AutoSamplingTheory.SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation

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 cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation :
    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.cycle80_conditional_law_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 80 lower compiles SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff for appendix.tex lines 1368-1377, using only supplied hypotheses. The wrapper composes the endpoint-to-conditional compatibility package with component conditional-integral field regularity: from endpoint Measure.map laws, the named hat rho_s marginal in both original and swapped orientations, a supplied swapped conditional-kernel compatibility bridge, supplied component integral fields, and supplied measurability/integrability closure, it returns endpoint laws, original-orientation kernel compatibility, and measurability/integrability of the selected bar b_{k,s} field. It does not construct condDistrib, condExpKernel, conditional expectations, density/AC, weak FP, or KL differentiation.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource — 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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
3. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
4. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
5. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
6. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
7. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
8. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
9. 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.

Proof-producing local wrapper under explicit hypotheses only. The Mathlib regular conditional law theorem, vector-valued conditional-expectation theorem, component field construction, density/absolute-continuity, weak conditional Fokker-Planck identity, log-ratio admissibility, KL differentiation, integration by parts, and theorem closure remain obligations.

def cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle80_conditional_law_lower"
  statement := "Cycle 80 lower compiles SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff for appendix.tex lines 1368-1377, using only supplied hypotheses. The wrapper composes the endpoint-to-conditional compatibility package with component conditional-integral field regularity: from endpoint Measure.map laws, the named hat rho_s marginal in both original and swapped orientations, a supplied swapped conditional-kernel compatibility bridge, supplied component integral fields, and supplied measurability/integrability closure, it returns endpoint laws, original-orientation kernel compatibility, and measurability/integrability of the selected bar b_{k,s} field. It does not construct condDistrib, condExpKernel, conditional expectations, density/AC, weak FP, or KL differentiation."
  source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
    "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing local wrapper under explicit hypotheses only. The Mathlib regular conditional law theorem, vector-valued conditional-expectation theorem, component field construction, density/absolute-continuity, weak conditional Fokker-Planck identity, log-ratio admissibility, KL differentiation, integration by parts, and theorem closure remain obligations."

/-- Cycle-80 proof-DAG pane for the conditional-law/measurability backfill. -/