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

AutoSamplingTheory.SALD.generalVaSaldDiscreteProofDag

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 generalVaSaldDiscreteProofDag : 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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                                                                                    1. AutoSamplingTheory.SALD.cycle49MainSkeletonAnalyticReadinessDag — audited data reference, not expanded and not a compiled dependency edge
                                                                                    2. AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
                                                                                  2. AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
                                                                                2. AutoSamplingTheory.SALD.cycle64MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
                                                                              2. AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
                                                                            2. AutoSamplingTheory.SALD.cycle70GeneralMovingTargetDiscreteConditionalLawDag — audited data reference, not expanded and not a compiled dependency edge
                                                                          2. AutoSamplingTheory.SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalDag — audited data reference, not expanded and not a compiled dependency edge
                                                                        2. AutoSamplingTheory.SALD.cycle72GeneralMovingTargetDiscreteWeakFpDag — audited data reference, not expanded and not a compiled dependency edge
                                                                      2. AutoSamplingTheory.SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag — audited data reference, not expanded and not a compiled dependency edge
                                                                    2. AutoSamplingTheory.SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag — audited data reference, not expanded and not a compiled dependency edge
                                                                  2. AutoSamplingTheory.SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillDag — audited data reference, not expanded and not a compiled dependency edge
                                                                2. AutoSamplingTheory.SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalDag — audited data reference, not expanded and not a compiled dependency edge
                                                              2. AutoSamplingTheory.SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag — audited data reference, not expanded and not a compiled dependency edge
                                                            2. AutoSamplingTheory.SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag — audited data reference, not expanded and not a compiled dependency edge
                                                          2. AutoSamplingTheory.SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag — audited data reference, not expanded and not a compiled dependency edge
                                                        2. AutoSamplingTheory.SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag — audited data reference, not expanded and not a compiled dependency edge
                                                      2. AutoSamplingTheory.SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalDag — audited data reference, not expanded and not a compiled dependency edge
                                                    2. AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag — audited data reference, not expanded and not a compiled dependency edge
                                                  2. AutoSamplingTheory.SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag — audited data reference, not expanded and not a compiled dependency edge
                                                2. AutoSamplingTheory.SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendDag — audited data reference, not expanded and not a compiled dependency edge
                                              2. AutoSamplingTheory.SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
                                            2. AutoSamplingTheory.SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
                                          2. AutoSamplingTheory.SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
                                        2. AutoSamplingTheory.SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityDag — audited data reference, not expanded and not a compiled dependency edge
                                      2. AutoSamplingTheory.SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelDag — audited data reference, not expanded and not a compiled dependency edge
                                    2. AutoSamplingTheory.SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitDag — audited data reference, not expanded and not a compiled dependency edge
                                  2. AutoSamplingTheory.SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeDag — audited data reference, not expanded and not a compiled dependency edge
                                2. AutoSamplingTheory.SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag — audited data reference, not expanded and not a compiled dependency edge
                              2. AutoSamplingTheory.SALD.cycle95DiscreteForwardKlClosurePressureDag — audited data reference, not expanded and not a compiled dependency edge
                            2. AutoSamplingTheory.SALD.cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag — audited data reference, not expanded and not a compiled dependency edge
                          2. AutoSamplingTheory.SALD.cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag — audited data reference, not expanded and not a compiled dependency edge
                        2. AutoSamplingTheory.SALD.cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryDag — audited data reference, not expanded and not a compiled dependency edge
                      2. AutoSamplingTheory.SALD.cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag — audited data reference, not expanded and not a compiled dependency edge
                    2. AutoSamplingTheory.SALD.cycle100GeneralMovingTargetDiscreteBarBWeakGradDefDag — audited data reference, not expanded and not a compiled dependency edge
                  2. 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.cycle48UnifiedDiscreteSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
          2. AutoSamplingTheory.SALD.cycle53UnifiedDiscreteGeneralDag — audited data reference, not expanded and not a compiled dependency edge
        2. AutoSamplingTheory.SALD.cycle58UnifiedDiscreteGeneralDag — audited data reference, not expanded and not a compiled dependency edge
      2. AutoSamplingTheory.SALD.cycle63UnifiedDiscreteGeneralDag — audited data reference, not expanded and not a compiled dependency edge
    2. AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralDag — audited data reference, not expanded and not a compiled dependency edge

  2. Ordered data items

    1. id : String (explicit)

      Stable plan-node identifier.

