AutoSamplingTheory.SALD.cycle95DiscreteForwardKlClosurePressureMiddleObligation

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 cycle95DiscreteForwardKlClosurePressureMiddleObligation :
    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_middle

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 middle synchronizes the thm:forward-KL-discrete pressure test with the active EM backend. The current compiled route passes through the cycle-94 barB weak-action handoff, the cycle-93 KL mass/log-ratio handoff, the existing LSI/DV/Gronwall interfaces, and the accumulated-error display wrappers, then stops at the same non-wrapper blocker selected by upper: ASTIS.SALD.cycle94.remaining_barB_divergence_boundary. The lower-ready boundary is the source-cited pair of facts at appendix.tex lines 1368-1387: prove the conditional-expectation generator pairing for barB via condDistrib/condexp, or prove the divergence/no-boundary theorem identifying that weak pairing with -driftDiv for hatRhoS * barB. 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.cycle95DiscreteForwardKlClosurePressureUpperObligation
2. SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation
3. SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction
7. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
8. SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar
9. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
10. SALD.discreteForwardKlMainDisplayBoundScalar
11. ASTIS.SALD.forward_KL_discrete.cycle95_pressure_route
12. ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker
13. ASTIS.SALD.cycle94.remaining_barB_divergence_boundary
14. Mathlib.Probability.Kernel.CondDistrib
15. Mathlib.Probability.Kernel.Condexp
16. Mathlib.MeasureTheory.Integral.DivergenceTheorem
17. appendix.tex:1368-1377
18. appendix.tex:1379-1387
19. main_body.tex:299-323
20. sald.general_moving_target_discrete.em_interpolation_fp
21. sald.discrete_forward_kl.em_interpolation_fp
22. sald.discrete_forward_kl.kl_derivative

note : String (explicit)

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

Middle source-map record only. It keeps the discrete theorem statement, constants, signs, source labels, and backend statuses unchanged, and rejects wrapper churn unless a later lower packet removes one of the two remaining barB weak-action inputs.

def cycle95DiscreteForwardKlClosurePressureMiddleObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle95_closure_pressure_middle"
  statement := "Cycle 95 middle synchronizes the thm:forward-KL-discrete pressure test with the active EM backend. The current compiled route passes through the cycle-94 barB weak-action handoff, the cycle-93 KL mass/log-ratio handoff, the existing LSI/DV/Gronwall interfaces, and the accumulated-error display wrappers, then stops at the same non-wrapper blocker selected by upper: ASTIS.SALD.cycle94.remaining_barB_divergence_boundary. The lower-ready boundary is the source-cited pair of facts at appendix.tex lines 1368-1387: prove the conditional-expectation generator pairing for barB via condDistrib/condexp, or prove the divergence/no-boundary theorem identifying that weak pairing with -driftDiv for hatRhoS * barB. Classification: narrows-source-cited-boundary."
  source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle95DiscreteForwardKlClosurePressureUpperObligation",
    "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation",
    "SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar",
    "SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar",
    "SALD.discreteForwardKlMainDisplayBoundScalar",
    "ASTIS.SALD.forward_KL_discrete.cycle95_pressure_route",
    "ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker",
    "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.MeasureTheory.Integral.DivergenceTheorem",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "main_body.tex:299-323",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.discrete_forward_kl.kl_derivative"
  ]
  note := "Middle source-map record only. It keeps the discrete theorem statement, constants, signs, source labels, and backend statuses unchanged, and rejects wrapper churn unless a later lower packet removes one of the two remaining barB weak-action inputs."

/-- Cycle-95 lower obligation for the component-pairing reduction of the
`barB` drift-action blocker. -/