AutoSamplingTheory.SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation

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 cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation :
    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.cycle83_kl_derivative_endpoint_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 83 compiles SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff for appendix.tex:1358-1387 and adds SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction as the lower companion. The wrapper composes SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff with SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns: once endpoint/conditional readiness, supplied generator/time derivative, drift/diffusion source actions, density/time regularity, boundary behavior, fpCoeff=sigma_eta^2/2, the differentiated KL display, and log-ratio admissibility are supplied, the resulting KL derivative display has the paper's negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term; the companion records the log-ratio weak-FP action and dK display as a pair.

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.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
3. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
6. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
7. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
8. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
9. sald.general_moving_target_discrete.em_interpolation_fp
10. 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 composition plus obligation only. It proves no conditional law, density/AC, weak Fokker-Planck theorem, KL differentiability, integration by parts, FI identification, LSI/KL/FI, DV, Gronwall, theorem closure, SLT import, or Lake dependency.

def cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle83_kl_derivative_endpoint_weak_fp_lower"
  statement := "Cycle 83 compiles SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff for appendix.tex:1358-1387 and adds SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction as the lower companion. The wrapper composes SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff with SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns: once endpoint/conditional readiness, supplied generator/time derivative, drift/diffusion source actions, density/time regularity, boundary behavior, fpCoeff=sigma_eta^2/2, the differentiated KL display, and log-ratio admissibility are supplied, the resulting KL derivative display has the paper's negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term; the companion records the log-ratio weak-FP action and dK display as a pair."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Proof-producing local composition plus obligation only. It proves no conditional law, density/AC, weak Fokker-Planck theorem, KL differentiability, integration by parts, FI identification, LSI/KL/FI, DV, Gronwall, theorem closure, SLT import, or Lake dependency."

/-- Cycle-83 proof-DAG pane for endpoint weak-FP source signs to KL
derivative handoff. -/