AutoSamplingTheory.SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation

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 cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation :
    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.cycle87_kl_log_ratio_boundary_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 87 lower compiles SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction for appendix.tex lines 1358-1366, and adds SALD.generalMovingTargetDiscreteKlLogRatioLlrDef plus SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl. The scalar handoffs replace the older supplied post-mass-drop hkl display with the strictly smaller inputs raw KL derivative with explicit massTerm, massTerm=0, admissible log-ratio test, and normalized weak-FP source signs. The log-ratio theorem discharges separate absolute-continuity, measurability, and integrability side hypotheses for the Mathlib llr weak test from finite KL. Classification: discharges-supplied-hypothesis for log-ratio regularity, and narrows-source-cited-boundary for the raw KL/mass split. The remaining exact analytic boundaries are raw KL differentiability under the integral, proof of integral partial_s hat rho_s dx=0, weak-test admissibility of the log-ratio, target-time derivative integrability, density/time regularity, plus downstream integration by parts and FI identification.

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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
4. SALD.generalMovingTargetDiscreteKlLogRatioLlrDef
5. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
7. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
8. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
9. Mathlib.InformationTheory.KullbackLeibler.Basic
10. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
11. eq:general_KL_derivative_0_discrete
12. sald.general_moving_target_discrete.kl_derivative
13. 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.

Formalized local scalar handoff plus Mathlib-backed log-ratio regularity. It narrows hkl to raw KL derivative plus mass conservation and removes separate log-ratio AC/measurability/integrability hypotheses under finite KL; it does not prove KL differentiability, mass conservation, log-ratio weak-test admissibility, weak FP, integration by parts, FI, LSI, DV, Gronwall, theorem closure, SLT reuse, or any Lake dependency.

def cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle87_kl_log_ratio_boundary_lower"
  statement := "Cycle 87 lower compiles SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction for appendix.tex lines 1358-1366, and adds SALD.generalMovingTargetDiscreteKlLogRatioLlrDef plus SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl. The scalar handoffs replace the older supplied post-mass-drop hkl display with the strictly smaller inputs raw KL derivative with explicit massTerm, massTerm=0, admissible log-ratio test, and normalized weak-FP source signs. The log-ratio theorem discharges separate absolute-continuity, measurability, and integrability side hypotheses for the Mathlib llr weak test from finite KL. Classification: discharges-supplied-hypothesis for log-ratio regularity, and narrows-source-cited-boundary for the raw KL/mass split. The remaining exact analytic boundaries are raw KL differentiability under the integral, proof of integral partial_s hat rho_s dx=0, weak-test admissibility of the log-ratio, target-time derivative integrability, density/time regularity, plus downstream integration by parts and FI identification."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioLlrDef",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
    "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "eq:general_KL_derivative_0_discrete",
    "sald.general_moving_target_discrete.kl_derivative",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Formalized local scalar handoff plus Mathlib-backed log-ratio regularity. It narrows hkl to raw KL derivative plus mass conservation and removes separate log-ratio AC/measurability/integrability hypotheses under finite KL; it does not prove KL differentiability, mass conservation, log-ratio weak-test admissibility, weak FP, integration by parts, FI, LSI, DV, Gronwall, theorem closure, SLT reuse, or any Lake dependency."

/-- Cycle-87 proof-DAG pane for the KL/log-ratio analytic boundary. -/