AutoSamplingTheory.SALD.cycle114GeneralMovingTargetDiscreteCanonicalBarBStateEventSetIntegralLowerObligation

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 cycle114GeneralMovingTargetDiscreteCanonicalBarBStateEventSetIntegralLowerObligation :
    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.cycle114_canonical_barB_state_event_set_integral_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 114 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib for appendix.tex:1368-1377. Classification: narrows-source-cited-boundary. The theorem proves the source state-event Bochner set-integral characterization for the canonical Mathlib condDistrib representative of barB: over every measurable state set t, the set integral of dotTk times the conditional guide integral plus sigmaCoeff times the conditional score integral, pulled back by hatXAtS, equals the set integral of the frozen guide-plus-score sample drift on {omega | hatXAtS omega in t}. This strictly narrows hbarBStateSetIntegral / ASTIS.SALD.cycle113.remaining_named_barB_state_event_set_integral to the remaining source version-selection theorem that the paper's selected named barB is the canonical condDistrib representative under hatRhoS, plus Integrable barB hatRhoS if a separate version is used.

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.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib
2. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'
3. MeasureTheory.setIntegral_condExp
4. MeasureTheory.setIntegral_congr_ae
5. MeasureTheory.Integrable.condDistrib_ae
6. appendix.tex:1368-1377
7. sald.general_moving_target_discrete.em_interpolation_fp
8. ASTIS.SALD.cycle113.remaining_named_barB_state_event_set_integral

note : String (explicit)

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

Dynamic-leaf worker packet only. It rejects wrapper churn around hbarBStateSetIntegral: the compiled theorem discharges the canonical condDistrib state-event integral part and leaves the smaller paper-version boundary. It does not prove weak FP, KL derivative, LSI, DV, Gronwall, theorem closure, SLT reuse, Lake changes, source-index rebaseline, or sald_version_2 content.

def cycle114GeneralMovingTargetDiscreteCanonicalBarBStateEventSetIntegralLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle114_canonical_barB_state_event_set_integral_lower"
  statement := "Cycle 114 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib for appendix.tex:1368-1377. Classification: narrows-source-cited-boundary. The theorem proves the source state-event Bochner set-integral characterization for the canonical Mathlib condDistrib representative of barB: over every measurable state set t, the set integral of dotTk times the conditional guide integral plus sigmaCoeff times the conditional score integral, pulled back by hatXAtS, equals the set integral of the frozen guide-plus-score sample drift on {omega | hatXAtS omega in t}. This strictly narrows hbarBStateSetIntegral / ASTIS.SALD.cycle113.remaining_named_barB_state_event_set_integral to the remaining source version-selection theorem that the paper's selected named barB is the canonical condDistrib representative under hatRhoS, plus Integrable barB hatRhoS if a separate version is used."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteCanonicalBarBStateSetIntegralOfCondDistrib",
    "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib'",
    "MeasureTheory.setIntegral_condExp",
    "MeasureTheory.setIntegral_congr_ae",
    "MeasureTheory.Integrable.condDistrib_ae",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "ASTIS.SALD.cycle113.remaining_named_barB_state_event_set_integral"
  ]
  note := "Dynamic-leaf worker packet only. It rejects wrapper churn around hbarBStateSetIntegral: the compiled theorem discharges the canonical condDistrib state-event integral part and leaves the smaller paper-version boundary. It does not prove weak FP, KL derivative, LSI, DV, Gronwall, theorem closure, SLT reuse, Lake changes, source-index rebaseline, or sald_version_2 content."

/-- Cycle-114 proof-DAG pane for the canonical state-event set-integral
narrowing. -/