AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticInterfaceObligation

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 cycle54MainSkeletonAnalyticInterfaceObligation : 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.main_skeleton.cycle54_analytic_interface_ledger

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 54 upper re-checks the five slow analytic interfaces after the theorem route has been threaded: Gronwall endpoint-safe differentiability/FTC, Donsker-Varadhan common-space/absolute-continuity/finite-KL/finite-log-mgf, LSI-to-KL/FI density/zero-set/admissible-test/entropy/Fisher-chain assumptions, continuous forward-KL and general Fokker-Planck/KL derivative identities, and Euler-Maruyama interpolation endpoint/conditional-law Fokker-Planck. It wires those interfaces back into thm:forward-KL, thm:forward-KL-discrete, prop:guided_path_residual, thm:general-moving-target-SALD, thm:unified-forward-KL, and thm:general-moving-target-SALD-discrete while keeping every unproved backend below formalized status; the cycle-54 lower sigma-weighted divergence regrouping is formalized only as algebra under explicit FP hypotheses.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle54MainSkeletonAnalyticInterfaceLedger
2. SALD.cycle44MainSkeletonAnalyticInterfaceObligation
3. SALD.cycle49MainSkeletonAnalyticReadinessObligation
4. SALD.cycle50ForwardKlSkeletonObligation
5. SALD.cycle51DiscreteForwardKlSkeletonObligation
6. SALD.cycle52GuidedGeneralSkeletonObligation
7. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
8. SALD.saldGronwallEndpointCalculusContract
9. dvVariationalFormulaInterface saldDvVariationSource
10. SALD.saldDvFiniteLogMgfContract
11. SALD.saldLsiKlFiDensityTestContract
12. SALD.forwardKlDerivativeCandidateContract
13. SALD.forwardKlDerivativeSideConditionContract
14. SALD.generalMovingTargetDerivativeCandidateContract
15. SALD.discreteForwardKlEmInterpolationSideConditionContract
16. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
17. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
18. SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
19. SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation
20. SALD.forwardKlProofDag
21. SALD.discreteForwardKlProofDag
22. SALD.generalVaSaldProofDag
23. SALD.generalVaSaldDiscreteProofDag

note : String (explicit)

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

This is an upper workflow obligation and route audit, not a new analytic theorem. It adds no hidden assumptions and does not promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL derivative, EM conditional-FP, or theorem statements.

def cycle54MainSkeletonAnalyticInterfaceObligation : ProofObligation where
  id := "sald.main_skeleton.cycle54_analytic_interface_ledger"
  statement := "Cycle 54 upper re-checks the five slow analytic interfaces after the theorem route has been threaded: Gronwall endpoint-safe differentiability/FTC, Donsker-Varadhan common-space/absolute-continuity/finite-KL/finite-log-mgf, LSI-to-KL/FI density/zero-set/admissible-test/entropy/Fisher-chain assumptions, continuous forward-KL and general Fokker-Planck/KL derivative identities, and Euler-Maruyama interpolation endpoint/conditional-law Fokker-Planck. It wires those interfaces back into thm:forward-KL, thm:forward-KL-discrete, prop:guided_path_residual, thm:general-moving-target-SALD, thm:unified-forward-KL, and thm:general-moving-target-SALD-discrete while keeping every unproved backend below formalized status; the cycle-54 lower sigma-weighted divergence regrouping is formalized only as algebra under explicit FP hypotheses."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle54MainSkeletonAnalyticInterfaceLedger",
    "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle50ForwardKlSkeletonObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonObligation",
    "SALD.cycle52GuidedGeneralSkeletonObligation",
    "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeCandidateContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
    "SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation",
    "SALD.forwardKlProofDag",
    "SALD.discreteForwardKlProofDag",
    "SALD.generalVaSaldProofDag",
    "SALD.generalVaSaldDiscreteProofDag"
  ]
  note := "This is an upper workflow obligation and route audit, not a new analytic theorem. It adds no hidden assumptions and does not promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL derivative, EM conditional-FP, or theorem statements."

/-- Cycle-54 middle audit of the repeated analytic-interface sprint.

This is source-to-Lean synchronization for the middle role.  It checks that the
upper ledger's five interfaces are actually consumed by the theorem DAGs in
paper order and keeps the lower packet focused on the theorem-useful
Euler-Maruyama conditional-law/Fokker-Planck backend.
-/