AutoSamplingTheory.SALD.cycle122GeneralMovingTargetDiscreteEmSampleIntLowerObligation

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 cycle122GeneralMovingTargetDiscreteEmSampleIntLowerObligation :
    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.cycle122_em_sample_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 122 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated for appendix.tex:1379-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hsampleInt from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasDominated. The theorem derives sample-space Integrable (fun omega => testEval phi (hatX s0 omega)) P from law-space htestInt on the named law hatRhoS s0, hhatRhoS s0 = Measure.map (hatX s0) P, and hhatX s0, then reuses the cycle-121 source EM interval route. Remaining exact boundary: hsampleDerivMeas, hsampleDerivBound, hboundInt, 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasDominated
3. MeasureTheory.Integrable.comp_aemeasurable
4. MeasureTheory.integrable_map_measure
5. MeasureTheory.Measure.map
6. ASTIS.SALD.cycle121.remaining_em_path_derivative_domination_after_sample_meas
7. ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative
8. eq:general_moving_target_SALD_frozen_interp
9. appendix.tex:1379-1387
10. appendix.tex:1368-1377
11. 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 hbarBCondExp wrapper churn, selected-representative replay, broad source-index or theorem-route audits, non-EM fallback, SLT import, Lake changes, theorem-status promotion, fake closure, and sald_version_2 content.

def cycle122GeneralMovingTargetDiscreteEmSampleIntLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle122_em_sample_int_lower"
  statement := "Cycle 122 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated for appendix.tex:1379-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hsampleInt from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasDominated. The theorem derives sample-space Integrable (fun omega => testEval phi (hatX s0 omega)) P from law-space htestInt on the named law hatRhoS s0, hhatRhoS s0 = Measure.map (hatX s0) P, and hhatX s0, then reuses the cycle-121 source EM interval route. Remaining exact boundary: hsampleDerivMeas, hsampleDerivBound, hboundInt, 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasDominated",
    "MeasureTheory.Integrable.comp_aemeasurable",
    "MeasureTheory.integrable_map_measure",
    "MeasureTheory.Measure.map",
    "ASTIS.SALD.cycle121.remaining_em_path_derivative_domination_after_sample_meas",
    "ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:1379-1387",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf worker lower packet. It rejects hbarBCondExp wrapper churn, selected-representative replay, broad source-index or theorem-route audits, non-EM fallback, SLT import, Lake changes, theorem-status promotion, fake closure, and sald_version_2 content."

/-- Cycle-122 proof-DAG pane for sample integrability discharge inside the EM
path-derivative/domination boundary. -/