and explicit weak-pairing congruence/additivity/scalar-linearity. Remaining exact boundary: canonical pairing measurability, gradient bound, no-boundary divergence, diffusion source action, and optional law-derivative/partialS uniqueness.

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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
4. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction
5. ASTIS.SALD.cycle126.remaining_canonical_source_actions_after_deriv_value
6. appendix.tex:1368-1377
7. appendix.tex:1379-1387
8. 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.

Dynamic-leaf worker packet. It rejects wrapper churn around hdriftBarBAction: the old direct canonical barB action continuation is absent from the theorem statement and is reconstructed from guide/score component pairings plus weak-pairing algebra. No broad source-index rebaseline, theorem-route audit, non-EM fallback, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, or sald_version_2 content is introduced.

def cycle127GeneralMovingTargetDiscreteEmDriftActionLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle127_em_drift_action_lower"
  statement := "Cycle 127 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated for appendix.tex:1368-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: the canonical hdriftBarBAction continuation from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated. The theorem derives driftAction phi equals the weak test-gradient pairing against canonicalBarB from the guideAction/scoreAction component split, the two canonical condDistrib component pairings, and explicit weak-pairing congruence/additivity/scalar-linearity. Remaining exact boundary: canonical pairing measurability, gradient bound, no-boundary divergence, diffusion source action, and optional law-derivative/partialS uniqueness."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDominated",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction",
    "ASTIS.SALD.cycle126.remaining_canonical_source_actions_after_deriv_value",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker packet. It rejects wrapper churn around hdriftBarBAction: the old direct canonical barB action continuation is absent from the theorem statement and is reconstructed from guide/score component pairings plus weak-pairing algebra. No broad source-index rebaseline, theorem-route audit, non-EM fallback, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, or sald_version_2 content is introduced."

/-- Cycle-127 lower obligation for discharging the raw canonical `barB`
pairing-measurability input from the drift-action packet. -/