AutoSamplingTheory.SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportUpperObligation

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 cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportUpperObligation :
    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.cycle104_named_law_transport_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 104 upper records the global phase judgment: cycle 103 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. Classification: discharges-supplied-hypothesis. The selected lower packet is the named-law generator-to-law weak-FP transport at appendix.tex:1379-1387: remove a separate named-law weak derivative/hlawDerivative premise once hatRhoS s = Measure.map (hatX s) P and the sample-space split-generator derivative are supplied. This uses the existing cycle-79 lawMapIntegral helpers and does not create another source-sign wrapper.

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. AutoSamplingTheory.lawMapIntegral
2. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
3. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff
6. SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation
7. appendix.tex:1379-1387
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.

Upper packet plus compiled local transport theorem. It rejects wrapper churn around hgenerator, hdriftSource, hdivNoBoundary, hgradNormBound, KL, LSI, DV, or Gronwall assumptions; the remaining analytic boundaries are sample-path/Bochner generator differentiation, drift/no-boundary source action, diffusion source action, admissible tests, density/time regularity, and conditional-law compatibility.

def cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportUpperObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle104_named_law_transport_upper"
  statement := "Cycle 104 upper records the global phase judgment: cycle 103 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. Classification: discharges-supplied-hypothesis. The selected lower packet is the named-law generator-to-law weak-FP transport at appendix.tex:1379-1387: remove a separate named-law weak derivative/hlawDerivative premise once hatRhoS s = Measure.map (hatX s) P and the sample-space split-generator derivative are supplied. This uses the existing cycle-79 lawMapIntegral helpers and does not create another source-sign wrapper."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Upper packet plus compiled local transport theorem. It rejects wrapper churn around hgenerator, hdriftSource, hdivNoBoundary, hgradNormBound, KL, LSI, DV, or Gronwall assumptions; the remaining analytic boundaries are sample-path/Bochner generator differentiation, drift/no-boundary source action, diffusion source action, admissible tests, density/time regularity, and conditional-law compatibility."

/-- Cycle-104 lower obligation for the compiled named-law weak derivative
transport theorem. -/