Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.unifiedForwardKlContract

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 unifiedForwardKlContract : TheoremContract

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)

Contract identifier.

ASTIS.SALD.unified_forward_KL
title : String (explicit)

Human-readable intended theorem/lemma title.

Unified VA-SALD forward KL theorem
mode : String (explicit)

Workflow mode as String, not a theorem assumption.

faithfulPaper
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor for the intended claim.

AutoSamplingTheory.SALD.saldUnifiedForwardKlSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)

Target Lean file/name as recorded text, not a declaration reference with type checking.

AutoSamplingTheory/SALD.lean
statementSummary : String (explicit)

Prose summary of intended content; no Prop is proved by this field.

The main-body VA-SALD bound is obtained from the general moving-target theorem with c_t specialized to u_t.
proofStatus : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus; defaults to contractOnly.

AutoSamplingTheory.ProofStatus.contractOnly — stored label only; no proof certification
obligations : List AutoSamplingTheory.ProofObligation (explicit)

List of ProofObligation data attached to the contract; defaults to empty, which does not certify completeness.

Ordered data items

  1. AutoSamplingTheory.SALD.cycle44MainSkeletonAnalyticInterfaceObligation — audited data reference, not expanded and not a compiled dependency edge
  2. AutoSamplingTheory.SALD.cycle49MainSkeletonAnalyticReadinessObligation — audited data reference, not expanded and not a compiled dependency edge
  3. AutoSamplingTheory.SALD.cycle49MainSkeletonAnalyticMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  4. AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticInterfaceObligation — audited data reference, not expanded and not a compiled dependency edge
  5. AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  6. AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticInterfaceObligation — audited data reference, not expanded and not a compiled dependency edge
  7. AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  8. AutoSamplingTheory.SALD.cycle64MainSkeletonAnalyticInterfaceObligation — audited data reference, not expanded and not a compiled dependency edge
  9. AutoSamplingTheory.SALD.cycle64MainSkeletonAnalyticMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  10. AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticInterfaceObligation — audited data reference, not expanded and not a compiled dependency edge
  11. AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  12. AutoSamplingTheory.SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation — audited data reference, not expanded and not a compiled dependency edge
  13. AutoSamplingTheory.SALD.cycle48UnifiedDiscreteSkeletonObligation — audited data reference, not expanded and not a compiled dependency edge
  14. AutoSamplingTheory.SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  15. AutoSamplingTheory.SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation — audited data reference, not expanded and not a compiled dependency edge
  16. AutoSamplingTheory.SALD.cycle53UnifiedDiscreteGeneralMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  17. AutoSamplingTheory.SALD.cycle58UnifiedDiscreteGeneralSkeletonObligation — audited data reference, not expanded and not a compiled dependency edge
  18. AutoSamplingTheory.SALD.cycle58UnifiedDiscreteGeneralMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  19. AutoSamplingTheory.SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation — audited data reference, not expanded and not a compiled dependency edge
  20. AutoSamplingTheory.SALD.cycle63UnifiedDiscreteGeneralMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  21. AutoSamplingTheory.SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation — audited data reference, not expanded and not a compiled dependency edge
  22. AutoSamplingTheory.SALD.cycle67GuidedGeneralSkeletonObligation — audited data reference, not expanded and not a compiled dependency edge
  23. AutoSamplingTheory.SALD.cycle67GuidedGeneralSkeletonMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  24. AutoSamplingTheory.SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation — audited data reference, not expanded and not a compiled dependency edge
  25. AutoSamplingTheory.SALD.cycle67GuidedGeneralResidualGronwallLowerObligation — audited data reference, not expanded and not a compiled dependency edge
  26. AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation — audited data reference, not expanded and not a compiled dependency edge
  27. AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  28. AutoSamplingTheory.SALD.guidedResidualIdentityObligation — audited data reference, not expanded and not a compiled dependency edge
