AutoSamplingTheory.SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation

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 cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation :
    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_middle

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 middle maps appendix.tex:1358-1387 without changing the paper statement: eq:general_KL_derivative_0_discrete supplies dK=partialS(logRatioTest)-targetTimeTerm after the mass-conservation drop; the cycle-82 endpoint/conditional wrapper supplies the weak-FP source signs for admissible tests; the log-density-ratio test enters only through an explicit admissibility hypothesis; and the local lower wrapper composes those facts before integration by parts, Laplacian split, FI identification, LSI, DV, Gronwall, or theorem closure.

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.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation
2. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
3. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
4. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
7. sald.general_moving_target_discrete.em_interpolation_fp
8. sald.general_moving_target_discrete.kl_derivative

note : String (explicit)

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

Middle synchronization only. Conditional law, density/AC, weak FP, KL differentiability, log-ratio admissibility, boundary behavior, integration by parts, FI, LSI, DV, and Gronwall remain obligations.

def cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle83_kl_derivative_endpoint_weak_fp_middle"
  statement := "Cycle 83 middle maps appendix.tex:1358-1387 without changing the paper statement: eq:general_KL_derivative_0_discrete supplies dK=partialS(logRatioTest)-targetTimeTerm after the mass-conservation drop; the cycle-82 endpoint/conditional wrapper supplies the weak-FP source signs for admissible tests; the log-density-ratio test enters only through an explicit admissibility hypothesis; and the local lower wrapper composes those facts before integration by parts, Laplacian split, FI identification, LSI, DV, Gronwall, or theorem closure."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle synchronization only. Conditional law, density/AC, weak FP, KL differentiability, log-ratio admissibility, boundary behavior, integration by parts, FI, LSI, DV, and Gronwall remain obligations."

/-- Cycle-83 lower obligation for the endpoint source-signs to KL wrapper. -/