AutoSamplingTheory.SALD.discreteForwardKlProofDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. 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 discreteForwardKlProofDag : List ProofDagBlock

Construction and field-by-field explanation

Concatenate the shown data expressions in source order. They remain symbolic and are not evaluated.

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.

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        AutoSamplingTheory.SALD.cycle49MainSkeletonAnalyticReadinessDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle64MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle70GeneralMovingTargetDiscreteConditionalLawDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle72GeneralMovingTargetDiscreteWeakFpDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle89DiscreteForwardKlClosurePressureDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle90DiscreteForwardKlMassConservationDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle95DiscreteForwardKlClosurePressureDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle100GeneralMovingTargetDiscreteBarBWeakGradDefDag — audited data reference, not expanded and not a compiled dependency edge
        AutoSamplingTheory.SALD.cycle100GeneralMovingTargetDiscreteBarBInnerGradientBoundDag — audited data reference, not expanded and not a compiled dependency edge
      2. AutoSamplingTheory.SALD.cycle101DiscreteForwardKlClosurePressureDag — audited data reference, not expanded and not a compiled dependency edge
    2. AutoSamplingTheory.SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionDag — audited data reference, not expanded and not a compiled dependency edge
  2. AutoSamplingTheory.SALD.cycle61DiscreteForwardKlSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
2. AutoSamplingTheory.SALD.cycle66DiscreteForwardKlSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
Ordered data items
1. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle46_theorem_skeleton_route
  interface : String (explicit)
  Text describing intended mathematical interface.
  Main skeleton sprint 3 route wrapper: compose the source statement, EM endpoint/conditional-FP backend, discrete KL derivative, frozen-defect/LSI handoff, DV velocity witness, Gronwall accumulation, and linear-slowdown accumulated-error bridge without changing the theorem display.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle44MainSkeletonAnalyticInterfaceObligation
  2. SALD.cycle46DiscreteForwardKlSkeletonUpperPacket
  3. SALD.cycle46DiscreteForwardKlSkeletonObligation
  4. SALD.cycle46DiscreteForwardKlSkeletonDag
  5. SALD.cycle46DiscreteForwardKlSkeletonMiddleContract
  6. SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation
  7. sald.discrete_forward_kl.cycle46_middle_route_audit
  8. SALD.discreteForwardKlStatementContract
  9. SALD.discreteForwardKlEmInterpolationSideConditionContract
  10. SALD.discreteForwardKlDerivativeCandidateContract
  11. SALD.frozenDeltaCrossLipSaldContract
  12. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  13. SALD.discreteForwardKlGronwallInstantiationContract
  14. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  15. SALD.saldLsiKlFiDensityTestContract
  16. SALD.saldGronwallCandidateContract
  17. dvVariationalFormulaInterface saldDvVariationSource
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. ASTIS-SALD-001 cycle 46
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
2. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle46_middle_route_audit
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle source-to-Lean audit for the discrete forward-KL skeleton: verify the exact main_body.tex:299-323 statement and appendix.tex:260-592 route, then select the accumulated-error bridge for lower work.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle46DiscreteForwardKlSkeletonMiddleContract
  2. SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation
  3. SALD.cycle46DiscreteForwardKlSkeletonObligation
  4. SALD.discreteForwardKlStatementContract
  5. SALD.discreteForwardKlEmInterpolationSideConditionContract
  6. SALD.discreteForwardKlDerivativeCandidateContract
  7. SALD.frozenDeltaCrossLipSaldContract
  8. SALD.saldLsiKlFiDensityTestContract
  9. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  10. SALD.discreteForwardKlGronwallInstantiationContract
  11. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  12. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle 46 lower accumulated-error packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
3. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle51_theorem_interface_route
  interface : String (explicit)
  Text describing intended mathematical interface.
  Post-cycle-50 discrete forward-KL route: consume the five-backend readiness check and the continuous derivative/DV scalar handoff, then route the discrete theorem through EM endpoint/conditional-FP, KL derivative with frozen defect and LSI, DV velocity, Gronwall, and accumulated-error interfaces without reproving EM/Fokker-Planck.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle51DiscreteForwardKlSkeletonUpperPacket
  2. SALD.cycle51DiscreteForwardKlSkeletonObligation
  3. SALD.cycle49MainSkeletonAnalyticReadinessObligation
  4. SALD.cycle46DiscreteForwardKlSkeletonObligation
  5. SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation
  6. SALD.cycle50ForwardKlDerivativeLowerObligation
  7. SALD.discreteForwardKlStatementContract
  8. SALD.discreteForwardKlEmInterpolationSideConditionContract
  9. sald.discrete_forward_kl.em_interpolation_fp
  10. SALD.discreteForwardKlDerivativeCandidateContract
  11. sald.discrete_forward_kl.kl_derivative
  12. SALD.frozenDeltaCrossLipSaldContract
  13. SALD.saldLsiKlFiDensityTestContract
  14. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  15. SALD.discreteForwardKlGronwallInstantiationContract
  16. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. ASTIS-SALD-001 cycle 51
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
4. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle51_middle_route_audit
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle source-to-Lean audit for the cycle-51 discrete forward-KL route: select appendix.tex:334-491 as the KL derivative lower backend, consuming appendix.tex:334-385 EM endpoint/conditional-FP interfaces explicitly rather than reproving them.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle51DiscreteForwardKlSkeletonMiddleContract
  2. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
  3. SALD.cycle51DiscreteForwardKlSkeletonObligation
  4. SALD.discreteForwardKlEmInterpolationSideConditionContract
  5. sald.discrete_forward_kl.em_endpoint_laws
  6. sald.discrete_forward_kl.conditional_drift_density
  7. sald.discrete_forward_kl.em_conditional_fokker_planck
  8. sald.discrete_forward_kl.em_interpolation_fp
  9. SALD.discreteForwardKlDerivativeCandidateContract
  10. SALD.discreteForwardKlDerivativeObligation
  11. SALD.discreteForwardKlPostLsiDerivativeBoundScalar
  12. SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
  13. SALD.frozenDeltaCrossLipSaldContract
  14. SALD.saldLsiKlFiDensityTestContract
  15. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  16. SALD.discreteForwardKlGronwallInstantiationContract
  17. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle 51 lower derivative packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
5. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle51_derivative_lower
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower scalar handoff for appendix.tex:388-491: consume the supplied EM conditional-FP derivative identity, frozen-defect bound, moving Young estimate, and LSI/KL/FI comparison to obtain the exact source pre-DV inequality before the separate DV velocity witness.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
  2. SALD.discreteForwardKlPostLsiDerivativeBoundScalar
  3. SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
  4. SALD.discreteForwardKlDerivativeCandidateContract
  5. SALD.discreteForwardKlDerivativeObligation
  6. sald.discrete_forward_kl.em_interpolation_fp
  7. sald.discrete_forward_kl.em_conditional_fokker_planck
  8. sald.discrete_forward_kl.frozen_delta_cross_lip
  9. SALD.frozenDeltaCrossLipSaldContract
  10. SALD.saldLsiKlFiDensityTestContract
  11. probability.lsi_to_kl_fi
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.kl_derivative
  2. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
6. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle56_theorem_interface_route
  interface : String (explicit)
  Text describing intended mathematical interface.