      ASTIS.SALD.general_moving_target_discrete.euler_maruyama
      interface : String (explicit)

      Text describing intended mathematical interface.

      Pin the general VA-SALD EM update, frozen interpolation, sigma_eta, and endpoint laws.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — 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.generalMovingTargetDiscreteEmEndpointLawPairHandoff
      3. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
      4. sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit
      5. sald.general_moving_target_discrete.em_interpolation_fp
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      status : AutoSamplingTheory.ProofStatus (explicit)

      Recorded workflow status, default planned.

      AutoSamplingTheory.ProofStatus.contractOnly — stored label only; no proof certification
    2. id : String (explicit)

      Stable plan-node identifier.

      ASTIS.SALD.general_moving_target_discrete.frozen_delta
      interface : String (explicit)

      Text describing intended mathematical interface.

      Bound the VA frozen-field error delta_pi^VA using the source Gamma and Delta definitions.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldFrozenDeltaCrossLipGeneralSource — 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. eq:general_discrete_delta_def
      2. lem:dv_variation
      3. def:alpha-complexity
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. lem:frozen_delta_cross_lip_sald
      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.general_moving_target_discrete.cycle28_upper_derivative_side_conditions
      interface : String (explicit)

      Text describing intended mathematical interface.

      Upper packet selecting the discrete general derivative side-condition bridge, with appendix.tex:1469-1511 frozen/residual algebra and Young coefficient bookkeeping as the preferred lower sub-slice.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle28GeneralVaSaldUpperPacket
      2. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
      3. sald.general_moving_target_discrete.em_interpolation_fp
      4. sald.general_moving_target_discrete.frozen_delta_cross_lip
      5. sald.forward_kl.schedule_time_change
      6. eq:LSI-KL-FI
      7. lem:dv_variation
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. cycle28 lower packet
      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.general_moving_target_discrete.cycle28_middle_derivative_side_conditions
      interface : String (explicit)

      Text describing intended mathematical interface.

      Middle packet mapping appendix.tex:1469-1511 to the frozen/residual algebra, two sigma_eta^2/8 Young shares, and compiled scalar coefficient helpers before lower proof search.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteYoungSource — 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.cycle28GeneralVaSaldUpperPacket
      2. SALD.cycle28GeneralVaSaldMiddleContract
      3. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
      4. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
      5. SALD.generalMovingTargetDiscreteYoungFisherShareScalar
      6. SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar
      7. SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar
      8. sald.general_moving_target_discrete.cycle28_derivative_side_middle
      9. sald.general_moving_target_discrete.em_interpolation_fp
      10. sald.general_moving_target_discrete.frozen_delta_cross_lip
      11. eq:LSI-KL-FI
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. sald.general_moving_target_discrete.derivative_side_conditions
      2. thm:general-moving-target-SALD-discrete
      3. cycle28 lower 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.general_moving_target_discrete.cycle28_lower_derivative_side_conditions
      interface : String (explicit)

      Text describing intended mathematical interface.

      Lower compiled module algebra for appendix.tex:1469-1478: after delta_pi^VA, tilde v_s, and m_t=v_t-c_t are identified, rewrite the cross field as delta_pi^VA+dot t(s)*m_t.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteYoungSource — 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.cycle28GeneralVaSaldMiddleContract
      2. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
      3. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
      4. sald.general_moving_target_discrete.cycle28_derivative_side_lower
      5. eq:general_discrete_delta_def
      6. sald.general_moving_target_discrete.em_interpolation_fp
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. sald.general_moving_target_discrete.derivative_side_conditions
      2. thm:general-moving-target-SALD-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.general_moving_target_discrete.derivative_side_conditions
      interface : String (explicit)

      Text describing intended mathematical interface.

