AutoSamplingTheory.SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation

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 cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation :
    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.cycle81_endpoint_conditional_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 81 lower compiles SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff for appendix.tex lines 1368-1377. This endpoint-only wrapper composes the cycle-76 endpoint Measure.map compatibility package with already-supplied bar b_{k,s} measurability/integrability and a supplied WeakFpPrereq consumer. It returns endpoint laws, original/swapped hat rho_s marginal views, swap equality, original-orientation kernel compatibility, bar b_{k,s} regularity, and the WeakFpPrereq without reconstructing conditional component fields or proving the weak Fokker-Planck theorem.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
3. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
4. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
6. SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
7. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
8. 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.

Lower proof-producing endpoint wrapper only. It uses supplied barB regularity and supplied WeakFpPrereq; regular conditional law, conditional expectation, density/AC, generator-to-law, weak FP, KL derivative, and theorem closure remain obligations.

def cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle81_endpoint_conditional_lower"
  statement := "Cycle 81 lower compiles SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff for appendix.tex lines 1368-1377. This endpoint-only wrapper composes the cycle-76 endpoint Measure.map compatibility package with already-supplied bar b_{k,s} measurability/integrability and a supplied WeakFpPrereq consumer. It returns endpoint laws, original/swapped hat rho_s marginal views, swap equality, original-orientation kernel compatibility, bar b_{k,s} regularity, and the WeakFpPrereq without reconstructing conditional component fields or proving the weak Fokker-Planck theorem."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Lower proof-producing endpoint wrapper only. It uses supplied barB regularity and supplied WeakFpPrereq; regular conditional law, conditional expectation, density/AC, generator-to-law, weak FP, KL derivative, and theorem closure remain obligations."

/-- Cycle-81 proof-DAG pane for the endpoint-to-conditional upper packet. -/