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

AutoSamplingTheory.SALD.generalVaSaldProofDag

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 generalVaSaldProofDag : 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.cycle47GuidedGeneralSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
                    2. AutoSamplingTheory.SALD.cycle52GuidedGeneralSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
                  2. AutoSamplingTheory.SALD.cycle57GuidedGeneralSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
                2. AutoSamplingTheory.SALD.cycle62GuidedGeneralSkeletonDag — audited data reference, not expanded and not a compiled dependency edge
              2. AutoSamplingTheory.SALD.cycle67GuidedGeneralSkeletonDag — 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. 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. Ordered data items

    1. id : String (explicit)

      Stable plan-node identifier.

      ASTIS.SALD.guided_path_residual.normalizer
      interface : String (explicit)

      Text describing intended mathematical interface.

      Differentiate Z_t and prove dot Z_t/Z_t=-E_{pi_t}[g_t] using the p_t transport equation.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGuidedResidualProofSource — 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. TransportVelocityContract
      2. GuidedTiltContract
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. prop:guided_path_residual
      2. thm:unified-forward-KL
      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.guided_path_residual.identity
      interface : String (explicit)

      Text describing intended mathematical interface.

      Differentiate pi_t=Z_t^(-1)*p_t*exp(-f_t), add div(pi_t*u_t), and obtain the centered residual identity.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGuidedResidualSource — 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.guided_path_residual.normalizer_derivative
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:unified-forward-KL
      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.derivative
      interface : String (explicit)

      Text describing intended mathematical interface.

      Derive the sigma-weighted KL derivative inequality with residual velocity m_t=v_t-c_t before DV.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDerivativeSource — 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_moving_target_SALD
      2. TransportVelocityContract
      3. eq:LSI-KL-FI
      4. SALD.generalMovingTargetPostYoungDerivativeBoundScalar
      5. SALD.generalMovingTargetLsiDerivativeBoundScalar
      6. SALD.generalMovingTargetTimeChangedDerivativeBoundScalar
      7. SALD.generalMovingTargetPreDvDerivativeBoundScalar
      8. sald.forward_kl.density_boundary_regular
      9. 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
      2. thm:unified-forward-KL
      3. thm:general-moving-target-SALD-discrete
      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.dv_finite_log_mgf_witness
      interface : String (explicit)

      Text describing intended mathematical interface.

      Expose the residual-field DV finite-log-mgf and common-space witness for Z=alpha*||m_t||^2 before bounding ||m_t||^2.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetResidualDvSource — 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.saldDvFiniteLogMgfContract
      4. sald.dv_variation.finite_log_mgf_interface
      5. sald.general_moving_target.kl_derivative
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      3. thm:general-moving-target-SALD-discrete
      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.dv_positive_alpha_scaling
      interface : String (explicit)

      Text describing intended mathematical interface.

      After the residual DV instantiation, divide by alpha>0, rewrite the log-mgf quotient as E_alpha(pi_t,m_t), and preserve the sigma-weighted alpha^(-1) coefficient.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetResidualDvSource — 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.generalMovingTargetDvFiniteLogMgfWitnessContract
      4. SALD.generalMovingTargetDvPositiveAlphaScalingContract
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      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.dv_m_energy
      interface : String (explicit)

      Text describing intended mathematical interface.

      Instantiate DV with Z=alpha*||m_t||^2 and rewrite the log-mgf as E_alpha(pi_t,m_t).
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetResidualDvSource — 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.dv_positive_alpha_scaling
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      3. 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.gronwall_application
      interface : String (explicit)

      Text describing intended mathematical interface.

      Apply lem:gronwall with sigma-weighted a(t), b(t), preserving the source exponent factors.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDvGronwallSource — 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.kl_derivative
      3. sald.general_moving_target.dv_m_energy
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      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.cycle24_upper_packet
      interface : String (explicit)

      Text describing intended mathematical interface.

      Upper packet selecting the continuous general Gronwall endpoint/exponent/pure-contraction side-condition bridge as the lower target.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDvGronwallSource — 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.cycle24GeneralVaSaldUpperPacket
      2. SALD.generalMovingTargetGronwallSideConditionContract
      3. sald.general_moving_target.gronwall_application
      4. sald.general_moving_target.dv_m_energy
      5. sald.gronwall.integrating_factor
      6. def:alpha-complexity
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      3. cycle24 lower packet
      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.cycle24_middle_gronwall_bridge
      interface : String (explicit)

      Text describing intended mathematical interface.

