AutoSamplingTheory.SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureMiddleObligation

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 cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureMiddleObligation :
    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.cycle79_weak_fp_generator_measure_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 79 middle maps appendix.tex:1379-1387 to the narrow source-cited weak generator-to-law interface without changing the paper route. The source first names hat rho_s=Law(hat X_s) and the conditional drift bar b_{k,s}; the Fokker-Planck invocation is translated as the missing theorem that differentiates the frozen EM Measure.map law/test integral for admissible weak tests and identifies the generator action before the cycle-77 source-sign wrappers and cycle-78 KL handoff consume it. The mapping keeps regular conditional laws, drift measurability/integrability, density/AC, boundary conditions, admissible-test approximation, generator calculus, weak Fokker-Planck, KL differentiation, integration by parts, LSI, DV, Gronwall, and theorem closure as explicit non-formalized obligations.

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.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation
2. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
3. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation
4. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
8. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
9. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
10. sald.general_moving_target_discrete.em_interpolation_fp
11. sald.discrete_forward_kl.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 source-to-Lean boundary for the cited measure/calculus theorem and does not promote Mathlib, SLT, EM weak FP, KL derivative, or theorem status.

def cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle79_weak_fp_generator_measure_middle"
  statement := "Cycle 79 middle maps appendix.tex:1379-1387 to the narrow source-cited weak generator-to-law interface without changing the paper route. The source first names hat rho_s=Law(hat X_s) and the conditional drift bar b_{k,s}; the Fokker-Planck invocation is translated as the missing theorem that differentiates the frozen EM Measure.map law/test integral for admissible weak tests and identifies the generator action before the cycle-77 source-sign wrappers and cycle-78 KL handoff consume it. The mapping keeps regular conditional laws, drift measurability/integrability, density/AC, boundary conditions, admissible-test approximation, generator calculus, weak Fokker-Planck, KL differentiation, integration by parts, LSI, DV, Gronwall, and theorem closure as explicit non-formalized obligations."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Middle synchronization only. It records the source-to-Lean boundary for the cited measure/calculus theorem and does not promote Mathlib, SLT, EM weak FP, KL derivative, or theorem status."

/-- Cycle-79 lower obligation for the local Measure.map weak-test handoff. -/