  Cycle-56 theorem-level route: consume the explicit EM endpoint/conditional-FP interfaces, cycle-51 derivative/LSI scalar handoff, discrete DV velocity witness, and appendix.tex:526-592 Gronwall/accumulated-error interfaces to match main_body.tex:299-323 without proving EM/Fokker-Planck from scratch.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle56DiscreteForwardKlSkeletonUpperPacket
  2. SALD.cycle56DiscreteForwardKlSkeletonObligation
  3. SALD.cycle55ForwardKlSkeletonObligation
  4. SALD.cycle51DiscreteForwardKlSkeletonObligation
  5. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
  6. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
  7. SALD.discreteForwardKlStatementContract
  8. SALD.discreteForwardKlEmInterpolationSideConditionContract
  9. sald.discrete_forward_kl.em_endpoint_laws
  10. sald.discrete_forward_kl.conditional_drift_density
  11. sald.discrete_forward_kl.em_conditional_fokker_planck
  12. sald.discrete_forward_kl.em_interpolation_fp
  13. SALD.discreteForwardKlDerivativeCandidateContract
  14. sald.discrete_forward_kl.kl_derivative
  15. SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
  16. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  17. sald.discrete_forward_kl.dv_velocity_bound
  18. SALD.discreteForwardKlGronwallInstantiationContract
  19. sald.discrete_forward_kl.gronwall_accumulation
  20. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  21. sald.discrete_forward_kl.accumulated_error_bridge
  22. lem:gronwall
  23. lem:dv_variation
  24. eq:LSI-KL-FI
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. ASTIS-SALD-001 cycle 56
  3. cycle56 lower Gronwall packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
7. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle56_middle_route_audit
  interface : String (explicit)
  Text describing intended mathematical interface.
  Cycle-56 middle audit: verify the upper discrete theorem route against main_body.tex:299-323 and appendix.tex:260-592, keep EM/Fokker-Planck as named source-cited interfaces, and select sald.discrete_forward_kl.gronwall_accumulation over appendix.tex:526-592 as the lower packet.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle56DiscreteForwardKlSkeletonMiddleContract
  2. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
  3. SALD.cycle56DiscreteForwardKlSkeletonObligation
  4. SALD.cycle54MainSkeletonAnalyticMiddleObligation
  5. SALD.cycle55ForwardKlSkeletonMiddleObligation
  6. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
  7. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
  8. SALD.discreteForwardKlStatementContract
  9. SALD.discreteForwardKlEmInterpolationSideConditionContract
  10. sald.discrete_forward_kl.em_interpolation_fp
  11. SALD.discreteForwardKlDerivativeCandidateContract
  12. sald.discrete_forward_kl.kl_derivative
  13. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  14. sald.discrete_forward_kl.dv_velocity_bound
  15. SALD.discreteForwardKlGronwallInstantiationContract
  16. sald.discrete_forward_kl.gronwall_accumulation
  17. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  18. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle56 lower Gronwall packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
8. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle56_gronwall_lower
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower scalar handoff for appendix.tex:526-553: consume the post-DV s-time inequality and inverse-schedule inputs to produce the exact t-time Gronwall coefficient and residual used by lem:gronwall.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteGronwallSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
  2. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
  3. SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged
  4. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar
  5. SALD.discreteForwardKlGronwallInstantiationContract
  6. sald.discrete_forward_kl.kl_derivative
  7. sald.discrete_forward_kl.dv_velocity_bound
  8. sald.forward_kl.schedule_time_change
  9. lem:gronwall
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.gronwall_accumulation
  2. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
9. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.euler_maruyama
  interface : String (explicit)
  Text describing intended mathematical interface.
  Pin the EM update and continuous frozen interpolation hat X_s with endpoint laws rho_k^eta.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. EulerMaruyamaContract
  2. sald.discrete_forward_kl.em_endpoint_laws
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.contractOnly — stored label only; no proof certification
10. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle35_em_fp_upper
  interface : String (explicit)
  Text describing intended mathematical interface.
