AutoSamplingTheory.SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation

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 cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation :
    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.cycle86_weak_fp_generator_boundary_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 86 upper records that cycle 85 passed and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower packet is appendix.tex:1379-1387: use the existing cycle-79 Measure.map/Bochner integral lawMapIntegral helpers plus the accepted cycle-85 conditional-field regularity progress to discharge or sharply narrow the generator-to-law weak Fokker-Planck boundary. The concrete target is the supplied generator/time-derivative hypothesis consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff; lower must either compile a local theorem removing that hypothesis for admissible weak tests, or name the smallest missing theorem boundary with imports and hypotheses. Classification is required: discharges-supplied-hypothesis, narrows-source-cited-boundary, or rejected-wrapper-churn.

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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket
2. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
3. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation
4. AutoSamplingTheory.lawMapIntegral
5. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
8. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
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.

Upper workflow obligation only. It fixes the lower packet and anti-wrapper-churn review discipline; it proves no generator theorem, weak Fokker-Planck identity, KL derivative, conditional law, theorem closure, or SLT result.

def cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle86_weak_fp_generator_boundary_upper"
  statement := "Cycle 86 upper records that cycle 85 passed and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower packet is appendix.tex:1379-1387: use the existing cycle-79 Measure.map/Bochner integral lawMapIntegral helpers plus the accepted cycle-85 conditional-field regularity progress to discharge or sharply narrow the generator-to-law weak Fokker-Planck boundary. The concrete target is the supplied generator/time-derivative hypothesis consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff; lower must either compile a local theorem removing that hypothesis for admissible weak tests, or name the smallest missing theorem boundary with imports and hypotheses. Classification is required: discharges-supplied-hypothesis, narrows-source-cited-boundary, or rejected-wrapper-churn."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation",
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Upper workflow obligation only. It fixes the lower packet and anti-wrapper-churn review discipline; it proves no generator theorem, weak Fokker-Planck identity, KL derivative, conditional law, theorem closure, or SLT result."

/-- Cycle-86 middle source map for the generator-to-law weak FP boundary.

This is not another source-sign wrapper. It translates the paper's invocation
of the Fokker--Planck equation associated with the frozen EM interpolation into
the exact theorem boundary lower should attack: an admissible weak-test
law-derivative statement obtained from sample-path generator differentiation
and `Measure.map` integral transport.
-/