AutoSamplingTheory.SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation

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 cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation :
    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.cycle70_conditional_law_middle

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 70 middle keeps the selected backend at sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and narrows the source-to-Lean packet to the conditional-law/measurability layer of appendix.tex:1368-1377: name the regular conditional kernel of X_k^eta given hat X_s=x, the component conditional fields condC_{k,s} and condScore_{k,s}, and the selected drift bar b_{k,s}; keep endpoint laws, density/AC, weak Fokker-Planck, KL differentiation, LSI, DV, and Gronwall as downstream obligations.

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.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
2. SALD.generalMovingTargetDiscreteConditionalDriftContract
3. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
4. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
5. SALD.cycle69MainSkeletonAnalyticMiddleObligation
6. SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation
7. 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.

Middle synchronization only. It records the cycle-70 global judgment: cycle 69 passed and needs no recovery; Phase 1 is stable enough for single-backend backfill; the best lower packet is conditional-law/measurability plus named conditional drift interfaces for bar b_{k,s}.

def cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle70_conditional_law_middle"
  statement := "Cycle 70 middle keeps the selected backend at sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and narrows the source-to-Lean packet to the conditional-law/measurability layer of appendix.tex:1368-1377: name the regular conditional kernel of X_k^eta given hat X_s=x, the component conditional fields condC_{k,s} and condScore_{k,s}, and the selected drift bar b_{k,s}; keep endpoint laws, density/AC, weak Fokker-Planck, KL differentiation, LSI, DV, and Gronwall as downstream obligations."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle69MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle synchronization only. It records the cycle-70 global judgment: cycle 69 passed and needs no recovery; Phase 1 is stable enough for single-backend backfill; the best lower packet is conditional-law/measurability plus named conditional drift interfaces for bar b_{k,s}."

/-- Cycle-70 lower obligation for the named conditional drift handoff. -/