AutoSamplingTheory.SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation

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 cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation :
    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.cycle78_kl_derivative_generator_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 78 middle maps appendix.tex:1358-1387 to the existing Lean route without changing the paper statement: appendix.tex:1358-1366 supplies the differentiated KL display dK=partialS(logRatioTest)-targetTimeTerm after the mass-conservation term is dropped; appendix.tex:1379-1387 supplies the weak conditional Fokker-Planck source signs through the cycle-77 generator/time-derivative, generator split, and separated drift/diffusion source-action hypotheses; the log-density-ratio test enters only by an explicit admissibility hypothesis; SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns is the normalized weak-FP-to-KL substitution, and the resulting generator-piece handoff is exactly SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces before any integration by parts, Laplacian split, FI identification, LSI, DV, Gronwall, or theorem closure.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperObligation
2. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns
7. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces
8. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
9. sald.general_moving_target_discrete.em_interpolation_fp
10. sald.general_moving_target_discrete.kl_derivative

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Middle synchronization only. It records the ordered source route from KL differentiation through the supplied generator-piece weak FP signs, and keeps density/AC, log-ratio admissibility, generator/weak-FP theorem, mass conservation, integration by parts, FI, LSI, DV, Gronwall, and theorem statuses below formalized.

def cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle78_kl_derivative_generator_middle"
  statement := "Cycle 78 middle maps appendix.tex:1358-1387 to the existing Lean route without changing the paper statement: appendix.tex:1358-1366 supplies the differentiated KL display dK=partialS(logRatioTest)-targetTimeTerm after the mass-conservation term is dropped; appendix.tex:1379-1387 supplies the weak conditional Fokker-Planck source signs through the cycle-77 generator/time-derivative, generator split, and separated drift/diffusion source-action hypotheses; the log-density-ratio test enters only by an explicit admissibility hypothesis; SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns is the normalized weak-FP-to-KL substitution, and the resulting generator-piece handoff is exactly SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces before any integration by parts, Laplacian split, FI identification, LSI, DV, Gronwall, or theorem closure."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperObligation",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle synchronization only. It records the ordered source route from KL differentiation through the supplied generator-piece weak FP signs, and keeps density/AC, log-ratio admissibility, generator/weak-FP theorem, mass conservation, integration by parts, FI, LSI, DV, Gronwall, and theorem statuses below formalized."

/-- Cycle-78 local wrapper obligation for generator-piece weak-FP to KL
derivative substitution. -/