      Middle packet mapping appendix.tex:909-945 to endpoint rewrites, sigma-weighted coefficient regularity, exponent splitting, residual-exponent monotonicity, and pure-contraction alpha-complexity obligations.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDvGronwallSource — 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.cycle24GeneralVaSaldUpperPacket
      2. SALD.cycle24GeneralVaSaldMiddleContract
      3. SALD.generalMovingTargetGronwallInstantiationContract
      4. SALD.generalMovingTargetGronwallSideConditionContract
      5. sald.general_moving_target.gronwall_application
      6. sald.general_moving_target.dv_m_energy
      7. sald.general_moving_target.kl_derivative
      8. sald.forward_kl.schedule_time_change
      9. sald.gronwall.integrating_factor
      10. SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable
      11. SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      3. cycle24 lower packet
      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.gronwall_side_conditions
      interface : String (explicit)

      Text describing intended mathematical interface.

      Expose K(0)/K(T) endpoint rewrites, sigma-weighted coefficient regularity, exponent splitting, residual-exponent sign facts, and zero-residual alpha-complexity for the final theorem display.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetDvGronwallSource — 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.cycle24GeneralVaSaldUpperPacket
      2. SALD.cycle24GeneralVaSaldMiddleContract
      3. ASTIS.SALD.general_moving_target.cycle24_upper_packet
      4. ASTIS.SALD.general_moving_target.cycle24_middle_gronwall_bridge
      5. sald.general_moving_target.cycle24_gronwall_middle
      6. sald.forward_kl.schedule_time_change
      7. sald.general_moving_target.kl_derivative
      8. sald.general_moving_target.dv_m_energy
      9. sald.general_moving_target.gronwall_application
      10. sald.gronwall.integrating_factor
      11. SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable
      12. SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces
      13. def:alpha-complexity
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      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.pure_contraction
      interface : String (explicit)

      Text describing intended mathematical interface.

      Specialize c_t=v_t so m_t=0 and the alpha-complexity residual vanishes.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetPureContractionSource — 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.gronwall_side_conditions
      2. sald.general_moving_target.gronwall_application
      3. def:alpha-complexity
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      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.unified_forward_KL.transport_bridge_middle
      interface : String (explicit)

      Text describing intended mathematical interface.

      Middle line ledger for main_body.tex:359-368: residual identity plus correction-field divergence cancel to make u_t+w_t transport pi_t, before the appendix specialization.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldUnifiedTransportBridgeSource — 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.cycle16GeneralVaSaldUpperPacket
      2. SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract
      3. SALD.unifiedForwardKlSpecializationContract
      4. sald.guided_path_residual.identity
      5. eq:poisson-eq
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. sald.unified_forward_kl.transport_velocity_bridge
      2. thm:unified-forward-KL
      3. cycle16 lower packet
      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.unified_forward_KL.transport_bridge_lower
      interface : String (explicit)

      Text describing intended mathematical interface.

      Lower slice for main_body.tex:359-368: preserve the residual/correction signs, expose divergence linearity, cancel the centered residual, and record v_t=u_t+w_t, c_t=u_t, m_t=w_t.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldUnifiedTransportBridgeSource — 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.cycle16UnifiedForwardKlTransportBridgeMiddleContract
      2. SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract
      3. sald.unified_forward_kl.transport_bridge_middle
      4. sald.guided_path_residual.identity
      5. eq:poisson-eq
      6. TransportVelocityContract
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. sald.unified_forward_kl.transport_velocity_bridge
      2. thm:unified-forward-KL
      3. cycle16 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.unified_forward_KL.transport_velocity_bridge
      interface : String (explicit)

      Text describing intended mathematical interface.

      Combine the centered guided residual identity with eq:poisson-eq to show u_t+w_t transports pi_t, then record v_t=u_t+w_t and m_t=w_t.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldCorrectionFieldSource — 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.unified_forward_kl.transport_bridge_middle
      2. sald.unified_forward_kl.transport_bridge_lower
      3. SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract
      4. prop:guided_path_residual
      5. eq:poisson-eq
      6. sald.guided_path_residual.identity
      7. TransportVelocityContract
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:unified-forward-KL
      2. cycle16 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.unified_forward_KL.specialization
      interface : String (explicit)

      Text describing intended mathematical interface.

      Specialize the general moving-target theorem with c_t=u_t, use the correction equation to choose v_t=u_t+w_t, and identify m_t=w_t.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldUnifiedForwardKlProofSource — 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. prop:guided_path_residual
      2. eq:poisson-eq
      3. eq:SALD_Ito
      4. thm:general-moving-target-SALD
      5. sald.unified_forward_kl.transport_velocity_bridge
      6. sald.unified_forward_kl.specialization
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:unified-forward-KL
      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.general_va_sald.guided_path_middle
      interface : String (explicit)

      Text describing intended mathematical interface.

      Middle packet mapping the guided residual proposition, continuous general theorem, unified specialization, and discrete general theorem to explicit lower obligations.
      source : AutoSamplingTheory.SourceAnchor (explicit)

      Source pointer.

