AutoSamplingTheory.SALD.cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation

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 cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation :
    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.cycle124_em_bound_int_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 124 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated for appendix.tex:1379-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hboundInt from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundDominated. The theorem derives sample-space Integrable (bound phi) P from an integrable joint-law bound on Measure.map (fun omega => (hatX s0 omega, Xk omega)) P plus an a.e. equality to the selected sample-space bound, using AEMeasurable.prodMk, Integrable.comp_aemeasurable, and Integrable.congr. Remaining exact boundary: hpathDeriv, hderivValue, canonical drift weak-action/pairing regularity, no-boundary divergence, diffusion source action, and optional law-derivative/partialS uniqueness.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundDominated
3. ASTIS.SALD.cycle124.remaining_em_path_derivative_domination_after_deriv_bound
4. ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative
5. MeasureTheory.AEMeasurable.prodMk
6. MeasureTheory.Integrable.comp_aemeasurable
7. MeasureTheory.Integrable.congr
8. appendix.tex:1379-1387
9. appendix.tex:1368-1377
10. 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.

Dynamic-leaf worker lower packet. It rejects wrapper churn around hboundInt, broad source-index or theorem-route audits, non-EM fallback, SLT import, Lake changes, theorem-status promotion, fake closure, and sald_version_2 content. The concrete joint-law moment estimate remains source-facing; this compiled theorem only transports that integrability to the selected sample-space bound.

def cycle124GeneralMovingTargetDiscreteEmBoundIntLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle124_em_bound_int_lower"
  statement := "Cycle 124 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated for appendix.tex:1379-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hboundInt from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundDominated. The theorem derives sample-space Integrable (bound phi) P from an integrable joint-law bound on Measure.map (fun omega => (hatX s0 omega, Xk omega)) P plus an a.e. equality to the selected sample-space bound, using AEMeasurable.prodMk, Integrable.comp_aemeasurable, and Integrable.congr. Remaining exact boundary: hpathDeriv, hderivValue, canonical drift weak-action/pairing regularity, no-boundary divergence, diffusion source action, and optional law-derivative/partialS uniqueness."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundDominated",
    "ASTIS.SALD.cycle124.remaining_em_path_derivative_domination_after_deriv_bound",
    "ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative",
    "MeasureTheory.AEMeasurable.prodMk",
    "MeasureTheory.Integrable.comp_aemeasurable",
    "MeasureTheory.Integrable.congr",
    "appendix.tex:1379-1387",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker lower packet. It rejects wrapper churn around hboundInt, broad source-index or theorem-route audits, non-EM fallback, SLT import, Lake changes, theorem-status promotion, fake closure, and sald_version_2 content. The concrete joint-law moment estimate remains source-facing; this compiled theorem only transports that integrability to the selected sample-space bound."

/-- Cycle-124 proof-DAG pane for bound-integrability transport inside the EM
path-derivative/domination boundary. -/