AutoSamplingTheory.SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation

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 cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation :
    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_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 96 middle rejects the non-EM LSI/DV/Gronwall fallback because cycle 96 upper found active named EM blockers, not an exhausted Mathlib/theory gap. The lower-ready boundary remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1358-1387, narrowed to appendix.tex lines 1368-1377: prove one component conditional-expectation generator pairing for condC or condScore from Mathlib condDistrib/condexp, named hatRhoS = Law(hatX_s), the joint law of (hatX_s, X_k^eta), the existing component conditional-integral regularity helpers, and the weak test-gradient pairing used by SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings. This removes or strictly narrows the component-pairing supplied input before any divergence/no-boundary theorem or non-EM backend is attempted. 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.cycle95DiscreteForwardKlClosurePressureLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings
4. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
5. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
6. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
7. AutoSamplingTheory.condDistribIntegralNamedLawAEStronglyMeasurable
8. AutoSamplingTheory.condDistribIntegralNamedLawIntegrable
9. Mathlib.Probability.Kernel.CondDistrib
10. Mathlib.Probability.Kernel.Condexp
11. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib
12. ProbabilityTheory.condExp_ae_eq_integral_condExpKernel
13. lean-stat-learning-theory/SLT/EfronStein.lean
14. lean-stat-learning-theory/SLT/GaussianMeasure.lean
15. ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker
16. ASTIS.SALD.cycle94.remaining_barB_divergence_boundary
17. appendix.tex:1368-1377
18. appendix.tex:1379-1387
19. sald.general_moving_target_discrete.em_interpolation_fp
20. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

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

Middle source-map record only. It adds no supplied-hypothesis wrapper, proves no component pairing, and promotes no theorem/backend status. Lower should either discharge one component generator-pairing input used by the cycle-95 barB component route, or record one smaller missing Mathlib conditional-expectation theorem with exact hypotheses.

def cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle96_condexp_generator_pairing_middle"
  statement := "Cycle 96 middle rejects the non-EM LSI/DV/Gronwall fallback because cycle 96 upper found active named EM blockers, not an exhausted Mathlib/theory gap. The lower-ready boundary remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1358-1387, narrowed to appendix.tex lines 1368-1377: prove one component conditional-expectation generator pairing for condC or condScore from Mathlib condDistrib/condexp, named hatRhoS = Law(hatX_s), the joint law of (hatX_s, X_k^eta), the existing component conditional-integral regularity helpers, and the weak test-gradient pairing used by SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings. This removes or strictly narrows the component-pairing supplied input before any divergence/no-boundary theorem or non-EM backend is attempted. Classification: narrows-source-cited-boundary."
  source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle95DiscreteForwardKlClosurePressureLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftActionOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBComponentPairings",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
    "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
    "AutoSamplingTheory.condDistribIntegralNamedLawAEStronglyMeasurable",
    "AutoSamplingTheory.condDistribIntegralNamedLawIntegrable",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Condexp",
    "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib",
    "ProbabilityTheory.condExp_ae_eq_integral_condExpKernel",
    "lean-stat-learning-theory/SLT/EfronStein.lean",
    "lean-stat-learning-theory/SLT/GaussianMeasure.lean",
    "ASTIS.SALD.forward_KL_discrete.cycle95_next_blocker",
    "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Middle source-map record only. It adds no supplied-hypothesis wrapper, proves no component pairing, and promotes no theorem/backend status. Lower should either discharge one component generator-pairing input used by the cycle-95 barB component route, or record one smaller missing Mathlib conditional-expectation theorem with exact hypotheses."

/-- Cycle-96 lower obligation for the compiled one-component pairing handoff. -/