      Expose endpoint laws, conditional-drift Fokker--Planck, frozen/residual algebra, Young coefficient bookkeeping, DV finite-log-mgf, and stitched time-change interfaces.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle28GeneralVaSaldMiddleContract
      2. sald.general_moving_target_discrete.cycle28_derivative_side_middle
      3. sald.general_moving_target_discrete.cycle28_derivative_side_lower
      4. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
      5. SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff
      6. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
      7. sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit
      8. sald.general_moving_target_discrete.em_interpolation_fp
      9. sald.general_moving_target_discrete.frozen_delta_cross_lip
      10. sald.forward_kl.schedule_time_change
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      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.general_moving_target_discrete.dv_finite_log_mgf_witness
      interface : String (explicit)

      Text describing intended mathematical interface.

      Expose the EM-interpolation residual DV witness for nu=hat rho_s, mu=tilde pi_s, and Z=alpha*||m_{t(s)}||^2 before the doubled residual-energy bound.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteResidualDvSource — 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.general_moving_target.dv_finite_log_mgf_witness
      4. sald.general_moving_target_discrete.em_interpolation_fp
      5. sald.general_moving_target_discrete.derivative_side_conditions
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. discrete VA-SALD guided specialization
      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.general_moving_target_discrete.dv_m_energy
      interface : String (explicit)

      Text describing intended mathematical interface.

      Instantiate DV under the EM interpolation law and preserve the doubled residual-energy coefficient before the s-to-t time change.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteResidualDvSource — 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.general_moving_target_discrete.dv_finite_log_mgf_witness
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. discrete VA-SALD guided specialization
      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.general_moving_target_discrete.derivative
      interface : String (explicit)

      Text describing intended mathematical interface.

      Differentiate KL(hat rho_s||tilde pi_s), split delta_pi^VA and dot{t}*m_t, then derive the source discrete differential inequality.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit
      2. SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff
      3. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
      4. sald.general_moving_target_discrete.derivative_side_conditions
      5. sald.general_moving_target_discrete.em_interpolation_fp
      6. sald.general_moving_target_discrete.frozen_delta_cross_lip
      7. SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar
      8. sald.general_moving_target_discrete.cycle53_derivative_dv_lower
      9. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
      10. sald.general_moving_target_discrete.dv_m_energy
      11. eq:LSI-KL-FI
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      status : AutoSamplingTheory.ProofStatus (explicit)

      Recorded workflow status, default planned.

      AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
    10. id : String (explicit)

      Stable plan-node identifier.

      ASTIS.SALD.general_moving_target_discrete.cycle53_derivative_dv_lower
      interface : String (explicit)

      Text describing intended mathematical interface.

      Lower proof-producing scalar handoff for appendix.tex:1469-1583: compose the supplied EM KL derivative, frozen/residual Young bounds, frozen-delta term, LSI comparison, residual DV estimate, and constant-schedule time change into the exact t-time pre-Gronwall inequality.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle53GeneralMovingTargetDiscreteDerivativeDvLowerObligation
      2. SALD.generalMovingTargetDiscretePostYoungDerivativeBoundScalar
      3. SALD.generalMovingTargetDiscretePostLsiDerivativeBoundScalar
      4. SALD.generalMovingTargetDiscretePostDvDerivativeBoundScalar
      5. SALD.generalMovingTargetDiscreteTimeChangedDerivativeBoundScalar
      6. SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar
      7. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
      8. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
      9. sald.general_moving_target_discrete.kl_derivative
      10. sald.general_moving_target_discrete.derivative_side_conditions
      11. sald.general_moving_target_discrete.frozen_delta_cross_lip
      12. sald.general_moving_target_discrete.dv_m_energy
      13. probability.lsi_to_kl_fi
      14. sald.forward_kl.schedule_time_change
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. sald.general_moving_target_discrete.kl_derivative
      2. thm:general-moving-target-SALD-discrete
      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.general_moving_target_discrete.constant_schedule
      interface : String (explicit)

      Text describing intended mathematical interface.

      Expose constant inverse-schedule and stitched-interval regularity for the final Gronwall step.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteSource — 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.forward_kl.schedule_time_change
      2. sald.general_moving_target_discrete.em_interpolation_fp
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      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.general_moving_target_discrete.gronwall_application
      interface : String (explicit)

      Text describing intended mathematical interface.

