AutoSamplingTheory.SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation

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 cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation :
    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.cycle73_kl_derivative_weak_fp_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 73 compiles SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns for appendix.tex:1358-1387: if the differentiated KL formula is supplied as dK=partialS(logRatioTest)-targetTimeTerm, the log-ratio test is admissible, the supplied weak conditional Fokker-Planck identity gives partialS(phi)=-(driftDiv phi)+sigmaCoeff*(laplacian phi) on admissible tests, and sigmaCoeff=sigma_eta^2/2, then the source-signed KL derivative display has the negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term. The second wrapper explicitly composes the KL handoff through the cycle-72 admissible weak-FP source-sign theorem.

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.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
7. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
8. sald.general_moving_target_discrete.em_interpolation_fp
9. 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 scalar substitution plus obligation only. The composed wrapper reuses the cycle-72 admissible weak-FP source-sign theorem under explicit hypotheses; it does not prove the weak FP theorem, admissible log-ratio test, density/AC, KL differentiation, mass conservation, integration by parts, Laplacian split, FI identification, LSI/KL/FI, DV, Gronwall, or theorem closure.

def cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle73_kl_derivative_weak_fp_lower"
  statement := "Cycle 73 compiles SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns for appendix.tex:1358-1387: if the differentiated KL formula is supplied as dK=partialS(logRatioTest)-targetTimeTerm, the log-ratio test is admissible, the supplied weak conditional Fokker-Planck identity gives partialS(phi)=-(driftDiv phi)+sigmaCoeff*(laplacian phi) on admissible tests, and sigmaCoeff=sigma_eta^2/2, then the source-signed KL derivative display has the negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term. The second wrapper explicitly composes the KL handoff through the cycle-72 admissible weak-FP source-sign theorem."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Proof-producing scalar substitution plus obligation only. The composed wrapper reuses the cycle-72 admissible weak-FP source-sign theorem under explicit hypotheses; it does not prove the weak FP theorem, admissible log-ratio test, density/AC, KL differentiation, mass conservation, integration by parts, Laplacian split, FI identification, LSI/KL/FI, DV, Gronwall, or theorem closure."

/-- Cycle-73 proof-DAG pane for weak-FP-to-KL derivative handoff. -/