AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticInterfaceObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle59MainSkeletonAnalyticInterfaceObligation : 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.cycle59_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 59 upper records the global phase judgment after the accepted cycle-58 reviewer/build pass: no recovery is needed; Phase 1 theorem-skeleton translation is stable enough for exactly one narrow cited-theory/SDE backend, not broad backfill; and the lower packet that best reduces remaining proof risk is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600. It rechecks the five slow analytic interfaces and wires them 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.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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

SALD.cycle59MainSkeletonAnalyticInterfaceLedger
SALD.cycle44MainSkeletonAnalyticInterfaceObligation
SALD.cycle54MainSkeletonAnalyticInterfaceObligation
SALD.cycle54MainSkeletonAnalyticMiddleObligation
SALD.cycle55ForwardKlSkeletonMiddleObligation
SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
SALD.cycle56DiscreteForwardKlGronwallLowerObligation
SALD.cycle57GuidedGeneralSkeletonMiddleObligation
SALD.cycle58UnifiedDiscreteGeneralMiddleObligation
SALD.saldGronwallEndpointCalculusContract
dvVariationalFormulaInterface saldDvVariationSource
SALD.saldDvFiniteLogMgfContract
SALD.saldLsiKlFiDensityTestContract
SALD.forwardKlDerivativeCandidateContract
SALD.forwardKlDerivativeSideConditionContract
SALD.generalMovingTargetDerivativeCandidateContract
SALD.discreteForwardKlEmInterpolationSideConditionContract
SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
SALD.generalMovingTargetDiscreteGronwallSideConditionContract
SALD.forwardKlProofDag
SALD.discreteForwardKlProofDag
SALD.generalVaSaldProofDag
SALD.generalVaSaldDiscreteProofDag

note : String (explicit)

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

This is upper workflow and source-to-Lean route data, not a proof of any analytic backend. It does not add theorem hypotheses or promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, EM conditional-FP, Gronwall stitching, theorem contracts, or SLT reuse statuses.

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle59MainSkeletonAnalyticInterfaceObligation : ProofObligation where
  id := "sald.main_skeleton.cycle59_analytic_interface_ledger"
  statement := "Cycle 59 upper records the global phase judgment after the accepted cycle-58 reviewer/build pass: no recovery is needed; Phase 1 theorem-skeleton translation is stable enough for exactly one narrow cited-theory/SDE backend, not broad backfill; and the lower packet that best reduces remaining proof risk is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600. It rechecks the five slow analytic interfaces and wires them 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."
  source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle59MainSkeletonAnalyticInterfaceLedger",
    "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle58UnifiedDiscreteGeneralMiddleObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeCandidateContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
    "SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput",
    "SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "SALD.forwardKlProofDag",
    "SALD.discreteForwardKlProofDag",
    "SALD.generalVaSaldProofDag",
    "SALD.generalVaSaldDiscreteProofDag"
  ]
  note := "This is upper workflow and source-to-Lean route data, not a proof of any analytic backend. It does not add theorem hypotheses or promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, EM conditional-FP, Gronwall stitching, theorem contracts, or SLT reuse statuses."

/-- Cycle-59 middle audit for the analytic-interface ledger.

This source-to-Lean synchronization layer checks the upper cycle-59 ledger
against the six theorem consumers and keeps lower work on the theorem-level
discrete general Gronwall/display side conditions.
-/

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