AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticMiddleObligation

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 cycle54MainSkeletonAnalyticMiddleObligation : 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_middle_interface_audit

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 middle verifies that the upper analytic-interface ledger is consumed in source order by 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. It sharpens the lower target to appendix.tex:1354-1387 for common-space, density/absolute-continuity, regular conditional drift, weak EM Fokker-Planck, KL differentiation, and integration-by-parts inputs, while keeping all unproved analytic backends obligation or sourceCited.

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

SALD.cycle54MainSkeletonAnalyticMiddleContract
SALD.cycle54MainSkeletonAnalyticInterfaceObligation
SALD.cycle49MainSkeletonAnalyticMiddleObligation
SALD.cycle50ForwardKlSkeletonMiddleObligation
SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
SALD.cycle52GuidedGeneralSkeletonMiddleObligation
SALD.cycle53UnifiedDiscreteGeneralMiddleObligation
SALD.saldGronwallEndpointCalculusContract
dvVariationalFormulaInterface saldDvVariationSource
SALD.saldDvFiniteLogMgfContract
SALD.saldLsiKlFiDensityTestContract
SALD.forwardKlDerivativeSideConditionContract
SALD.generalMovingTargetDerivativeCandidateContract
SALD.discreteForwardKlEmInterpolationSideConditionContract
SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
sald.general_moving_target_discrete.em_interpolation_fp
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 workflow audit only. It does not add theorem hypotheses, change source constants, or promote Gronwall, DV, LSI/KL/FI, continuous FP/KL derivative, EM conditional-FP, or theorem statements.

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 cycle54MainSkeletonAnalyticMiddleObligation : ProofObligation where
  id := "sald.main_skeleton.cycle54_middle_interface_audit"
  statement := "Cycle 54 middle verifies that the upper analytic-interface ledger is consumed in source order by 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. It sharpens the lower target to appendix.tex:1354-1387 for common-space, density/absolute-continuity, regular conditional drift, weak EM Fokker-Planck, KL differentiation, and integration-by-parts inputs, while keeping all unproved analytic backends obligation or sourceCited."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle54MainSkeletonAnalyticMiddleContract",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle50ForwardKlSkeletonMiddleObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle53UnifiedDiscreteGeneralMiddleObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle workflow audit only. It does not add theorem hypotheses, change source constants, or promote Gronwall, DV, LSI/KL/FI, continuous FP/KL derivative, EM conditional-FP, or theorem statements."

/-- Cycle-54 proof-DAG pane for the repeated analytic-interface ledger. -/

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