AutoSamplingTheory.SALD.discreteSaldContract

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.TheoremContract. 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 discreteSaldContract : TheoremContract

Construction and field-by-field explanation

Construction explanation requires review; no value was guessed.

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.

Unresolved: unsupported expression or unaudited data reference

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 discreteSaldContract : TheoremContract where
  id := "ASTIS.SALD.forward_KL_discrete"
  title := "Discrete-time SALD forward KL theorem"
  mode := "faithfulPaper"
  source := saldForwardKlDiscreteSource
  targetLean := "AutoSamplingTheory/SALD.lean"
  statementSummary := "For linear slowdown t(s)=s/r, Euler--Maruyama SALD satisfies the source forward-KL bound with the continuous alpha-complexity term plus accumulated discretization terms 2*r*eta^2*barGamma/alpha' and 2*r*eta*barDelta_{alpha'}."
  proofStatus := ProofStatus.contractOnly
  obligations := [
    cycle44MainSkeletonAnalyticInterfaceObligation,
    cycle49MainSkeletonAnalyticReadinessObligation,
    cycle49MainSkeletonAnalyticMiddleObligation,
    cycle54MainSkeletonAnalyticInterfaceObligation,
    cycle54MainSkeletonAnalyticMiddleObligation,
    cycle59MainSkeletonAnalyticInterfaceObligation,
    cycle59MainSkeletonAnalyticMiddleObligation,
    cycle64MainSkeletonAnalyticInterfaceObligation,
    cycle64MainSkeletonAnalyticMiddleObligation,
    cycle69MainSkeletonAnalyticInterfaceObligation,
    cycle69MainSkeletonAnalyticMiddleObligation,
    cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation,
    cycle70GeneralMovingTargetDiscreteConditionalLawLowerObligation,
    cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation,
    cycle71GeneralMovingTargetDiscreteEndpointConditionalLowerObligation,
    cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation,
    cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation,
    cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpUpperObligation,
    cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation,
    cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation,
    cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface,
    cycle74GeneralMovingTargetDiscreteMeasureInterfaceUpperObligation,
    cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation,
    cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation,
    cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperObligation,
    cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation,
    cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation,
    cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperObligation,
    cycle76GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation,
    cycle76GeneralMovingTargetDiscreteEndpointConditionalLowerObligation,
    cycle77GeneralMovingTargetDiscreteWeakFpGeneratorMiddleObligation,
    cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation,
    cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperObligation,
    cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorMiddleObligation,
    cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation,
    cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface,
    cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation,
    cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureMiddleObligation,
    cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation,
    cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperObligation,
    cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation,
    cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation,
    cycle81GeneralMovingTargetDiscreteEndpointConditionalUpperObligation,
    cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation,
    cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation,
    cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation,
    cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation,
    cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation,
    cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation,
    cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation,
    cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation,
    cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation,
    cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation,
    cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryUpperObligation,
    cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryMiddleObligation,
    cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation,
    cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation,
    cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation,
      cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation,
      cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation,
      cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation,
      cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddleObligation,
      cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation,
      cycle89DiscreteForwardKlClosurePressureUpperObligation,
      cycle89DiscreteForwardKlClosurePressureMiddleObligation,
      cycle89DiscreteForwardKlClosurePressureLowerObligation,
      cycle90DiscreteForwardKlMassConservationUpperObligation,
      cycle90DiscreteForwardKlMassConservationMiddleObligation,
      cycle90DiscreteForwardKlMassConservationLowerObligation,
      cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation,
      cycle91GeneralMovingTargetDiscreteConditionalKernelLowerObligation,
      cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitMiddleObligation,
      cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation,
      cycle93GeneralMovingTargetDiscreteKlMassDerivativeMiddleObligation,
      cycle93GeneralMovingTargetDiscreteKlMassDerivativeLowerObligation,
      cycle94GeneralMovingTargetDiscreteWeakFpDriftActionMiddleObligation,
      cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation,
      cycle95DiscreteForwardKlClosurePressureUpperObligation,
      cycle95DiscreteForwardKlClosurePressureMiddleObligation,
      cycle95DiscreteForwardKlClosurePressureLowerObligation,
      cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingMiddleObligation,
      cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingLowerObligation,
      cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingMiddleObligation,
      cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingLowerObligation,
      cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryMiddleObligation,
      cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryLowerObligation,
      cycle99GeneralMovingTargetDiscreteRawKlDerivativeMiddleObligation,
      cycle99GeneralMovingTargetDiscreteRawKlDerivativeLowerObligation,
      cycle100GeneralMovingTargetDiscreteBarBWeakGradDefMiddleObligation,
      cycle100GeneralMovingTargetDiscreteBarBWeakGradDefLowerObligation,
      cycle100GeneralMovingTargetDiscreteBarBInnerGradientBoundLowerObligation,
      cycle101DiscreteForwardKlClosurePressureMiddleObligation,
      cycle101DiscreteForwardKlNoBoundaryProductRuleLowerObligation,
      cycle102DiscreteForwardKlZeroFluxTraceBoundaryMiddleObligation,
      cycle102DiscreteForwardKlTraceZeroLowerObligation,
      cycle103GeneralMovingTargetDiscreteConditionalKernelVersionMiddleObligation,
      cycle66DiscreteForwardKlSkeletonObligation,
    cycle66DiscreteForwardKlSkeletonMiddleObligation,
    cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation,
    cycle61DiscreteForwardKlSkeletonObligation,
    cycle61DiscreteForwardKlSkeletonMiddleObligation,
    cycle56DiscreteForwardKlSkeletonObligation,
    cycle56DiscreteForwardKlSkeletonMiddleObligation,
    cycle56DiscreteForwardKlGronwallLowerObligation,
    cycle51DiscreteForwardKlSkeletonObligation,
    cycle51DiscreteForwardKlSkeletonMiddleObligation,
    cycle46DiscreteForwardKlSkeletonObligation,
    cycle46DiscreteForwardKlSkeletonMiddleObligation,
    lsiToKlFiObligation saldKlFiLsiSource,
    dvVariationalObligation saldDvVariationSource,
    gronwallAnalyticObligation,
    forwardKlDensityBoundaryObligation,
    forwardKlScheduleTimeChangeObligation,
    discreteForwardKlEmEndpointObligation,
    discreteForwardKlEmConditionalFpObligation,
    cycle15DiscreteForwardKlConditionalDriftDensityObligation,
    discreteForwardKlStitchedIntervalRegularityObligation,
    discreteForwardKlEmInterpolationObligation,
    cycle15DiscreteForwardKlMiddleEmSpineObligation,
    cycle15DiscreteForwardKlEmConditionalFpLowerObligation,
    cycle35DiscreteForwardKlEmFpUpperObligation,
    cycle35DiscreteForwardKlEmFpMiddleObligation,
    cycle35DiscreteForwardKlEmFpLowerObligation,
    cycle40DiscreteForwardKlEmFpMiddleObligation,
    cycle40DiscreteForwardKlEmEndpointLowerObligation,
    discreteForwardKlFrozenDeltaObligation,
    discreteForwardKlDerivativeObligation,
    cycle51DiscreteForwardKlDerivativeLowerObligation,
    discreteForwardKlDvFiniteLogMgfWitnessObligation,
    discreteForwardKlDvVelocityObligation,
    discreteForwardKlGronwallAccumulationObligation,
    discreteForwardKlLinearSlowdownObligation,
    discreteForwardKlResidualExponentBoundObligation,
    discreteForwardKlAccumulatedErrorBridgeObligation,
    cycle61DiscreteForwardKlAccumulatedErrorLowerObligation,
    cycle19DiscreteForwardKlAccumulatedErrorMiddleObligation,
    discreteForwardKlEmDefectAccumulationMiddleObligation,
      cycle23DiscreteForwardKlCoefficientChainMiddleObligation,
      discreteForwardKlCoefficientChainObligation,
      cycle27DiscreteForwardKlAccumulatedCollectionUpperObligation,
      cycle27DiscreteForwardKlAccumulatedCollectionMiddleObligation,
      cycle27DiscreteForwardKlAccumulatedCollectionLowerObligation
    ]

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