AutoSamplingTheory.SALD.cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation

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 cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation :
    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.cycle123_em_sample_deriv_meas_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 123 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated for appendix.tex:1379-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hsampleDerivMeas from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated. The theorem derives sample-space AEStronglyMeasurable (sampleDeriv phi s0) P from a concrete EM derivative representative fun omega => deriv (fun t => testEval phi (hatX t omega)) s0, its AEStronglyMeasurable proof, and an ae-equality to sampleDeriv phi s0 via AEStronglyMeasurable.congr, then reuses the cycle-122 source EM interval route. Remaining exact boundary: 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated
2. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated
3. MeasureTheory.AEStronglyMeasurable.congr
4. Mathlib.Analysis.Calculus.FDeriv.Measurable.aestronglyMeasurable_deriv_with_param
5. ASTIS.SALD.cycle122.remaining_em_path_derivative_domination_after_sample_int
6. ASTIS.SALD.cycle120.remaining_source_actions_after_path_derivative
7. eq:general_moving_target_SALD_frozen_interp
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 hbarBCondExp wrapper churn, 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 derivative-with-parameter Mathlib theorem was consulted as the eventual route for the concrete representative, but no extra topological assumptions are added here.

def cycle123GeneralMovingTargetDiscreteEmSampleDerivMeasLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle123_em_sample_deriv_meas_lower"
  statement := "Cycle 123 lower compiles SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated for appendix.tex:1379-1387. Classification: discharges-supplied-hypothesis. Exact supplied hypothesis discharged: hsampleDerivMeas from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated. The theorem derives sample-space AEStronglyMeasurable (sampleDeriv phi s0) P from a concrete EM derivative representative fun omega => deriv (fun t => testEval phi (hatX t omega)) s0, its AEStronglyMeasurable proof, and an ae-equality to sampleDeriv phi s0 via AEStronglyMeasurable.congr, then reuses the cycle-122 source EM interval route. Remaining exact boundary: 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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasDominated",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDominated",
    "MeasureTheory.AEStronglyMeasurable.congr",
    "Mathlib.Analysis.Calculus.FDeriv.Measurable.aestronglyMeasurable_deriv_with_param",
    "ASTIS.SALD.cycle122.remaining_em_path_derivative_domination_after_sample_int",
    "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, 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 derivative-with-parameter Mathlib theorem was consulted as the eventual route for the concrete representative, but no extra topological assumptions are added here."

/-- Cycle-123 proof-DAG pane for derivative measurability discharge inside the
EM path-derivative/domination boundary. -/