  29. AutoSamplingTheory.SALD.generalMovingTargetDerivativeObligation — audited data reference, not expanded and not a compiled dependency edge
  30. AutoSamplingTheory.SALD.cycle52GuidedGeneralDerivativeDvLowerObligation — audited data reference, not expanded and not a compiled dependency edge
  31. AutoSamplingTheory.SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation — audited data reference, not expanded and not a compiled dependency edge
  32. AutoSamplingTheory.SALD.generalMovingTargetDvPositiveAlphaScalingObligation — audited data reference, not expanded and not a compiled dependency edge
  33. AutoSamplingTheory.SALD.generalMovingTargetDvFiniteLogMgfWitnessObligation — audited data reference, not expanded and not a compiled dependency edge
  34. AutoSamplingTheory.SALD.generalMovingTargetDvEnergyObligation — audited data reference, not expanded and not a compiled dependency edge
  35. AutoSamplingTheory.SALD.generalMovingTargetGronwallApplicationObligation — audited data reference, not expanded and not a compiled dependency edge
  36. AutoSamplingTheory.SALD.cycle24GeneralVaSaldGronwallMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  37. AutoSamplingTheory.SALD.generalMovingTargetGronwallSideConditionObligation — audited data reference, not expanded and not a compiled dependency edge
  38. AutoSamplingTheory.SALD.cycle16UnifiedForwardKlTransportBridgeMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  39. AutoSamplingTheory.SALD.cycle16UnifiedForwardKlTransportBridgeLowerObligation — audited data reference, not expanded and not a compiled dependency edge
  40. AutoSamplingTheory.SALD.unifiedForwardKlTransportBridgeObligation — audited data reference, not expanded and not a compiled dependency edge
  41. AutoSamplingTheory.SALD.unifiedForwardKlSpecializationObligation — audited data reference, not expanded and not a compiled dependency edge
  42. AutoSamplingTheory.SALD.generalVaSaldGuidedPathMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
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 unifiedForwardKlContract : TheoremContract where
  id := "ASTIS.SALD.unified_forward_KL"
  title := "Unified VA-SALD forward KL theorem"
  mode := "faithfulPaper"
  source := saldUnifiedForwardKlSource
  targetLean := "AutoSamplingTheory/SALD.lean"
  statementSummary := "The main-body VA-SALD bound is obtained from the general moving-target theorem with c_t specialized to u_t."
  proofStatus := ProofStatus.contractOnly
  obligations := [
    cycle44MainSkeletonAnalyticInterfaceObligation,
    cycle49MainSkeletonAnalyticReadinessObligation,
    cycle49MainSkeletonAnalyticMiddleObligation,
    cycle54MainSkeletonAnalyticInterfaceObligation,
    cycle54MainSkeletonAnalyticMiddleObligation,
    cycle59MainSkeletonAnalyticInterfaceObligation,
    cycle59MainSkeletonAnalyticMiddleObligation,
    cycle64MainSkeletonAnalyticInterfaceObligation,
    cycle64MainSkeletonAnalyticMiddleObligation,
    cycle69MainSkeletonAnalyticInterfaceObligation,
    cycle69MainSkeletonAnalyticMiddleObligation,
    cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation,
    cycle48UnifiedDiscreteSkeletonObligation,
    cycle48UnifiedDiscreteSkeletonMiddleObligation,
    cycle53UnifiedDiscreteGeneralSkeletonObligation,
    cycle53UnifiedDiscreteGeneralMiddleObligation,
    cycle58UnifiedDiscreteGeneralSkeletonObligation,
    cycle58UnifiedDiscreteGeneralMiddleObligation,
    cycle63UnifiedDiscreteGeneralSkeletonObligation,
      cycle63UnifiedDiscreteGeneralMiddleObligation,
      cycle63UnifiedDiscreteGeneralMeasureBackfillObligation,
      cycle67GuidedGeneralSkeletonObligation,
      cycle67GuidedGeneralSkeletonMiddleObligation,
      cycle67GuidedGeneralResidualGronwallBridgeObligation,
      cycle67GuidedGeneralResidualGronwallLowerObligation,
      cycle68UnifiedDiscreteGeneralSkeletonObligation,
      cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation,
      guidedResidualIdentityObligation,
      generalMovingTargetDerivativeObligation,
      cycle52GuidedGeneralDerivativeDvLowerObligation,
      cycle57GuidedGeneralDerivativeSplitLowerObligation,
      generalMovingTargetDvPositiveAlphaScalingObligation,
    generalMovingTargetDvFiniteLogMgfWitnessObligation,
    generalMovingTargetDvEnergyObligation,
    generalMovingTargetGronwallApplicationObligation,
    cycle24GeneralVaSaldGronwallMiddleObligation,
    generalMovingTargetGronwallSideConditionObligation,
    cycle16UnifiedForwardKlTransportBridgeMiddleObligation,
    cycle16UnifiedForwardKlTransportBridgeLowerObligation,
    unifiedForwardKlTransportBridgeObligation,
    unifiedForwardKlSpecializationObligation,
    generalVaSaldGuidedPathMiddleObligation
  ]

Existing module entry · Audited data-reader index · All teaching coverage