  Upper proof-closure packet for appendix.tex:260-385 selecting the EM endpoint laws and conditional-drift Fokker--Planck backend as the lower target after the earlier Gronwall, DV, LSI, and continuous-derivative proof-sprint slices.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle35DiscreteForwardKlEmFpUpperPacket
  2. sald.discrete_forward_kl.cycle35_em_fp_upper
  3. sald.discrete_forward_kl.em_endpoint_laws
  4. sald.discrete_forward_kl.conditional_drift_density
  5. sald.discrete_forward_kl.em_conditional_fokker_planck
  6. sald.discrete_forward_kl.em_interpolation_fp
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle35 lower EM-FP packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
11. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle35_em_fp_middle
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle source-to-Lean packet for appendix.tex:260-385: compiled endpoint-vector algebra and divergence-regrouping algebra, with stochastic endpoint laws and conditional-drift Fokker--Planck still explicit obligations.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle35DiscreteForwardKlEmFpMiddleContract
  2. sald.discrete_forward_kl.cycle35_em_fp_middle
  3. SALD.discreteForwardKlEmInterpolationLeftEndpointVector
  4. SALD.discreteForwardKlEmInterpolationRightEndpointVector
  5. SALD.discreteForwardKlConditionalFpDivergenceDriftSplit
  6. sald.discrete_forward_kl.em_endpoint_laws
  7. sald.discrete_forward_kl.conditional_drift_density
  8. sald.discrete_forward_kl.em_conditional_fokker_planck
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle35 lower EM-FP packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
12. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle35_em_fp_lower
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower proof-producing handoff for appendix.tex:357-385: compose the supplied conditional-drift Fokker--Planck equation and supplied Laplacian split into the source regrouped divergence form, without promoting the analytic FP, density, or integration-by-parts backend.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle35DiscreteForwardKlEmFpMiddleContract
  2. SALD.cycle35DiscreteForwardKlEmFpMiddleObligation
  3. SALD.discreteForwardKlConditionalFpDivergenceDriftSplit
  4. SALD.discreteForwardKlConditionalFpLaplacianSplitHandoff
  5. SALD.cycle35DiscreteForwardKlEmFpLowerObligation
  6. sald.discrete_forward_kl.conditional_drift_density
  7. sald.discrete_forward_kl.em_conditional_fokker_planck
  8. sald.discrete_forward_kl.em_interpolation_fp
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.em_conditional_fokker_planck
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
13. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle40_em_fp_middle
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle proof-closure handoff for appendix.tex:260-385: add abstract endpoint-law equality transport from pointwise EM interpolation identities, while keeping conditional drift density and conditional-drift Fokker--Planck as obligations.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle40DiscreteForwardKlEmFpMiddleContract
  2. SALD.cycle40DiscreteForwardKlEmFpMiddleObligation
  3. SALD.discreteForwardKlLawEqOfPointwise
  4. SALD.discreteForwardKlEmInterpolationLeftEndpointLawHandoff
  5. SALD.discreteForwardKlEmInterpolationRightEndpointLawHandoff
  6. SALD.discreteForwardKlEmEndpointLawPairHandoff
  7. SALD.discreteForwardKlConditionalFpLaplacianSplitHandoff
  8. sald.discrete_forward_kl.em_endpoint_laws
  9. sald.discrete_forward_kl.conditional_drift_density
  10. sald.discrete_forward_kl.em_conditional_fokker_planck
  11. sald.discrete_forward_kl.em_interpolation_fp
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle40 lower EM endpoint/conditional-FP packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
14. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle40_em_endpoint_lower
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower endpoint-law representation handoff for appendix.tex:334-335: from explicit named law representations for hat rho_s and rho_k^eta, prove both endpoint law equalities using the compiled law handoff lemmas.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.discreteForwardKlEmEndpointLawPairHandoff
  2. SALD.discreteForwardKlEmInterpolationLeftEndpointLawHandoff
  3. SALD.discreteForwardKlEmInterpolationRightEndpointLawHandoff
  4. sald.discrete_forward_kl.em_endpoint_laws
  5. sald.discrete_forward_kl.conditional_drift_density
  6. sald.discrete_forward_kl.em_conditional_fokker_planck
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.em_endpoint_laws
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
15. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle15_upper_packet
  interface : String (explicit)
  Text describing intended mathematical interface.
  Upper packet selecting the EM interpolation side-condition spine as the next lower target while keeping the discrete theorem statement and accumulated-error constants unchanged.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle15DiscreteForwardKlUpperPacket
  2. sald.discrete_forward_kl.em_endpoint_laws
  3. sald.discrete_forward_kl.em_conditional_fokker_planck
  4. sald.discrete_forward_kl.stitched_interval_regularity
  5. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle15 lower packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
16. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle15_middle_em_spine
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle packet mapping the cycle-15 EM side-condition spine into ordered lower obligations, with the conditional-drift Fokker--Planck equation as the first lower slice.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle15DiscreteForwardKlMiddleContract
  2. sald.discrete_forward_kl.cycle15_middle_em_spine
  3. sald.discrete_forward_kl.em_endpoint_laws
  4. sald.discrete_forward_kl.em_conditional_fokker_planck
  5. sald.discrete_forward_kl.stitched_interval_regularity
  6. sald.discrete_forward_kl.em_interpolation_fp
  7. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle15 lower packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
17. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.conditional_drift_density
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower sub-obligation for appendix.tex:347-354: construct the regular conditional-law, density, measurability, and integrability interface needed to treat bar b_{k,s} as a drift field.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract
  2. sald.discrete_forward_kl.conditional_drift_density
  3. eq:frozen_interp_terminal_disc_prop_additive_final
  4. sald.discrete_forward_kl.em_endpoint_laws
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.em_conditional_fokker_planck
  2. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
18. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle15_conditional_fp_lower_packet
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower-ready line ledger for appendix.tex:347-385: conditional frozen drift, conditional-drift Fokker--Planck equation, Laplacian split, and KL-derivative handoff.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract
  2. SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract
  3. sald.discrete_forward_kl.cycle15_conditional_fp_lower_packet
  4. sald.discrete_forward_kl.conditional_drift_density
  5. sald.discrete_forward_kl.em_conditional_fokker_planck
  6. sald.discrete_forward_kl.em_endpoint_laws
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle15 lower packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
19. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.em_interpolation_side_conditions
  interface : String (explicit)
  Text describing intended mathematical interface.
  Separate endpoint law matching, conditional-drift Fokker--Planck, and stitched-interval regularity for the EM interpolation.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.em_endpoint_laws
  2. sald.discrete_forward_kl.em_conditional_fokker_planck
  3. sald.discrete_forward_kl.stitched_interval_regularity
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
20. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.frozen_delta
  interface : String (explicit)
  Text describing intended mathematical interface.
  Bound the one-step frozen score-defect cross term by (1/4)*FI plus Gamma and Delta contributions.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldFrozenDeltaCrossLipSaldSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. lem:frozen_delta_cross_lip
  2. eq:lip_SALD_1
  3. eq:lip_SALD_2
  4. lem:dv_variation
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. thm:general-moving-target-SALD-discrete specialization
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
21. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.derivative
  interface : String (explicit)
  Text describing intended mathematical interface.
  Differentiate KL(hat rho_s||tilde pi_s) on each EM interval and derive the discrete differential inequality before Gronwall.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.em_conditional_fokker_planck
  2. sald.discrete_forward_kl.frozen_delta_cross_lip
  3. sald.discrete_forward_kl.dv_finite_log_mgf_witness
  4. sald.discrete_forward_kl.dv_velocity_bound
  5. eq:LSI-KL-FI
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
22. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.dv_finite_log_mgf_witness
  interface : String (explicit)
  Text describing intended mathematical interface.
  Expose the EM-interpolation DV witness for nu=hat rho_s, mu=tilde pi_s, and Z=alpha*||v_{t(s)}||^2 before bounding ||tilde v_s||^2.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteDvVelocitySource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. lem:dv_variation
  2. def:alpha-complexity
  3. sald.forward_kl.dv_alpha_mgf_monotonicity
  4. sald.forward_kl.dv_finite_log_mgf_witness
  5. sald.discrete_forward_kl.em_interpolation_fp
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.dv_velocity_bound
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
23. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.gronwall_accumulation
  interface : String (explicit)
  Text describing intended mathematical interface.