      AutoSamplingTheory.SALD.saldGeneralMovingTargetSource — 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.guided_path_residual.identity
      2. sald.general_moving_target.kl_derivative
      3. sald.general_moving_target.dv_finite_log_mgf_witness
      4. sald.general_moving_target.dv_m_energy
      5. sald.general_moving_target.gronwall_application
      6. sald.general_moving_target.gronwall_side_conditions
      7. sald.unified_forward_kl.transport_bridge_middle
      8. sald.unified_forward_kl.transport_velocity_bridge
      9. sald.unified_forward_kl.specialization
      10. sald.general_moving_target_discrete.derivative_side_conditions
      11. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
      12. sald.general_moving_target_discrete.gronwall_side_conditions
      13. sald.general_moving_target_discrete.unified_specialization
      reusedBy : List String (explicit)

      Declared consumers as strings, default empty.

      Ordered data items

      1. thm:general-moving-target-SALD
      2. thm:unified-forward-KL
      3. thm:general-moving-target-SALD-discrete
      4. cycle12 lower packets
      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 generalVaSaldProofDag : List ProofDagBlock :=
  cycle49MainSkeletonAnalyticReadinessDag ++
  cycle54MainSkeletonAnalyticInterfaceDag ++
  cycle59MainSkeletonAnalyticInterfaceDag ++
  cycle64MainSkeletonAnalyticInterfaceDag ++
  cycle69MainSkeletonAnalyticInterfaceDag ++
  cycle70GeneralMovingTargetDiscreteConditionalLawDag ++
  cycle71GeneralMovingTargetDiscreteEndpointConditionalDag ++
  cycle72GeneralMovingTargetDiscreteWeakFpDag ++
  cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpDag ++
  cycle74GeneralMovingTargetDiscreteMeasureInterfaceDag ++
  cycle75GeneralMovingTargetDiscreteConditionalLawBackfillDag ++
  cycle76GeneralMovingTargetDiscreteEndpointConditionalDag ++
  cycle77GeneralMovingTargetDiscreteWeakFpGeneratorDag ++
  cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorDag ++
  cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag ++
  cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityDag ++
  cycle81GeneralMovingTargetDiscreteEndpointConditionalDag ++
  cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag ++
  cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag ++
  cycle84GeneralMovingTargetDiscreteActiveEmBackendDag ++
  cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryDag ++
  cycle47GuidedGeneralSkeletonDag ++
  cycle52GuidedGeneralSkeletonDag ++
  cycle57GuidedGeneralSkeletonDag ++
  cycle62GuidedGeneralSkeletonDag ++
  cycle67GuidedGeneralSkeletonDag ++
  cycle68UnifiedDiscreteGeneralDag ++
  cycle48UnifiedDiscreteSkeletonDag ++
  cycle53UnifiedDiscreteGeneralDag ++
  cycle58UnifiedDiscreteGeneralDag ++
  cycle63UnifiedDiscreteGeneralDag ++
  [
    {
      id := "ASTIS.SALD.guided_path_residual.normalizer"
      interface := "Differentiate Z_t and prove dot Z_t/Z_t=-E_{pi_t}[g_t] using the p_t transport equation."
      source := saldGuidedResidualProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["TransportVelocityContract", "GuidedTiltContract"]
      reusedBy := ["prop:guided_path_residual", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_path_residual.identity"
      interface := "Differentiate pi_t=Z_t^(-1)*p_t*exp(-f_t), add div(pi_t*u_t), and obtain the centered residual identity."
      source := saldGuidedResidualSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["sald.guided_path_residual.normalizer_derivative"]
      reusedBy := ["thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.derivative"
      interface := "Derive the sigma-weighted KL derivative inequality with residual velocity m_t=v_t-c_t before DV."
      source := saldGeneralMovingTargetDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "eq:general_moving_target_SALD",
        "TransportVelocityContract",
        "eq:LSI-KL-FI",
        "SALD.generalMovingTargetPostYoungDerivativeBoundScalar",
        "SALD.generalMovingTargetLsiDerivativeBoundScalar",
        "SALD.generalMovingTargetTimeChangedDerivativeBoundScalar",
        "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
        "sald.forward_kl.density_boundary_regular",
        "sald.forward_kl.schedule_time_change"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.dv_finite_log_mgf_witness"
      interface := "Expose the residual-field DV finite-log-mgf and common-space witness for Z=alpha*||m_t||^2 before bounding ||m_t||^2."
      source := saldGeneralMovingTargetResidualDvSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "lem:dv_variation",
        "def:alpha-complexity",
        "SALD.saldDvFiniteLogMgfContract",
        "sald.dv_variation.finite_log_mgf_interface",
        "sald.general_moving_target.kl_derivative"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.dv_positive_alpha_scaling"
      interface := "After the residual DV instantiation, divide by alpha>0, rewrite the log-mgf quotient as E_alpha(pi_t,m_t), and preserve the sigma-weighted alpha^(-1) coefficient."
      source := saldGeneralMovingTargetResidualDvSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "lem:dv_variation",
        "def:alpha-complexity",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDvPositiveAlphaScalingContract"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.dv_m_energy"
