AutoSamplingTheory.SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface

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 cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface :
    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_interface

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 records the narrow source-cited Mathlib/measure-calculus interface still blocking sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, especially lines 1379-1387. For the frozen EM interpolation law hat rho_s=Law(hat X_s), an admissible weak test phi, the conditional drift bar b_{k,s}, and diffusion coefficient sigma_eta^2/2, a future local theorem must justify differentiating the Measure.map law/test integral in s and identifying the derivative with the generator action that has negative drift-divergence and positive diffusion signs. This is the missing weak generator-to-law theorem consumed by the cycle-77 and cycle-78 supplied-hypothesis wrappers.

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.sourceCited — 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. Mathlib.Analysis.Calculus.ParametricIntegral
2. Mathlib.MeasureTheory.Integral.Bochner.FundThmCalculus
3. Mathlib.MeasureTheory.Measure.Map
4. Mathlib.MeasureTheory.Integral.Bochner.Basic
5. AutoSamplingTheory.lawMapIntegral
6. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
7. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
8. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
9. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
10. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
11. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation
12. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
13. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
14. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
15. 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.

Source-cited interface only. It does not import a new Mathlib module, construct the EM process, prove differentiability of the law, prove Ito/generator calculus, prove density/AC, prove boundary integration by parts, prove log-ratio admissibility, or close the weak Fokker-Planck/KL derivative backend.

def cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle79_weak_fp_generator_measure_interface"
  statement := "Cycle 79 records the narrow source-cited Mathlib/measure-calculus interface still blocking sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, especially lines 1379-1387. For the frozen EM interpolation law hat rho_s=Law(hat X_s), an admissible weak test phi, the conditional drift bar b_{k,s}, and diffusion coefficient sigma_eta^2/2, a future local theorem must justify differentiating the Measure.map law/test integral in s and identifying the derivative with the generator action that has negative drift-divergence and positive diffusion signs. This is the missing weak generator-to-law theorem consumed by the cycle-77 and cycle-78 supplied-hypothesis wrappers."
  source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
  status := ProofStatus.sourceCited
  dependsOn := [
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.FundThmCalculus",
    "Mathlib.MeasureTheory.Measure.Map",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Source-cited interface only. It does not import a new Mathlib module, construct the EM process, prove differentiability of the law, prove Ito/generator calculus, prove density/AC, prove boundary integration by parts, prove log-ratio admissibility, or close the weak Fokker-Planck/KL derivative backend."

/-- Cycle-79 upper packet for the minimal cited weak-FP generator interface. -/