AutoSamplingTheory.SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperObligation

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 cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperObligation :
    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.cycle76_endpoint_conditional_upper

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 76 upper records that cycle 75 passed and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active lower packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower work is endpoint-law-to-conditional compatibility: combine the endpoint Measure.map handoffs for hat rho_{s_k} and hat rho_{s_{k+1}} with the swapped condDistrib orientation (hat X_s,X_k^eta), then bridge back to the paper's (X_k^eta,hat X_s) orientation for the weak FP interface.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperPacket
2. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
3. SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
5. 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.

Upper workflow obligation only. It fixes the lower packet and does not prove disintegration, weak FP, KL differentiation, density/AC, LSI, DV, Gronwall, or theorem closure.

def cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle76_endpoint_conditional_upper"
  statement := "Cycle 76 upper records that cycle 75 passed and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active lower packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower work is endpoint-law-to-conditional compatibility: combine the endpoint Measure.map handoffs for hat rho_{s_k} and hat rho_{s_{k+1}} with the swapped condDistrib orientation (hat X_s,X_k^eta), then bridge back to the paper's (X_k^eta,hat X_s) orientation for the weak FP interface."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperPacket",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Upper workflow obligation only. It fixes the lower packet and does not prove disintegration, weak FP, KL differentiation, density/AC, LSI, DV, Gronwall, or theorem closure."

/-- Cycle-76 middle map for endpoint-law to conditional-law compatibility. -/