AutoSamplingTheory.SALD.cycle105GeneralMovingTargetDiscretePureRawKlDerivativeLowerObligation

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 cycle105GeneralMovingTargetDiscretePureRawKlDerivativeLowerObligation :
    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_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 105 lower compiles SALD.generalMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlrHkl and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfPureNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction. The compiled handoff extracts the no-mass display from the pure finite-KL llr source-cited package, uses the existing finite-KL admissibility closure to select the admissible log-ratio weak test, and feeds the result into the existing source-sign-with-log-action theorem. Classification: narrows-source-cited-boundary because the remaining missing theorem is smaller than cycle 99: it is measure-path KL differentiability only, with no sample-space law or mass-derivative fields.

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.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr
2. SALD.generalMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlrHkl
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfPureNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
5. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
6. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
7. SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation
8. Mathlib.InformationTheory.KullbackLeibler.Basic
9. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
10. eq:general_KL_derivative_0_discrete
11. appendix.tex:1358-1366
12. 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.

Proof-producing equality handoff plus source-cited analytic boundary. It does not prove endpoint-safe KL differentiation, target-time derivative, weak FP, log-ratio closure internals, IBP/FI, theorem closure, SLT import, or any Lake dependency.

def cycle105GeneralMovingTargetDiscretePureRawKlDerivativeLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle105_pure_raw_kl_derivative_lower"
  statement := "Cycle 105 lower compiles SALD.generalMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlrHkl and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfPureNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction. The compiled handoff extracts the no-mass display from the pure finite-KL llr source-cited package, uses the existing finite-KL admissibility closure to select the admissible log-ratio weak test, and feeds the result into the existing source-sign-with-log-action theorem. Classification: narrows-source-cited-boundary because the remaining missing theorem is smaller than cycle 99: it is measure-path KL differentiability only, with no sample-space law or mass-derivative fields."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr",
    "SALD.generalMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlrHkl",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfPureNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "eq:general_KL_derivative_0_discrete",
    "appendix.tex:1358-1366",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Proof-producing equality handoff plus source-cited analytic boundary. It does not prove endpoint-safe KL differentiation, target-time derivative, weak FP, log-ratio closure internals, IBP/FI, theorem closure, SLT import, or any Lake dependency."

/-- Cycle-105 proof-DAG pane for the pure no-mass KL/log-ratio boundary. -/