AutoSamplingTheory.SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation

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 cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation :
    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.cycle84_active_em_backend_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 84 lower compiles SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction for appendix.tex:1358-1387. The wrapper consumes the cycle-81 endpoint/conditional WeakFpPrereq readiness, the cycle-82 endpoint weak-FP source-sign handoff, and the cycle-83 log-ratio weak-FP-to-KL handoff; under explicit supplied hypotheses it returns both the log-ratio weak-FP action and the resulting dK display with the paper's negative drift-divergence sign, positive sigma_eta^2/2 Laplacian coefficient, and unchanged target-time term. No new Mathlib/measure fallback was needed.

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.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
3. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
5. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
6. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
7. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
8. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
9. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
10. sald.general_moving_target_discrete.em_interpolation_fp
11. 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. Conditional law, density/AC, weak Fokker-Planck theorem, generator-to-law differentiation, KL differentiability, integration by parts, FI identification, LSI/KL/FI, DV, Gronwall, theorem closure, SLT import, and Lake dependency remain unpromoted.

def cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle84_active_em_backend_lower"
  statement := "Cycle 84 lower compiles SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction for appendix.tex:1358-1387. The wrapper consumes the cycle-81 endpoint/conditional WeakFpPrereq readiness, the cycle-82 endpoint weak-FP source-sign handoff, and the cycle-83 log-ratio weak-FP-to-KL handoff; under explicit supplied hypotheses it returns both the log-ratio weak-FP action and the resulting dK display with the paper's negative drift-divergence sign, positive sigma_eta^2/2 Laplacian coefficient, and unchanged target-time term. No new Mathlib/measure fallback was needed."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "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. Conditional law, density/AC, weak Fokker-Planck theorem, generator-to-law differentiation, KL differentiability, integration by parts, FI identification, LSI/KL/FI, DV, Gronwall, theorem closure, SLT import, and Lake dependency remain unpromoted."

/-- Cycle-84 proof-DAG pane for the active EM-backend handoff/fallback
decision. -/