AutoSamplingTheory.SALD.cycle95DiscreteForwardKlClosurePressureLowerObligation

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 cycle95DiscreteForwardKlClosurePressureLowerObligation :
    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.discrete_forward_kl.cycle95_closure_pressure_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 95 lower compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings and SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings. This pressure-test result does not add another theorem-route wrapper: it narrows the first half of ASTIS.SALD.cycle94.remaining_barB_divergence_boundary by replacing the direct supplied fact driftAction phi = weakGradPairing barB phi with component conditional-drift pairings for condC and condScore plus linearity/congruence of the weak gradient pairing and the existing barB component formula. The next non-wrapper analytic blocker is now sharper: prove the component conditional-expectation generator pairings from condDistrib/condexp at appendix.tex lines 1368-1377, and still prove the no-boundary divergence theorem weakGradPairing barB phi = -(driftDiv phi) for hatRhoS * barB at appendix.tex lines 1379-1387. Classification: narrows-source-cited-boundary.

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.cycle95DiscreteForwardKlClosurePressureMiddleObligation
2. SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
6. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
7. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
8. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
9. Mathlib.Probability.Kernel.CondDistrib
10. Mathlib.Probability.Kernel.Condexp
11. Mathlib.MeasureTheory.Integral.DivergenceTheorem
12. appendix.tex:1368-1377
13. appendix.tex:1379-1387
14. sald.general_moving_target_discrete.em_interpolation_fp
15. 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 local algebra plus remaining obligation. It removes the direct barB action premise in favor of component conditional-expectation pairings and weak-pairing linearity, but it does not prove those component pairings, the divergence/no-boundary theorem, weak FP, KL differentiability, LSI, DV, Gronwall, accumulated-error closure, or either discrete theorem.

def cycle95DiscreteForwardKlClosurePressureLowerObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle95_closure_pressure_lower"
  statement := "Cycle 95 lower compiles SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings and SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings. This pressure-test result does not add another theorem-route wrapper: it narrows the first half of ASTIS.SALD.cycle94.remaining_barB_divergence_boundary by replacing the direct supplied fact driftAction phi = weakGradPairing barB phi with component conditional-drift pairings for condC and condScore plus linearity/congruence of the weak gradient pairing and the existing barB component formula. The next non-wrapper analytic blocker is now sharper: prove the component conditional-expectation generator pairings from condDistrib/condexp at appendix.tex lines 1368-1377, and still prove the no-boundary divergence theorem weakGradPairing barB phi = -(driftDiv phi) for hatRhoS * barB at appendix.tex lines 1379-1387. Classification: narrows-source-cited-boundary."
  source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle95DiscreteForwardKlClosurePressureMiddleObligation",
    "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "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 local algebra plus remaining obligation. It removes the direct barB action premise in favor of component conditional-expectation pairings and weak-pairing linearity, but it does not prove those component pairings, the divergence/no-boundary theorem, weak FP, KL differentiability, LSI, DV, Gronwall, accumulated-error closure, or either discrete theorem."

/-- Cycle-95 proof-DAG pane for the post-cycle-94 pressure test. -/