AutoSamplingTheory.SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation :
    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_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 99 lower-ready interface compiles SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw, SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction, and the stricter no-mass route SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction. The source-cited analytic package SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr removes the mapped-law mass-derivative field from the remaining raw-KL boundary by proving the constant mapped-law weak-test derivative locally from AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample. The remaining appendix.tex:1358-1366 theorem boundary is the endpoint-safe no-mass KL differentiation display at the finite-KL llr test with target-time integrability/formula; cycle-88 admissibility closure and downstream weak-FP/IBP/FI remain separate.

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

SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation
SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr
SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw
SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction
SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr
SALD.generalMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlrHkl
SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction
SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction
SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
Mathlib.InformationTheory.KullbackLeibler.Basic
Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
Mathlib.Analysis.Calculus.ParametricIntegral
Mathlib.MeasureTheory.Integral.Bochner.Basic
appendix.tex:1358-1366

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

The compiled no-mass handoff is local composition plus the concrete mapped-law constant-test derivative. It discharges the mass-derivative field for this finite-KL llr route, but the no-mass raw KL differentiability theorem remains source-cited/obligation-level and must be proved before marking hklRaw discharged.

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle99_raw_kl_derivative_lower"
  statement := "Cycle 99 lower-ready interface compiles SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw, SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction, and the stricter no-mass route SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction. The source-cited analytic package SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr removes the mapped-law mass-derivative field from the remaining raw-KL boundary by proving the constant mapped-law weak-test derivative locally from AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample. The remaining appendix.tex:1358-1366 theorem boundary is the endpoint-safe no-mass KL differentiation display at the finite-KL llr test with target-time integrability/formula; cycle-88 admissibility closure and downstream weak-FP/IBP/FI remain separate."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation",
    "SALD.GeneralMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlr",
    "SALD.generalMovingTargetDiscreteRawKlDerivativeAtFiniteKlLlrHklRaw",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlBoundaryAtFiniteKlLlrWithLogAction",
    "SALD.GeneralMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlr",
    "SALD.generalMovingTargetDiscreteRawKlDerivativeNoMassAtFiniteKlLlrHkl",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfNoMassRawKlBoundaryAtFiniteKlLlrWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "appendix.tex:1358-1366"
  ]
  note := "The compiled no-mass handoff is local composition plus the concrete mapped-law constant-test derivative. It discharges the mass-derivative field for this finite-KL llr route, but the no-mass raw KL differentiability theorem remains source-cited/obligation-level and must be proved before marking hklRaw discharged."

/-- Cycle-99 proof-DAG pane for the raw KL finite-KL `llr` boundary. -/

Existing module entry · Audited data-reader index · All teaching coverage