      Apply lem:gronwall with the source sigma_eta, Gamma, Delta, and doubled residual-energy coefficients.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSource — 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.general_moving_target_discrete.kl_derivative
      3. sald.general_moving_target_discrete.dv_m_energy
      4. sald.general_moving_target_discrete.constant_schedule_stitching
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. discrete VA-SALD guided specialization
      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.general_moving_target_discrete.cycle20_upper_packet
      interface : String (explicit)

      Text describing intended mathematical interface.

      Upper packet selecting the final discrete general Gronwall side-condition/display bridge as the lower target.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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.cycle20GeneralVaSaldUpperPacket
      2. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
      3. sald.general_moving_target_discrete.gronwall_application
      4. sald.general_moving_target_discrete.constant_schedule_stitching
      5. sald.general_moving_target_discrete.kl_derivative
      6. sald.gronwall.integrating_factor
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. cycle20 lower 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.general_moving_target_discrete.cycle20_middle_gronwall_bridge
      interface : String (explicit)

      Text describing intended mathematical interface.

      Middle source-to-Lean map for appendix.tex:1573-1600: K(t) stitching, constant-schedule coefficient rewrites, coefficient regularity, and exact Gronwall-display matching.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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.cycle20GeneralVaSaldUpperPacket
      2. SALD.cycle20GeneralVaSaldMiddleContract
      3. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
      4. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
      5. SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar
      6. SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar
      7. SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar
      8. SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar
      9. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
      10. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
      11. SALD.cycle59GeneralMovingTargetDiscreteGronwallLowerObligation
      12. sald.general_moving_target_discrete.cycle20_gronwall_middle
      13. sald.general_moving_target_discrete.gronwall_application
      14. sald.general_moving_target_discrete.constant_schedule_stitching
      15. sald.gronwall.integrating_factor
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. cycle20 lower packet
      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.general_moving_target_discrete.gronwall_side_conditions
      interface : String (explicit)

      Text describing intended mathematical interface.