  Apply lem:gronwall with the added Gamma term to the source general-schedule differential inequality.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteGronwallSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. lem:gronwall
  2. sald.discrete_forward_kl.kl_derivative
  3. sald.discrete_forward_kl.dv_velocity_bound
  4. sald.discrete_forward_kl.stitched_interval_regularity
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
24. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle19_upper_packet
  interface : String (explicit)
  Text describing intended mathematical interface.
  Upper packet selecting the accumulated-error bridge from the appendix Gronwall display to the main-body linear-slowdown theorem constants.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle19DiscreteForwardKlUpperPacket
  2. sald.discrete_forward_kl.gronwall_accumulation
  3. sald.discrete_forward_kl.linear_slowdown_specialization
  4. sald.discrete_forward_kl.residual_exponent_bound
  5. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
  6. SALD.discreteForwardKlResidualExponentBoundScalar
  7. SALD.discreteForwardKlResidualExpBoundScalar
  8. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle19 lower packet
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
25. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle19_middle_accumulated_error
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle packet translating the accumulated-error bridge into lower-ready endpoint, exponent, residual-exponent, and integral-collection sub-slices.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle19DiscreteForwardKlUpperPacket
  2. SALD.cycle19DiscreteForwardKlMiddleContract
  3. sald.discrete_forward_kl.gronwall_accumulation
  4. sald.discrete_forward_kl.linear_slowdown_specialization
  5. sald.discrete_forward_kl.residual_exponent_bound
  6. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
  7. SALD.discreteForwardKlResidualExponentBoundScalar
  8. SALD.discreteForwardKlResidualExpBoundScalar
  9. sald.discrete_forward_kl.accumulated_error_bridge
  10. sald.discrete_forward_kl.cycle19_accumulated_error_middle
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle19 lower accumulated-error bridge
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
26. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.linear_slowdown_specialization
  interface : String (explicit)
  Text describing intended mathematical interface.
  Substitute dot{s}=r, collect bar Gamma and bar Delta, and recover the main-body discrete theorem constants.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.gronwall_accumulation
  2. def:alpha-complexity
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
27. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.residual_exponent_bound
  interface : String (explicit)
  Text describing intended mathematical interface.
  Bound the residual Gronwall exponent after linear slowdown by the full positive factor T/(r*alpha)+2*r*eta^2*barGamma/alpha'.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.gronwall_accumulation
  2. sald.discrete_forward_kl.linear_slowdown_specialization
  3. sald.gronwall.integrating_factor
  4. SALD.discreteForwardKlResidualExponentBoundScalar
  5. SALD.discreteForwardKlResidualExpBoundScalar
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.accumulated_error_bridge
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
28. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.accumulated_error_bridge
  interface : String (explicit)
  Text describing intended mathematical interface.
  Rewrite the appendix Gronwall output into the main-body theorem display by endpoint matching, exponent splitting, and barGamma/barDelta collection.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.gronwall_accumulation
  2. sald.discrete_forward_kl.linear_slowdown_specialization
  3. sald.discrete_forward_kl.residual_exponent_bound
  4. SALD.discreteForwardKlGronwallCoeffIntervalIntegrable
  5. SALD.discreteForwardKlGronwallCoeffIntegralSubSub
  6. SALD.discreteForwardKlGronwallInitialExponentSplitScalar
  7. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
  8. SALD.discreteForwardKlResidualExponentBoundScalar
  9. SALD.discreteForwardKlResidualExpBoundScalar
  10. SALD.discreteForwardKlAlphaComplexityCollectionScalar
  11. SALD.discreteForwardKlDeltaAccumulationScalar
  12. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
  13. SALD.discreteForwardKlResidualIntegralDisplayBoundScalar
  14. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.coefficient_chain_audit
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
29. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle27_upper_accumulated_collection
  interface : String (explicit)
  Text describing intended mathematical interface.
  Upper packet selecting the accumulated-error collection slice after the coefficient-chain audit: endpoint rewrites, linear-slowdown exponent split, and A_alpha/barGamma/barDelta collection.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle27DiscreteForwardKlUpperPacket
  2. sald.discrete_forward_kl.cycle27_accumulated_collection_upper
  3. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  4. sald.discrete_forward_kl.accumulated_error_bridge
  5. sald.discrete_forward_kl.linear_slowdown_specialization
  6. sald.discrete_forward_kl.residual_exponent_bound
  7. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
  8. SALD.discreteForwardKlResidualExponentBoundScalar
  9. SALD.discreteForwardKlResidualExpBoundScalar
  10. SALD.discreteForwardKlAlphaComplexityCollectionScalar
  11. SALD.discreteForwardKlDeltaAccumulationScalar
  12. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
  13. sald.discrete_forward_kl.coefficient_chain_audit
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle27 lower accumulated-error bridge
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
30. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle27_middle_accumulated_collection
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle packet translating the cycle-27 accumulated-error target into lower-ready endpointBridge, alphaComplexityCollection, and deltaAccumulation sub-slices.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle27DiscreteForwardKlUpperPacket
  2. SALD.cycle27DiscreteForwardKlMiddleContract
  3. sald.discrete_forward_kl.cycle27_accumulated_collection_upper
  4. sald.discrete_forward_kl.cycle27_accumulated_collection_middle
  5. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  6. sald.discrete_forward_kl.accumulated_error_bridge
  7. sald.discrete_forward_kl.linear_slowdown_specialization
  8. sald.discrete_forward_kl.residual_exponent_bound
  9. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
  10. SALD.discreteForwardKlResidualExponentBoundScalar
  11. SALD.discreteForwardKlResidualExpBoundScalar
  12. SALD.discreteForwardKlAlphaComplexityCollectionScalar
  13. SALD.discreteForwardKlDeltaAccumulationScalar
  14. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
  15. sald.discrete_forward_kl.coefficient_chain_audit
  16. def:alpha-complexity
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle27 lower accumulated-error bridge
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
31. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle27_lower_accumulated_collection
  interface : String (explicit)
  Text describing intended mathematical interface.
