AutoSamplingTheory.SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation

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 cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation :
    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.cycle88_kl_log_ratio_admissibility_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 88 lower compiles SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure for appendix.tex lines 1358-1366. The theorem uses cycle-87 finite-KL llr regularity to derive the measure-regularity inputs and replaces the older broad hlog : Admissible logRatioTest hypothesis, when logRatioTest is llr hatRhoS tildePiS, by the strictly smaller source-cited closure package SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure. That closure package names the remaining smoothing/Sobolev approximation, density/time regularity, zero-set convention, boundary/no-flux control, drift-divergence action closure, Laplacian action closure, and target-time integrability theorem. Classification: narrows-source-cited-boundary; it removes the opaque hlog shape but does not prove the approximation/closure theorem itself.

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.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddleObligation
2. SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure
3. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
4. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
5. SALD.generalMovingTargetDiscreteKlLogRatioLlrDef
6. Mathlib.InformationTheory.KullbackLeibler.Basic
7. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
8. eq:general_KL_derivative_0_discrete
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.

Compiled finite-KL-to-admissible-llr handoff plus a narrowed closure boundary. Remaining analytic blockers are the closure package fields, raw KL differentiability, mass conservation, target-time derivative integrability, weak FP, integration by parts, FI, theorem closure, and any SLT reuse.

def cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle88_kl_log_ratio_admissibility_lower"
  statement := "Cycle 88 lower compiles SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure for appendix.tex lines 1358-1366. The theorem uses cycle-87 finite-KL llr regularity to derive the measure-regularity inputs and replaces the older broad hlog : Admissible logRatioTest hypothesis, when logRatioTest is llr hatRhoS tildePiS, by the strictly smaller source-cited closure package SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure. That closure package names the remaining smoothing/Sobolev approximation, density/time regularity, zero-set convention, boundary/no-flux control, drift-divergence action closure, Laplacian action closure, and target-time integrability theorem. Classification: narrows-source-cited-boundary; it removes the opaque hlog shape but does not prove the approximation/closure theorem itself."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddleObligation",
    "SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlLogRatioLlrDef",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "eq:general_KL_derivative_0_discrete",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Compiled finite-KL-to-admissible-llr handoff plus a narrowed closure boundary. Remaining analytic blockers are the closure package fields, raw KL differentiability, mass conservation, target-time derivative integrability, weak FP, integration by parts, FI, theorem closure, and any SLT reuse."

/-- Cycle-88 proof-DAG pane for the log-ratio admissibility boundary. -/