      Expose stitched endpoint laws, constant-schedule coefficient rewrites, coefficient regularity, and exact matching of the Gronwall output to the theorem display.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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.cycle20GeneralVaSaldUpperPacket
      2. SALD.cycle20GeneralVaSaldMiddleContract
      3. SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar
      4. SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar
      5. SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar
      6. SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar
      7. sald.general_moving_target_discrete.cycle20_gronwall_middle
      8. sald.general_moving_target_discrete.gronwall_application
      9. sald.general_moving_target_discrete.constant_schedule_stitching
      10. sald.general_moving_target_discrete.kl_derivative
      11. sald.gronwall.integrating_factor
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD-discrete
      2. discrete VA-SALD guided specialization
      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 generalVaSaldDiscreteProofDag : 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 ++
  cycle91GeneralMovingTargetDiscreteConditionalKernelDag ++
  cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitDag ++
  cycle93GeneralMovingTargetDiscreteKlMassDerivativeDag ++
  cycle94GeneralMovingTargetDiscreteWeakFpDriftActionDag ++
  cycle95DiscreteForwardKlClosurePressureDag ++
  cycle96GeneralMovingTargetDiscreteCondexpGeneratorPairingDag ++
  cycle97GeneralMovingTargetDiscreteCanonicalCondDistribPairingDag ++
  cycle98GeneralMovingTargetDiscreteBarBDivergenceNoBoundaryDag ++
  cycle99GeneralMovingTargetDiscreteRawKlDerivativeDag ++
  cycle100GeneralMovingTargetDiscreteBarBWeakGradDefDag ++
  cycle100GeneralMovingTargetDiscreteBarBInnerGradientBoundDag ++
  cycle101DiscreteForwardKlClosurePressureDag ++
  cycle103GeneralMovingTargetDiscreteConditionalKernelVersionDag ++
  cycle48UnifiedDiscreteSkeletonDag ++
  cycle53UnifiedDiscreteGeneralDag ++
  cycle58UnifiedDiscreteGeneralDag ++
  cycle63UnifiedDiscreteGeneralDag ++
  cycle68UnifiedDiscreteGeneralDag ++
  [
    {
      id := "ASTIS.SALD.general_moving_target_discrete.euler_maruyama"
      interface := "Pin the general VA-SALD EM update, frozen interpolation, sigma_eta, and endpoint laws."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["EulerMaruyamaContract", "SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff", "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation", "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit", "sald.general_moving_target_discrete.em_interpolation_fp"]
      reusedBy := ["thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.contractOnly
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.frozen_delta"
      interface := "Bound the VA frozen-field error delta_pi^VA using the source Gamma and Delta definitions."
      source := saldFrozenDeltaCrossLipGeneralSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["eq:general_discrete_delta_def", "lem:dv_variation", "def:alpha-complexity"]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "lem:frozen_delta_cross_lip_sald"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle28_upper_derivative_side_conditions"
      interface := "Upper packet selecting the discrete general derivative side-condition bridge, with appendix.tex:1469-1511 frozen/residual algebra and Young coefficient bookkeeping as the preferred lower sub-slice."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle28GeneralVaSaldUpperPacket",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "sald.forward_kl.schedule_time_change",
        "eq:LSI-KL-FI",
        "lem:dv_variation"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "cycle28 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle28_middle_derivative_side_conditions"
      interface := "Middle packet mapping appendix.tex:1469-1511 to the frozen/residual algebra, two sigma_eta^2/8 Young shares, and compiled scalar coefficient helpers before lower proof search."
      source := saldGeneralMovingTargetDiscreteYoungSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle28GeneralVaSaldUpperPacket",
        "SALD.cycle28GeneralVaSaldMiddleContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
        "SALD.generalMovingTargetDiscreteYoungFisherShareScalar",
        "SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar",
        "SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar",
        "sald.general_moving_target_discrete.cycle28_derivative_side_middle",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "eq:LSI-KL-FI"
      ]
      reusedBy := ["sald.general_moving_target_discrete.derivative_side_conditions", "thm:general-moving-target-SALD-discrete", "cycle28 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle28_lower_derivative_side_conditions"
      interface := "Lower compiled module algebra for appendix.tex:1469-1478: after delta_pi^VA, tilde v_s, and m_t=v_t-c_t are identified, rewrite the cross field as delta_pi^VA+dot t(s)*m_t."
      source := saldGeneralMovingTargetDiscreteYoungSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle28GeneralVaSaldMiddleContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
        "sald.general_moving_target_discrete.cycle28_derivative_side_lower",
        "eq:general_discrete_delta_def",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := ["sald.general_moving_target_discrete.derivative_side_conditions", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.derivative_side_conditions"
      interface := "Expose endpoint laws, conditional-drift Fokker--Planck, frozen/residual algebra, Young coefficient bookkeeping, DV finite-log-mgf, and stitched time-change interfaces."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle28GeneralVaSaldMiddleContract",
        "sald.general_moving_target_discrete.cycle28_derivative_side_middle",
        "sald.general_moving_target_discrete.cycle28_derivative_side_lower",
        "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
        "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "sald.forward_kl.schedule_time_change"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.dv_finite_log_mgf_witness"
      interface := "Expose the EM-interpolation residual DV witness for nu=hat rho_s, mu=tilde pi_s, and Z=alpha*||m_{t(s)}||^2 before the doubled residual-energy bound."
      source := saldGeneralMovingTargetDiscreteResidualDvSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "lem:dv_variation",
        "def:alpha-complexity",