  Lower scalar/integral core for collecting the additive E_alpha and Delta residual integrals into r^(-1)*A_alpha plus 2*r*eta*barDelta after linear slowdown.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle27DiscreteForwardKlMiddleContract
  2. SALD.discreteForwardKlAlphaComplexityCollectionScalar
  3. SALD.discreteForwardKlDeltaAccumulationScalar
  4. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
  5. sald.discrete_forward_kl.cycle27_accumulated_collection_lower
  6. sald.discrete_forward_kl.accumulated_error_bridge
  7. sald.discrete_forward_kl.linear_slowdown_specialization
  8. def:alpha-complexity
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.accumulated_error_bridge
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
32. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.em_defect_accumulation_middle
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle packet mapping the EM interpolation, one-step defects, DV velocity witness, Gronwall accumulation, and accumulated-error collection to explicit lower obligations.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteCoefficientChainSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. sald.discrete_forward_kl.em_interpolation_fp
  2. sald.discrete_forward_kl.frozen_delta_cross_lip
  3. sald.discrete_forward_kl.kl_derivative
  4. sald.discrete_forward_kl.dv_finite_log_mgf_witness
  5. sald.discrete_forward_kl.dv_velocity_bound
  6. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar
  7. sald.discrete_forward_kl.gronwall_accumulation
  8. sald.discrete_forward_kl.residual_exponent_bound
  9. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle11 lower packets
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
33. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle23_upper_packet
  interface : String (explicit)
  Text describing intended mathematical interface.
  Upper packet rebaselining the discrete forward-KL spine and selecting the coefficient-chain audit as the single lower target.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteCoefficientChainSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle23DiscreteForwardKlUpperPacket
  2. SALD.cycle15DiscreteForwardKlUpperPacket
  3. SALD.cycle19DiscreteForwardKlUpperPacket
  4. sald.discrete_forward_kl.em_interpolation_fp
  5. sald.discrete_forward_kl.frozen_delta_cross_lip
  6. sald.discrete_forward_kl.dv_velocity_bound
  7. sald.discrete_forward_kl.gronwall_accumulation
  8. sald.discrete_forward_kl.accumulated_error_bridge
  9. sald.discrete_forward_kl.coefficient_chain_audit
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. cycle23 lower coefficient-chain audit
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
34. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.cycle23_middle_coefficient_chain
  interface : String (explicit)
  Text describing intended mathematical interface.
  Middle packet translating the cycle-23 coefficient-chain target into the appendix.tex:454-553 first lower slice, with the accumulated-error bridge kept separate.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteCoefficientChainSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle23DiscreteForwardKlUpperPacket
  2. SALD.cycle23DiscreteForwardKlMiddleContract
  3. sald.discrete_forward_kl.cycle23_coefficient_chain_middle
  4. SALD.discreteForwardKlCoefficientChainAuditContract
  5. sald.discrete_forward_kl.frozen_delta_cross_lip
  6. sald.discrete_forward_kl.kl_derivative
  7. sald.discrete_forward_kl.dv_finite_log_mgf_witness
  8. sald.discrete_forward_kl.dv_velocity_bound
  9. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar
  10. sald.discrete_forward_kl.gronwall_accumulation
  11. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. sald.discrete_forward_kl.coefficient_chain_audit
  3. cycle23 lower coefficient-chain audit
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
35. id : String (explicit)
  Stable plan-node identifier.
  ASTIS.SALD.forward_KL_discrete.coefficient_chain_audit
  interface : String (explicit)
  Text describing intended mathematical interface.
  Audit the one-step Gamma/Delta coefficients from frozen/moving cross terms through time change, Gronwall, and linear-slowdown accumulation.
  source : AutoSamplingTheory.SourceAnchor (explicit)
  Source pointer.
  AutoSamplingTheory.SALD.saldForwardKlDiscreteCoefficientChainSource — audited data reference, not expanded and not a compiled dependency edge
  targetLean : String (explicit)
  Textual planned implementation destination.
  AutoSamplingTheory/SALD.lean
  dependsOn : List String (explicit)
  Declared input names as strings, default empty.
  Ordered data items
  1. SALD.cycle23DiscreteForwardKlMiddleContract
  2. sald.discrete_forward_kl.cycle23_coefficient_chain_middle
  3. sald.discrete_forward_kl.stitched_interval_regularity
  4. sald.discrete_forward_kl.frozen_delta_cross_lip
  5. sald.discrete_forward_kl.kl_derivative
  6. sald.discrete_forward_kl.dv_velocity_bound
  7. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar
  8. sald.discrete_forward_kl.gronwall_accumulation
  9. sald.discrete_forward_kl.linear_slowdown_specialization
  10. sald.discrete_forward_kl.residual_exponent_bound
  11. sald.discrete_forward_kl.accumulated_error_bridge
  reusedBy : List String (explicit)
  Declared consumers as strings, default empty.
  Ordered data items
  1. thm:forward-KL-discrete
  2. thm:general-moving-target-SALD-discrete coefficient pattern
  status : AutoSamplingTheory.ProofStatus (explicit)
  Recorded workflow status, default planned.
  AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

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 discreteForwardKlProofDag : List ProofDagBlock :=
  cycle49MainSkeletonAnalyticReadinessDag ++
  cycle54MainSkeletonAnalyticInterfaceDag ++
  cycle59MainSkeletonAnalyticInterfaceDag ++
  cycle64MainSkeletonAnalyticInterfaceDag ++
  cycle69MainSkeletonAnalyticInterfaceDag ++
  cycle70GeneralMovingTargetDiscreteConditionalLawDag ++
  cycle71GeneralMovingTargetDiscreteEndpointConditionalDag ++
  cycle72GeneralMovingTargetDiscreteWeakFpDag ++
  cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag ++
  cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag ++
  cycle75GeneralMovingTargetDiscreteConditionalLawBackfillDag ++
  cycle76GeneralMovingTargetDiscreteEndpointConditionalDag ++
  cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag ++
  cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag ++
  cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag ++
  cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag ++
  cycle81GeneralMovingTargetDiscreteEndpointConditionalDag ++
  cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag ++
  cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag ++
  cycle84GeneralMovingTargetDiscreteActiveEmBackendDag ++
  cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryDag ++
  cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryDag ++
  cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryDag ++
  cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityDag ++
  cycle89DiscreteForwardKlClosurePressureDag ++
  cycle90DiscreteForwardKlMassConservationDag ++
  cycle91GeneralMovingTargetDiscreteConditionalKernelDag ++
  cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitDag ++
  cycle93GeneralMovingTargetDiscreteKlMassDerivativeDag ++
  cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag ++
  cycle95DiscreteForwardKlClosurePressureDag ++
  cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag ++
  cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag ++
  cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryDag ++
  cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag ++
  cycle100GeneralMovingTargetDiscreteBarBWeakGradDefDag ++
  cycle100GeneralMovingTargetDiscreteBarBInnerGradientBoundDag ++
  cycle101DiscreteForwardKlClosurePressureDag ++
  cycle103GeneralMovingTargetDiscreteConditionalKernelVersionDag ++
  cycle61DiscreteForwardKlSkeletonDag ++
  cycle66DiscreteForwardKlSkeletonDag ++
  [
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle46_theorem_skeleton_route"
      interface := "Main skeleton sprint 3 route wrapper: compose the source statement, EM endpoint/conditional-FP backend, discrete KL derivative, frozen-defect/LSI handoff, DV velocity witness, Gronwall accumulation, and linear-slowdown accumulated-error bridge without changing the theorem display."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle46DiscreteForwardKlSkeletonUpperPacket",
        "SALD.cycle46DiscreteForwardKlSkeletonObligation",
        "SALD.cycle46DiscreteForwardKlSkeletonDag",
        "SALD.cycle46DiscreteForwardKlSkeletonMiddleContract",
        "SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation",
        "sald.discrete_forward_kl.cycle46_middle_route_audit",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "SALD.frozenDeltaCrossLipSaldContract",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.saldGronwallCandidateContract",
        "dvVariationalFormulaInterface saldDvVariationSource"
      ]
      reusedBy := ["thm:forward-KL-discrete", "ASTIS-SALD-001 cycle 46"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle46_middle_route_audit"
      interface := "Middle source-to-Lean audit for the discrete forward-KL skeleton: verify the exact main_body.tex:299-323 statement and appendix.tex:260-592 route, then select the accumulated-error bridge for lower work."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle46DiscreteForwardKlSkeletonMiddleContract",
        "SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle46DiscreteForwardKlSkeletonObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "SALD.frozenDeltaCrossLipSaldContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle 46 lower accumulated-error packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle51_theorem_interface_route"
      interface := "Post-cycle-50 discrete forward-KL route: consume the five-backend readiness check and the continuous derivative/DV scalar handoff, then route the discrete theorem through EM endpoint/conditional-FP, KL derivative with frozen defect and LSI, DV velocity, Gronwall, and accumulated-error interfaces without reproving EM/Fokker-Planck."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle51DiscreteForwardKlSkeletonUpperPacket",
        "SALD.cycle51DiscreteForwardKlSkeletonObligation",
        "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
        "SALD.cycle46DiscreteForwardKlSkeletonObligation",
        "SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle50ForwardKlDerivativeLowerObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.frozenDeltaCrossLipSaldContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract"
      ]
      reusedBy := ["thm:forward-KL-discrete", "ASTIS-SALD-001 cycle 51"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle51_middle_route_audit"
      interface := "Middle source-to-Lean audit for the cycle-51 discrete forward-KL route: select appendix.tex:334-491 as the KL derivative lower backend, consuming appendix.tex:334-385 EM endpoint/conditional-FP interfaces explicitly rather than reproving them."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle51DiscreteForwardKlSkeletonMiddleContract",
        "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle51DiscreteForwardKlSkeletonObligation",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "SALD.discreteForwardKlDerivativeObligation",
        "SALD.discreteForwardKlPostLsiDerivativeBoundScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
        "SALD.frozenDeltaCrossLipSaldContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle 51 lower derivative packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle51_derivative_lower"
      interface := "Lower scalar handoff for appendix.tex:388-491: consume the supplied EM conditional-FP derivative identity, frozen-defect bound, moving Young estimate, and LSI/KL/FI comparison to obtain the exact source pre-DV inequality before the separate DV velocity witness."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "SALD.discreteForwardKlPostLsiDerivativeBoundScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "SALD.discreteForwardKlDerivativeObligation",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.frozen_delta_cross_lip",
        "SALD.frozenDeltaCrossLipSaldContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "probability.lsi_to_kl_fi"
      ]
      reusedBy := ["sald.discrete_forward_kl.kl_derivative", "thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle56_theorem_interface_route"
      interface := "Cycle-56 theorem-level route: consume the explicit EM endpoint/conditional-FP interfaces, cycle-51 derivative/LSI scalar handoff, discrete DV velocity witness, and appendix.tex:526-592 Gronwall/accumulated-error interfaces to match main_body.tex:299-323 without proving EM/Fokker-Planck from scratch."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle56DiscreteForwardKlSkeletonUpperPacket",
        "SALD.cycle56DiscreteForwardKlSkeletonObligation",
        "SALD.cycle55ForwardKlSkeletonObligation",
        "SALD.cycle51DiscreteForwardKlSkeletonObligation",
        "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "lem:gronwall",
        "lem:dv_variation",
        "eq:LSI-KL-FI"
      ]
      reusedBy := ["thm:forward-KL-discrete", "ASTIS-SALD-001 cycle 56", "cycle56 lower Gronwall packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle56_middle_route_audit"
      interface := "Cycle-56 middle audit: verify the upper discrete theorem route against main_body.tex:299-323 and appendix.tex:260-592, keep EM/Fokker-Planck as named source-cited interfaces, and select sald.discrete_forward_kl.gronwall_accumulation over appendix.tex:526-592 as the lower packet."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle56DiscreteForwardKlSkeletonMiddleContract",
        "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonObligation",
        "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle55ForwardKlSkeletonMiddleObligation",
        "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle56 lower Gronwall packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle56_gronwall_lower"
      interface := "Lower scalar handoff for appendix.tex:526-553: consume the post-DV s-time inequality and inverse-schedule inputs to produce the exact t-time Gronwall coefficient and residual used by lem:gronwall."
      source := saldForwardKlDiscreteGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
        "SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar",
        "SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged",
        "SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "sald.discrete_forward_kl.kl_derivative",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "sald.forward_kl.schedule_time_change",
        "lem:gronwall"
      ]
      reusedBy := ["sald.discrete_forward_kl.gronwall_accumulation", "thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.euler_maruyama"
      interface := "Pin the EM update and continuous frozen interpolation hat X_s with endpoint laws rho_k^eta."
      source := saldForwardKlDiscreteInterpolationSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["EulerMaruyamaContract", "sald.discrete_forward_kl.em_endpoint_laws"]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.contractOnly
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle35_em_fp_upper"
      interface := "Upper proof-closure packet for appendix.tex:260-385 selecting the EM endpoint laws and conditional-drift Fokker--Planck backend as the lower target after the earlier Gronwall, DV, LSI, and continuous-derivative proof-sprint slices."
      source := saldForwardKlDiscreteInterpolationSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle35DiscreteForwardKlEmFpUpperPacket",
        "sald.discrete_forward_kl.cycle35_em_fp_upper",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle35 lower EM-FP packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle35_em_fp_middle"
      interface := "Middle source-to-Lean packet for appendix.tex:260-385: compiled endpoint-vector algebra and divergence-regrouping algebra, with stochastic endpoint laws and conditional-drift Fokker--Planck still explicit obligations."
      source := saldForwardKlDiscreteConditionalFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle35DiscreteForwardKlEmFpMiddleContract",
        "sald.discrete_forward_kl.cycle35_em_fp_middle",
        "SALD.discreteForwardKlEmInterpolationLeftEndpointVector",
        "SALD.discreteForwardKlEmInterpolationRightEndpointVector",
        "SALD.discreteForwardKlConditionalFpDivergenceDriftSplit",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle35 lower EM-FP packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle35_em_fp_lower"
      interface := "Lower proof-producing handoff for appendix.tex:357-385: compose the supplied conditional-drift Fokker--Planck equation and supplied Laplacian split into the source regrouped divergence form, without promoting the analytic FP, density, or integration-by-parts backend."
      source := saldForwardKlDiscreteConditionalFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle35DiscreteForwardKlEmFpMiddleContract",
        "SALD.cycle35DiscreteForwardKlEmFpMiddleObligation",
        "SALD.discreteForwardKlConditionalFpDivergenceDriftSplit",
        "SALD.discreteForwardKlConditionalFpLaplacianSplitHandoff",
        "SALD.cycle35DiscreteForwardKlEmFpLowerObligation",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.em_conditional_fokker_planck"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle40_em_fp_middle"
      interface := "Middle proof-closure handoff for appendix.tex:260-385: add abstract endpoint-law equality transport from pointwise EM interpolation identities, while keeping conditional drift density and conditional-drift Fokker--Planck as obligations."
      source := saldForwardKlDiscreteInterpolationSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle40DiscreteForwardKlEmFpMiddleContract",
        "SALD.cycle40DiscreteForwardKlEmFpMiddleObligation",
        "SALD.discreteForwardKlLawEqOfPointwise",
        "SALD.discreteForwardKlEmInterpolationLeftEndpointLawHandoff",
        "SALD.discreteForwardKlEmInterpolationRightEndpointLawHandoff",
        "SALD.discreteForwardKlEmEndpointLawPairHandoff",
        "SALD.discreteForwardKlConditionalFpLaplacianSplitHandoff",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle40 lower EM endpoint/conditional-FP packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle40_em_endpoint_lower"
      interface := "Lower endpoint-law representation handoff for appendix.tex:334-335: from explicit named law representations for hat rho_s and rho_k^eta, prove both endpoint law equalities using the compiled law handoff lemmas."
      source := saldForwardKlDiscreteInterpolationSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.discreteForwardKlEmEndpointLawPairHandoff",
        "SALD.discreteForwardKlEmInterpolationLeftEndpointLawHandoff",
        "SALD.discreteForwardKlEmInterpolationRightEndpointLawHandoff",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.em_endpoint_laws"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle15_upper_packet"
      interface := "Upper packet selecting the EM interpolation side-condition spine as the next lower target while keeping the discrete theorem statement and accumulated-error constants unchanged."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle15DiscreteForwardKlUpperPacket",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.stitched_interval_regularity",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle15 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle15_middle_em_spine"
      interface := "Middle packet mapping the cycle-15 EM side-condition spine into ordered lower obligations, with the conditional-drift Fokker--Planck equation as the first lower slice."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle15DiscreteForwardKlMiddleContract",
        "sald.discrete_forward_kl.cycle15_middle_em_spine",
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.stitched_interval_regularity",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle15 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.conditional_drift_density"
      interface := "Lower sub-obligation for appendix.tex:347-354: construct the regular conditional-law, density, measurability, and integrability interface needed to treat bar b_{k,s} as a drift field."
      source := saldForwardKlDiscreteConditionalFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract",
        "sald.discrete_forward_kl.conditional_drift_density",
        "eq:frozen_interp_terminal_disc_prop_additive_final",
        "sald.discrete_forward_kl.em_endpoint_laws"
      ]
      reusedBy := ["sald.discrete_forward_kl.em_conditional_fokker_planck", "thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle15_conditional_fp_lower_packet"
      interface := "Lower-ready line ledger for appendix.tex:347-385: conditional frozen drift, conditional-drift Fokker--Planck equation, Laplacian split, and KL-derivative handoff."
      source := saldForwardKlDiscreteConditionalFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract",
        "SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract",
        "sald.discrete_forward_kl.cycle15_conditional_fp_lower_packet",
        "sald.discrete_forward_kl.conditional_drift_density",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.em_endpoint_laws"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle15 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.em_interpolation_side_conditions"
      interface := "Separate endpoint law matching, conditional-drift Fokker--Planck, and stitched-interval regularity for the EM interpolation."
      source := saldForwardKlDiscreteInterpolationSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.discrete_forward_kl.em_endpoint_laws",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "sald.discrete_forward_kl.stitched_interval_regularity"
      ]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.frozen_delta"
      interface := "Bound the one-step frozen score-defect cross term by (1/4)*FI plus Gamma and Delta contributions."
      source := saldFrozenDeltaCrossLipSaldSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["lem:frozen_delta_cross_lip", "eq:lip_SALD_1", "eq:lip_SALD_2", "lem:dv_variation"]
      reusedBy := ["thm:forward-KL-discrete", "thm:general-moving-target-SALD-discrete specialization"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.derivative"
      interface := "Differentiate KL(hat rho_s||tilde pi_s) on each EM interval and derive the discrete differential inequality before Gronwall."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["sald.discrete_forward_kl.em_conditional_fokker_planck", "sald.discrete_forward_kl.frozen_delta_cross_lip", "sald.discrete_forward_kl.dv_finite_log_mgf_witness", "sald.discrete_forward_kl.dv_velocity_bound", "eq:LSI-KL-FI"]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.dv_finite_log_mgf_witness"
      interface := "Expose the EM-interpolation DV witness for nu=hat rho_s, mu=tilde pi_s, and Z=alpha*||v_{t(s)}||^2 before bounding ||tilde v_s||^2."
      source := saldForwardKlDiscreteDvVelocitySource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "lem:dv_variation",
        "def:alpha-complexity",
        "sald.forward_kl.dv_alpha_mgf_monotonicity",
        "sald.forward_kl.dv_finite_log_mgf_witness",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.dv_velocity_bound"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.gronwall_accumulation"
      interface := "Apply lem:gronwall with the added Gamma term to the source general-schedule differential inequality."
      source := saldForwardKlDiscreteGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["lem:gronwall", "sald.discrete_forward_kl.kl_derivative", "sald.discrete_forward_kl.dv_velocity_bound", "sald.discrete_forward_kl.stitched_interval_regularity"]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle19_upper_packet"
      interface := "Upper packet selecting the accumulated-error bridge from the appendix Gronwall display to the main-body linear-slowdown theorem constants."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle19DiscreteForwardKlUpperPacket",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle19 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle19_middle_accumulated_error"
      interface := "Middle packet translating the accumulated-error bridge into lower-ready endpoint, exponent, residual-exponent, and integral-collection sub-slices."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle19DiscreteForwardKlUpperPacket",
        "SALD.cycle19DiscreteForwardKlMiddleContract",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "sald.discrete_forward_kl.cycle19_accumulated_error_middle"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle19 lower accumulated-error bridge"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.linear_slowdown_specialization"
      interface := "Substitute dot{s}=r, collect bar Gamma and bar Delta, and recover the main-body discrete theorem constants."
      source := saldForwardKlDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["sald.discrete_forward_kl.gronwall_accumulation", "def:alpha-complexity"]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.residual_exponent_bound"
      interface := "Bound the residual Gronwall exponent after linear slowdown by the full positive factor T/(r*alpha)+2*r*eta^2*barGamma/alpha'."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.gronwall.integrating_factor",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.accumulated_error_bridge"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.accumulated_error_bridge"
      interface := "Rewrite the appendix Gronwall output into the main-body theorem display by endpoint matching, exponent splitting, and barGamma/barDelta collection."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "SALD.discreteForwardKlGronwallCoeffIntervalIntegrable",
        "SALD.discreteForwardKlGronwallCoeffIntegralSubSub",
        "SALD.discreteForwardKlGronwallInitialExponentSplitScalar",
        "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar",
        "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
        "SALD.discreteForwardKlDeltaAccumulationScalar",
        "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
        "SALD.discreteForwardKlResidualIntegralDisplayBoundScalar",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.coefficient_chain_audit"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle27_upper_accumulated_collection"
      interface := "Upper packet selecting the accumulated-error collection slice after the coefficient-chain audit: endpoint rewrites, linear-slowdown exponent split, and A_alpha/barGamma/barDelta collection."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle27DiscreteForwardKlUpperPacket",
        "sald.discrete_forward_kl.cycle27_accumulated_collection_upper",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar",
        "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
        "SALD.discreteForwardKlDeltaAccumulationScalar",
        "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
        "sald.discrete_forward_kl.coefficient_chain_audit"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle27 lower accumulated-error bridge"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle27_middle_accumulated_collection"
      interface := "Middle packet translating the cycle-27 accumulated-error target into lower-ready endpointBridge, alphaComplexityCollection, and deltaAccumulation sub-slices."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle27DiscreteForwardKlUpperPacket",
        "SALD.cycle27DiscreteForwardKlMiddleContract",
        "sald.discrete_forward_kl.cycle27_accumulated_collection_upper",
        "sald.discrete_forward_kl.cycle27_accumulated_collection_middle",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar",
        "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
        "SALD.discreteForwardKlDeltaAccumulationScalar",
        "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
        "sald.discrete_forward_kl.coefficient_chain_audit",
        "def:alpha-complexity"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle27 lower accumulated-error bridge"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle27_lower_accumulated_collection"
      interface := "Lower scalar/integral core for collecting the additive E_alpha and Delta residual integrals into r^(-1)*A_alpha plus 2*r*eta*barDelta after linear slowdown."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle27DiscreteForwardKlMiddleContract",
        "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
        "SALD.discreteForwardKlDeltaAccumulationScalar",
        "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
        "sald.discrete_forward_kl.cycle27_accumulated_collection_lower",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "def:alpha-complexity"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.accumulated_error_bridge"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.em_defect_accumulation_middle"
      interface := "Middle packet mapping the EM interpolation, one-step defects, DV velocity witness, Gronwall accumulation, and accumulated-error collection to explicit lower obligations."
      source := saldForwardKlDiscreteCoefficientChainSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.discrete_forward_kl.em_interpolation_fp",
        "sald.discrete_forward_kl.frozen_delta_cross_lip",
        "sald.discrete_forward_kl.kl_derivative",
        "sald.discrete_forward_kl.dv_finite_log_mgf_witness",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle11 lower packets"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle23_upper_packet"
      interface := "Upper packet rebaselining the discrete forward-KL spine and selecting the coefficient-chain audit as the single lower target."
      source := saldForwardKlDiscreteCoefficientChainSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle23DiscreteForwardKlUpperPacket",
        "SALD.cycle15DiscreteForwardKlUpperPacket",
        "SALD.cycle19DiscreteForwardKlUpperPacket",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "sald.discrete_forward_kl.frozen_delta_cross_lip",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "sald.discrete_forward_kl.coefficient_chain_audit"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle23 lower coefficient-chain audit"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle23_middle_coefficient_chain"
      interface := "Middle packet translating the cycle-23 coefficient-chain target into the appendix.tex:454-553 first lower slice, with the accumulated-error bridge kept separate."
      source := saldForwardKlDiscreteCoefficientChainSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle23DiscreteForwardKlUpperPacket",
        "SALD.cycle23DiscreteForwardKlMiddleContract",
        "sald.discrete_forward_kl.cycle23_coefficient_chain_middle",
        "SALD.discreteForwardKlCoefficientChainAuditContract",
        "sald.discrete_forward_kl.frozen_delta_cross_lip",
        "sald.discrete_forward_kl.kl_derivative",
        "sald.discrete_forward_kl.dv_finite_log_mgf_witness",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "sald.discrete_forward_kl.coefficient_chain_audit", "cycle23 lower coefficient-chain audit"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.coefficient_chain_audit"
      interface := "Audit the one-step Gamma/Delta coefficients from frozen/moving cross terms through time change, Gronwall, and linear-slowdown accumulation."
      source := saldForwardKlDiscreteCoefficientChainSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle23DiscreteForwardKlMiddleContract",
        "sald.discrete_forward_kl.cycle23_coefficient_chain_middle",
        "sald.discrete_forward_kl.stitched_interval_regularity",
        "sald.discrete_forward_kl.frozen_delta_cross_lip",
        "sald.discrete_forward_kl.kl_derivative",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "thm:general-moving-target-SALD-discrete coefficient pattern"]
      status := ProofStatus.obligation
    }
  ]

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