AutoSamplingTheory.SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation

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 cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation :
    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.cycle93_kl_mass_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 93 lower compiles SALD.generalMovingTargetDiscreteKlMassTermZeroOfLawConstantTestDerivative, SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfLawConstantTestMassAndSourceSignsWithLogAction, and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction for appendix.tex:1358-1366. The new handoffs remove the primitive hmass : massTerm=0 premise when massTerm is identified as the HasDerivAt derivative of the constant weak-test pairing integral 1 d Law(hat X_s), and remove the primitive hlog premise for the exact Mathlib llr hatRho tildePi test by using finite KL plus the cycle-88 admissibility closure package. They use AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, derivative uniqueness for a constant sample-space integral, and SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure. Classification: discharges-supplied-hypothesis for primitive hmass and primitive hlog in the llr-specialized handoff; narrows-source-cited-boundary for the remaining massTerm-to-constant-test-derivative identification and closure package. Remaining exact analytic boundaries are the raw KL differentiability formula hklRaw, target-time derivative identification, the closure package internals, weak-FP source signs, 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.cycle93GeneralMovingTargetDiscreteKlMassDerivativeMiddleObligation
2. SALD.generalMovingTargetDiscreteKlMassTermZeroOfLawConstantTestDerivative
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfLawConstantTestMassAndSourceSignsWithLogAction
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
6. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
7. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff
8. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
9. Mathlib.MeasureTheory.Integral.Bochner.Basic
10. Mathlib.Analysis.Calculus.Deriv.Basic
11. eq:general_KL_derivative_0_discrete
12. appendix.tex:1358-1366
13. sald.general_moving_target_discrete.em_interpolation_fp
14. sald.general_moving_target_discrete.kl_derivative

note : String (explicit)

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

Proof-producing local theorem plus remaining obligation. It removes hmass as a primitive scalar input for the general moving-target KL handoff, but does not prove the raw KL derivative display, target-time term, admissible log-ratio closure, weak FP, integration by parts, FI, LSI, DV, Gronwall, theorem closure, or any SLT result.

def cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle93_kl_mass_derivative_lower"
  statement := "Cycle 93 lower compiles SALD.generalMovingTargetDiscreteKlMassTermZeroOfLawConstantTestDerivative, SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfLawConstantTestMassAndSourceSignsWithLogAction, and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction for appendix.tex:1358-1366. The new handoffs remove the primitive hmass : massTerm=0 premise when massTerm is identified as the HasDerivAt derivative of the constant weak-test pairing integral 1 d Law(hat X_s), and remove the primitive hlog premise for the exact Mathlib llr hatRho tildePi test by using finite KL plus the cycle-88 admissibility closure package. They use AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, derivative uniqueness for a constant sample-space integral, and SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure. Classification: discharges-supplied-hypothesis for primitive hmass and primitive hlog in the llr-specialized handoff; narrows-source-cited-boundary for the remaining massTerm-to-constant-test-derivative identification and closure package. Remaining exact analytic boundaries are the raw KL differentiability formula hklRaw, target-time derivative identification, the closure package internals, weak-FP source signs, integration by parts, and FI identification."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeMiddleObligation",
    "SALD.generalMovingTargetDiscreteKlMassTermZeroOfLawConstantTestDerivative",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfLawConstantTestMassAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorHandoff",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "Mathlib.Analysis.Calculus.Deriv.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 := "Proof-producing local theorem plus remaining obligation. It removes hmass as a primitive scalar input for the general moving-target KL handoff, but does not prove the raw KL derivative display, target-time term, admissible log-ratio closure, weak FP, integration by parts, FI, LSI, DV, Gronwall, theorem closure, or any SLT result."

/-- Cycle-93 proof-DAG pane for the KL/log-ratio mass derivative boundary. -/