        "sald.general_moving_target.dv_finite_log_mgf_witness",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.derivative_side_conditions"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "discrete VA-SALD guided specialization"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.dv_m_energy"
      interface := "Instantiate DV under the EM interpolation law and preserve the doubled residual-energy coefficient before the s-to-t time change."
      source := saldGeneralMovingTargetDiscreteResidualDvSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "lem:dv_variation",
        "def:alpha-complexity",
        "sald.general_moving_target_discrete.dv_finite_log_mgf_witness"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "discrete VA-SALD guided specialization"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.derivative"
      interface := "Differentiate KL(hat rho_s||tilde pi_s), split delta_pi^VA and dot{t}*m_t, then derive the source discrete differential inequality."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
        "sald.general_moving_target_discrete.derivative_side_conditions",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar",
        "sald.general_moving_target_discrete.cycle53_derivative_dv_lower",
        "sald.general_moving_target_discrete.dv_finite_log_mgf_witness",
        "sald.general_moving_target_discrete.dv_m_energy",
        "eq:LSI-KL-FI"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle53_derivative_dv_lower"
      interface := "Lower proof-producing scalar handoff for appendix.tex:1469-1583: compose the supplied EM KL derivative, frozen/residual Young bounds, frozen-delta term, LSI comparison, residual DV estimate, and constant-schedule time change into the exact t-time pre-Gronwall inequality."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle53GeneralMovingTargetDiscreteDerivativeDvLowerObligation",
        "SALD.generalMovingTargetDiscretePostYoungDerivativeBoundScalar",
        "SALD.generalMovingTargetDiscretePostLsiDerivativeBoundScalar",
        "SALD.generalMovingTargetDiscretePostDvDerivativeBoundScalar",
        "SALD.generalMovingTargetDiscreteTimeChangedDerivativeBoundScalar",
        "SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar",
        "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.derivative_side_conditions",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "sald.general_moving_target_discrete.dv_m_energy",
        "probability.lsi_to_kl_fi",
        "sald.forward_kl.schedule_time_change"
      ]
      reusedBy := ["sald.general_moving_target_discrete.kl_derivative", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.constant_schedule"
      interface := "Expose constant inverse-schedule and stitched-interval regularity for the final Gronwall step."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["sald.forward_kl.schedule_time_change", "sald.general_moving_target_discrete.em_interpolation_fp"]
      reusedBy := ["thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.gronwall_application"
      interface := "Apply lem:gronwall with the source sigma_eta, Gamma, Delta, and doubled residual-energy coefficients."
      source := saldGeneralMovingTargetDiscreteGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "lem:gronwall",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.constant_schedule_stitching"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "discrete VA-SALD guided specialization"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle20_upper_packet"
      interface := "Upper packet selecting the final discrete general Gronwall side-condition/display bridge as the lower target."
      source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle20GeneralVaSaldUpperPacket",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
        "sald.general_moving_target_discrete.gronwall_application",
        "sald.general_moving_target_discrete.constant_schedule_stitching",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.gronwall.integrating_factor"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "cycle20 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle20_middle_gronwall_bridge"
      interface := "Middle source-to-Lean map for appendix.tex:1573-1600: K(t) stitching, constant-schedule coefficient rewrites, coefficient regularity, and exact Gronwall-display matching."
      source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle20GeneralVaSaldUpperPacket",
        "SALD.cycle20GeneralVaSaldMiddleContract",
        "SALD.generalMovingTargetDiscreteGronwallInstantiationContract",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
        "SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar",
        "SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar",
        "SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar",
        "SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar",
        "SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput",
        "SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar",
        "SALD.cycle59GeneralMovingTargetDiscreteGronwallLowerObligation",
        "sald.general_moving_target_discrete.cycle20_gronwall_middle",
        "sald.general_moving_target_discrete.gronwall_application",
        "sald.general_moving_target_discrete.constant_schedule_stitching",
        "sald.gronwall.integrating_factor"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "cycle20 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.gronwall_side_conditions"
      interface := "Expose stitched endpoint laws, constant-schedule coefficient rewrites, coefficient regularity, and exact matching of the Gronwall output to the theorem display."
      source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle20GeneralVaSaldUpperPacket",
        "SALD.cycle20GeneralVaSaldMiddleContract",
        "SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar",
        "SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar",
        "SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar",
        "SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar",
        "sald.general_moving_target_discrete.cycle20_gronwall_middle",
        "sald.general_moving_target_discrete.gronwall_application",
        "sald.general_moving_target_discrete.constant_schedule_stitching",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.gronwall.integrating_factor"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "discrete VA-SALD guided specialization"]
      status := ProofStatus.obligation
    }
  ]

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