AutoSamplingTheory.SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation

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 cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation :
    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.cycle96_condexp_generator_pairing_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 96 lower compiles SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion for appendix.tex lines 1368-1377. This one-component handoff narrows the supplied condC/condScore generator-pairing premise: if the named component field is hatRhoS-a.e. equal to the canonical condDistrib integral and the weak test-gradient pairing is congruent under that hatRhoS-a.e. equality, then it is enough to prove the generator action against the canonical conditional-integral field. Classification: narrows-source-cited-boundary. The remaining smaller theorem is the Mathlib/local-analysis conditional-expectation generator identity for that canonical condDistrib/condexp integral; divergence/no-boundary for hatRhoS * barB remains separate.

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.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation
2. SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
4. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
5. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
6. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
7. Mathlib.Probability.Kernel.CondDistrib
8. Mathlib.Probability.Kernel.Condexp
9. appendix.tex:1368-1377
10. sald.general_moving_target_discrete.em_interpolation_fp
11. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

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

Lower proof-producing boundary narrowing only. It proves the local a.e.-version-to-named-field weak-pairing handoff, but it does not prove the canonical condDistrib/condexp generator theorem, regular conditional law, weak FP equation, KL derivative, divergence/no-boundary theorem, theorem closure, SLT import, or Lake dependency change.

def cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle96_condexp_generator_pairing_lower"
  statement := "Cycle 96 lower compiles SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion for appendix.tex lines 1368-1377. This one-component handoff narrows the supplied condC/condScore generator-pairing premise: if the named component field is hatRhoS-a.e. equal to the canonical condDistrib integral and the weak test-gradient pairing is congruent under that hatRhoS-a.e. equality, then it is enough to prove the generator action against the canonical conditional-integral field. Classification: narrows-source-cited-boundary. The remaining smaller theorem is the Mathlib/local-analysis conditional-expectation generator identity for that canonical condDistrib/condexp integral; divergence/no-boundary for hatRhoS * barB remains separate."
  source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation",
    "SALD.generalMovingTargetDiscreteCondDistribComponentWeakPairingOfAeVersion",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
    "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Condexp",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Lower proof-producing boundary narrowing only. It proves the local a.e.-version-to-named-field weak-pairing handoff, but it does not prove the canonical condDistrib/condexp generator theorem, regular conditional law, weak FP equation, KL derivative, divergence/no-boundary theorem, theorem closure, SLT import, or Lake dependency change."

/-- Cycle-96 proof-DAG pane for the condexp generator-pairing middle packet. -/