AutoSamplingTheory.SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation

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 cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation :
    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.cycle97_canonical_condDistrib_pairing_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 97 lower compiles SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction for appendix.tex lines 1368-1377. The theorem uses AutoSamplingTheory.condDistribIntegralNamedLawIntegral with X=hatX_s, Y=X_k^eta, hatRhoS=Law(hatX_s), and f=(test-gradient pairing with one frozen component integrand), then feeds SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion. It removes the raw cycle-96 hcanonical premise under explicit paired-integrand integrability, componentAction definition, weakGradPairing canonical-integral definition, hfieldAe, and hweakAeCongr hypotheses. Classification: narrows-source-cited-boundary; the remaining exact boundary is proving those SALD definition-alignment and paired-integrability facts from the paper weak-test-gradient semantics.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingMiddleObligation
2. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction
3. AutoSamplingTheory.condDistribIntegralNamedLawIntegral
4. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
6. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings
7. ASTIS.SALD.cycle96.lower_condDistrib_component_pairing_handoff
8. appendix.tex:1368-1377
9. appendix.tex:1379-1387

note : String (explicit)

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

This is not a fresh supplied-hypothesis wrapper. The compiled theorem removes hcanonical as a primitive assumption and leaves smaller obligations: paired-integrand integrability, sample component-action definition, canonical weak-pairing definition, field a.e. version, and a.e.-congruence for the weak pairing.

def cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle97_canonical_condDistrib_pairing_lower_ready"
  statement := "Cycle 97 lower compiles SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction for appendix.tex lines 1368-1377. The theorem uses AutoSamplingTheory.condDistribIntegralNamedLawIntegral with X=hatX_s, Y=X_k^eta, hatRhoS=Law(hatX_s), and f=(test-gradient pairing with one frozen component integrand), then feeds SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion. It removes the raw cycle-96 hcanonical premise under explicit paired-integrand integrability, componentAction definition, weakGradPairing canonical-integral definition, hfieldAe, and hweakAeCongr hypotheses. Classification: narrows-source-cited-boundary; the remaining exact boundary is proving those SALD definition-alignment and paired-integrability facts from the paper weak-test-gradient semantics."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingMiddleObligation",
    "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfIntegralAction",
    "AutoSamplingTheory.condDistribIntegralNamedLawIntegral",
    "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings",
    "ASTIS.SALD.cycle96.lower_condDistrib_component_pairing_handoff",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387"
  ]
  note := "This is not a fresh supplied-hypothesis wrapper. The compiled theorem removes hcanonical as a primitive assumption and leaves smaller obligations: paired-integrand integrability, sample component-action definition, canonical weak-pairing definition, field a.e. version, and a.e.-congruence for the weak pairing."

/-- Cycle-97 proof-DAG pane for the canonical `condDistrib` pairing packet. -/