AutoSamplingTheory.SALD.cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportLowerObligation

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 cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportLowerObligation :
    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_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 104 lower compiles AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample and SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff. The generic helper transports a supplied sample-space derivative to a named law path rho s when rho s = Measure.map (X s) P; the SALD theorem specializes it to hatRhoS and the split generator driftAction + diffusionAction, yielding the weak-test derivative with the paper source signs. Classification: discharges-supplied-hypothesis for a primitive named-law hlawDerivative/named-law rewrite premise in the generator-to-law weak-FP boundary. Remaining exact boundaries are the sample-path split-generator derivative, drift source through barB/no-boundary, diffusion source action, weak-test measurability, density/time regularity, and conditional-law compatibility.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource — 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.lawIntegralHasDerivAtOfMeasureMapEqAndSample
2. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
3. SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
5. SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation
6. Mathlib.Analysis.Calculus.ParametricIntegral
7. Mathlib.MeasureTheory.Integral.Bochner.Basic
8. appendix.tex:1379-1387
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.

Proof-producing transport handoff only. It does not prove the EM generator theorem, parametric-integral differentiation, drift/no-boundary theorem, diffusion/Laplacian source action, weak FP closure, KL differentiation, theorem closure, SLT import, or any Lake dependency.

def cycle104GeneralMovingTargetDiscreteWeakFpNamedLawTransportLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle104_named_law_transport_lower"
  statement := "Cycle 104 lower compiles AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample and SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff. The generic helper transports a supplied sample-space derivative to a named law path rho s when rho s = Measure.map (X s) P; the SALD theorem specializes it to hatRhoS and the split generator driftAction + diffusionAction, yielding the weak-test derivative with the paper source signs. Classification: discharges-supplied-hypothesis for a primitive named-law hlawDerivative/named-law rewrite premise in the generator-to-law weak-FP boundary. Remaining exact boundaries are the sample-path split-generator derivative, drift source through barB/no-boundary, diffusion source action, weak-test measurability, density/time regularity, and conditional-law compatibility."
  source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndSample",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpNamedLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
    "SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing transport handoff only. It does not prove the EM generator theorem, parametric-integral differentiation, drift/no-boundary theorem, diffusion/Laplacian source action, weak FP closure, KL differentiation, theorem closure, SLT import, or any Lake dependency."

/-- Cycle-104 proof-DAG pane for the named-law generator-to-law weak-FP
transport packet. -/