AutoSamplingTheory.SALD.cycle115GeneralMovingTargetDiscreteNamedBarBSelectedVersionMiddleObligation

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 cycle115GeneralMovingTargetDiscreteNamedBarBSelectedVersionMiddleObligation :
    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.cycle115_named_barB_selected_version_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 115 middle compiles SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq for appendix.tex:1368-1377. Classification: narrows-source-cited-boundary. The theorem shows that once the paper-selected named barB is hatRhoS-a.e. equal to the canonical Mathlib condDistrib guide-plus-score representative, the remaining hbarBStateSetIntegral premise follows on all state events by pulling the a.e. equality back through hatXAtS and applying MeasureTheory.setIntegral_congr_ae to the cycle-114 canonical state-event theorem. The same selected-to-canonical a.e. equality also yields Integrable barB hatRhoS from SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq. Remaining exact boundary: prove the source selected-version equality between the paper conditional-expectation representative and the canonical condDistrib field.

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.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
2. SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq
4. MeasureTheory.ae_eq_comp
5. MeasureTheory.setIntegral_congr_ae
6. ASTIS.SALD.cycle114.remaining_named_barB_version_after_canonical_state_event_integral
7. appendix.tex:1368-1377
8. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

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

Illness-area refiner packet. It rejects wrapper churn: the compiled theorem derives the old state-event set-integral and integrability inputs from the smaller selected-to-canonical a.e. equality, leaving that equality as the only selected-version theorem boundary. No weak FP, KL derivative, LSI, DV, Gronwall, theorem-status promotion, SLT import, Lake change, source-index rebaseline, or sald_version_2 content.

def cycle115GeneralMovingTargetDiscreteNamedBarBSelectedVersionMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle115_named_barB_selected_version_middle"
  statement := "Cycle 115 middle compiles SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq for appendix.tex:1368-1377. Classification: narrows-source-cited-boundary. The theorem shows that once the paper-selected named barB is hatRhoS-a.e. equal to the canonical Mathlib condDistrib guide-plus-score representative, the remaining hbarBStateSetIntegral premise follows on all state events by pulling the a.e. equality back through hatXAtS and applying MeasureTheory.setIntegral_congr_ae to the cycle-114 canonical state-event theorem. The same selected-to-canonical a.e. equality also yields Integrable barB hatRhoS from SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq. Remaining exact boundary: prove the source selected-version equality between the paper conditional-expectation representative and the canonical condDistrib field."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
    "SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq",
    "MeasureTheory.ae_eq_comp",
    "MeasureTheory.setIntegral_congr_ae",
    "ASTIS.SALD.cycle114.remaining_named_barB_version_after_canonical_state_event_integral",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet. It rejects wrapper churn: the compiled theorem derives the old state-event set-integral and integrability inputs from the smaller selected-to-canonical a.e. equality, leaving that equality as the only selected-version theorem boundary. No weak FP, KL derivative, LSI, DV, Gronwall, theorem-status promotion, SLT import, Lake change, source-index rebaseline, or sald_version_2 content."

/-- Cycle-115 lower obligation for the source conditional-expectation version
of the selected `barB` bridge. -/