AutoSamplingTheory.SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddleObligation

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 cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddleObligation :
    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_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 88 middle replaces the broad supplied hlog : Admissible logRatioTest hypothesis used by the cycle-83/cycle-84 weak-FP-to-KL handoffs with the smaller source-cited boundary: prove that the Mathlib llr hatRhoS tildePiS representative of log(hat rho_s/tilde pi_s) is an admissible weak-FP test under cycle-87 finite-KL regularity, density/time regularity, smoothing or Sobolev approximation, boundary/no-flux control, and closure of drift-divergence and Laplacian weak actions. Classification: narrows-source-cited-boundary. This does not prove raw KL differentiability, mass conservation, target-time integrability, weak FP, integration by parts, FI, theorem closure, or any SLT result.

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.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddlePacket
2. SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation
3. SALD.generalMovingTargetDiscreteKlLogRatioLlrDef
4. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
7. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
8. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
9. Mathlib.InformationTheory.KullbackLeibler.Basic
10. eq:general_KL_derivative_0_discrete
11. sald.general_moving_target_discrete.em_interpolation_fp
12. 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 boundary only. It selects exactly one older supplied EM/KL hypothesis, hlog : Admissible logRatioTest, and narrows it to a named approximation/closure theorem for the Mathlib llr weak test. No backend or theorem status is promoted.

def cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle88_kl_log_ratio_admissibility_middle"
  statement := "Cycle 88 middle replaces the broad supplied hlog : Admissible logRatioTest hypothesis used by the cycle-83/cycle-84 weak-FP-to-KL handoffs with the smaller source-cited boundary: prove that the Mathlib llr hatRhoS tildePiS representative of log(hat rho_s/tilde pi_s) is an admissible weak-FP test under cycle-87 finite-KL regularity, density/time regularity, smoothing or Sobolev approximation, boundary/no-flux control, and closure of drift-divergence and Laplacian weak actions. Classification: narrows-source-cited-boundary. This does not prove raw KL differentiability, mass conservation, target-time integrability, weak FP, integration by parts, FI, theorem closure, or any SLT result."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddlePacket",
    "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation",
    "SALD.generalMovingTargetDiscreteKlLogRatioLlrDef",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "eq:general_KL_derivative_0_discrete",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle boundary only. It selects exactly one older supplied EM/KL hypothesis, hlog : Admissible logRatioTest, and narrows it to a named approximation/closure theorem for the Mathlib llr weak test. No backend or theorem status is promoted."

/-- Cycle-88 lower handoff for log-ratio weak-test admissibility. -/