AutoSamplingTheory.SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation

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 cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation :
    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.cycle99_raw_kl_derivative_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 99 middle records the active KL/log-ratio packet over appendix.tex:1358-1366. Classification: narrows-source-cited-boundary. The exact missing theorem boundary is no longer a primitive scalar hklRaw; it is SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr, a finite-KL llr raw-differentiability package exposing density/path regularity, endpoint-safe differentiation under the KL integral, llr weak-action integrability, target-time term integrability and formula, and the mapped-law constant-test mass derivative. The compiled handoff SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction then feeds that package into the existing finite-KL llr, law-mass, and weak-FP source-sign route. Theorem statements, source signs, coefficients, and statuses remain unchanged.

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.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction
3. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
4. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
5. SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr
6. SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw
7. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction
8. Mathlib.InformationTheory.KullbackLeibler.Basic
9. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
10. Mathlib.Analysis.Calculus.ParametricIntegral
11. Mathlib.MeasureTheory.Integral.Bochner.Basic
12. eq:general_KL_derivative_0_discrete
13. appendix.tex:1358-1366
14. sald.general_moving_target_discrete.em_interpolation_fp
15. 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 source-to-Lean synchronization only. It rejects wrapper churn around hklRaw and records the smaller source-cited KL differentiability theorem with explicit Mathlib/local hypotheses. No KL differentiation theorem, weak FP theorem, IBP/FI identity, theorem closure, SLT result, or Lake dependency is promoted.

def cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle99_raw_kl_derivative_middle"
  statement := "Cycle 99 middle records the active KL/log-ratio packet over appendix.tex:1358-1366. Classification: narrows-source-cited-boundary. The exact missing theorem boundary is no longer a primitive scalar hklRaw; it is SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr, a finite-KL llr raw-differentiability package exposing density/path regularity, endpoint-safe differentiation under the KL integral, llr weak-action integrability, target-time term integrability and formula, and the mapped-law constant-test mass derivative. The compiled handoff SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction then feeds that package into the existing finite-KL llr, law-mass, and weak-FP source-sign route. Theorem statements, source signs, coefficients, and statuses remain unchanged."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr",
    "SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "eq:general_KL_derivative_0_discrete",
    "appendix.tex:1358-1366",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle source-to-Lean synchronization only. It rejects wrapper churn around hklRaw and records the smaller source-cited KL differentiability theorem with explicit Mathlib/local hypotheses. No KL differentiation theorem, weak FP theorem, IBP/FI identity, theorem closure, SLT result, or Lake dependency is promoted."

/-- Cycle-99 lower-ready obligation for the finite-KL `llr` raw-KL package. -/