AutoSamplingTheory.SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation

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 cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation :
    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_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 73 middle synchronizes appendix.tex:1358-1387 into the active EM backend: eq:general_KL_derivative_0_discrete supplies the differentiated KL display with the target-time term, cycles 70-72 supply conditional-law, endpoint compatibility, and weak FP source signs under explicit hypotheses, and the selected lower wrappers substitute the supplied weak FP identity at the admissible log-density-ratio test before later integration-by-parts and Fisher-information handoffs.

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.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpUpperObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
4. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
5. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
6. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
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. Log-ratio admissibility, density/absolute-continuity, KL differentiability, mass conservation, weak FP theorem, boundary/integration-by-parts, and FI identification remain obligations.

def cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle73_kl_derivative_weak_fp_middle"
  statement := "Cycle 73 middle synchronizes appendix.tex:1358-1387 into the active EM backend: eq:general_KL_derivative_0_discrete supplies the differentiated KL display with the target-time term, cycles 70-72 supply conditional-law, endpoint compatibility, and weak FP source signs under explicit hypotheses, and the selected lower wrappers substitute the supplied weak FP identity at the admissible log-density-ratio test before later integration-by-parts and Fisher-information handoffs."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpUpperObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle synchronization only. Log-ratio admissibility, density/absolute-continuity, KL differentiability, mass conservation, weak FP theorem, boundary/integration-by-parts, and FI identification remain obligations."

/-- Cycle-73 local wrapper obligation for weak-FP-to-KL derivative substitution. -/