AutoSamplingTheory.SALD.cycle105GeneralMovingTargetDiscretePureRawKlDerivativeMiddleObligation

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 cycle105GeneralMovingTargetDiscretePureRawKlDerivativeMiddleObligation :
    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.cycle105_pure_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 105 middle keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and narrows the KL/log-ratio analytic boundary at appendix.tex:1358-1366. Classification: narrows-source-cited-boundary. The exact missing theorem is now the pure no-mass finite-KL llr KL-differentiability statement: finite KL supplies the Mathlib llr representative and its regularity, while endpoint-safe KL differentiation, llr weak-action integrability, target-time integrability, and the target-time derivative formula imply dK = partialS (llr hatRho tildePi) - targetTimeTerm. The boundary no longer carries sample-space P, hatX, s0, hatX a.e. measurability, or a mapped-law mass derivative.

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.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr
2. SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr
3. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
4. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
5. Mathlib.InformationTheory.KullbackLeibler.Basic
6. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
7. Mathlib.Analysis.Calculus.ParametricIntegral
8. Mathlib.MeasureTheory.Integral.Bochner.Basic
9. eq:general_KL_derivative_0_discrete
10. appendix.tex:1358-1366
11. 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 rejects wrappers around hklRaw, hlog, hmass, weak-FP source signs, barB no-boundary, LSI, DV, or Gronwall. The theorem statements and backend statuses are unchanged.

def cycle105GeneralMovingTargetDiscretePureRawKlDerivativeMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle105_pure_raw_kl_derivative_middle"
  statement := "Cycle 105 middle keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and narrows the KL/log-ratio analytic boundary at appendix.tex:1358-1366. Classification: narrows-source-cited-boundary. The exact missing theorem is now the pure no-mass finite-KL llr KL-differentiability statement: finite KL supplies the Mathlib llr representative and its regularity, while endpoint-safe KL differentiation, llr weak-action integrability, target-time integrability, and the target-time derivative formula imply dK = partialS (llr hatRho tildePi) - targetTimeTerm. The boundary no longer carries sample-space P, hatX, s0, hatX a.e. measurability, or a mapped-law mass derivative."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr",
    "SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "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.kl_derivative"
  ]
  note := "Middle synchronization only. It rejects wrappers around hklRaw, hlog, hmass, weak-FP source signs, barB no-boundary, LSI, DV, or Gronwall. The theorem statements and backend statuses are unchanged."

/-- Cycle-105 lower obligation for the compiled pure no-mass KL handoff. -/