      interface := "Instantiate DV with Z=alpha*||m_t||^2 and rewrite the log-mgf as E_alpha(pi_t,m_t)."
      source := saldGeneralMovingTargetResidualDvSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["lem:dv_variation", "def:alpha-complexity", "sald.general_moving_target.dv_finite_log_mgf_witness", "sald.general_moving_target.dv_positive_alpha_scaling"]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.gronwall_application"
      interface := "Apply lem:gronwall with sigma-weighted a(t), b(t), preserving the source exponent factors."
      source := saldGeneralMovingTargetDvGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["lem:gronwall", "sald.general_moving_target.kl_derivative", "sald.general_moving_target.dv_m_energy"]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.cycle24_upper_packet"
      interface := "Upper packet selecting the continuous general Gronwall endpoint/exponent/pure-contraction side-condition bridge as the lower target."
      source := saldGeneralMovingTargetDvGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle24GeneralVaSaldUpperPacket",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "sald.general_moving_target.gronwall_application",
        "sald.general_moving_target.dv_m_energy",
        "sald.gronwall.integrating_factor",
        "def:alpha-complexity"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "cycle24 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.cycle24_middle_gronwall_bridge"
      interface := "Middle packet mapping appendix.tex:909-945 to endpoint rewrites, sigma-weighted coefficient regularity, exponent splitting, residual-exponent monotonicity, and pure-contraction alpha-complexity obligations."
      source := saldGeneralMovingTargetDvGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle24GeneralVaSaldUpperPacket",
        "SALD.cycle24GeneralVaSaldMiddleContract",
        "SALD.generalMovingTargetGronwallInstantiationContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "sald.general_moving_target.gronwall_application",
        "sald.general_moving_target.dv_m_energy",
        "sald.general_moving_target.kl_derivative",
        "sald.forward_kl.schedule_time_change",
        "sald.gronwall.integrating_factor",
        "SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable",
        "SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "cycle24 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.gronwall_side_conditions"
      interface := "Expose K(0)/K(T) endpoint rewrites, sigma-weighted coefficient regularity, exponent splitting, residual-exponent sign facts, and zero-residual alpha-complexity for the final theorem display."
      source := saldGeneralMovingTargetDvGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle24GeneralVaSaldUpperPacket",
        "SALD.cycle24GeneralVaSaldMiddleContract",
        "ASTIS.SALD.general_moving_target.cycle24_upper_packet",
        "ASTIS.SALD.general_moving_target.cycle24_middle_gronwall_bridge",
        "sald.general_moving_target.cycle24_gronwall_middle",
        "sald.forward_kl.schedule_time_change",
        "sald.general_moving_target.kl_derivative",
        "sald.general_moving_target.dv_m_energy",
        "sald.general_moving_target.gronwall_application",
        "sald.gronwall.integrating_factor",
        "SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable",
        "SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces",
        "def:alpha-complexity"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.pure_contraction"
      interface := "Specialize c_t=v_t so m_t=0 and the alpha-complexity residual vanishes."
      source := saldGeneralMovingTargetPureContractionSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := ["sald.general_moving_target.gronwall_side_conditions", "sald.general_moving_target.gronwall_application", "def:alpha-complexity"]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_forward_KL.transport_bridge_middle"
      interface := "Middle line ledger for main_body.tex:359-368: residual identity plus correction-field divergence cancel to make u_t+w_t transport pi_t, before the appendix specialization."
      source := saldUnifiedTransportBridgeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle16GeneralVaSaldUpperPacket",
        "SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract",
        "SALD.unifiedForwardKlSpecializationContract",
        "sald.guided_path_residual.identity",
        "eq:poisson-eq"
      ]
      reusedBy := ["sald.unified_forward_kl.transport_velocity_bridge", "thm:unified-forward-KL", "cycle16 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_forward_KL.transport_bridge_lower"
      interface := "Lower slice for main_body.tex:359-368: preserve the residual/correction signs, expose divergence linearity, cancel the centered residual, and record v_t=u_t+w_t, c_t=u_t, m_t=w_t."
      source := saldUnifiedTransportBridgeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract",
        "SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract",
        "sald.unified_forward_kl.transport_bridge_middle",
        "sald.guided_path_residual.identity",
        "eq:poisson-eq",
        "TransportVelocityContract"
      ]
      reusedBy := ["sald.unified_forward_kl.transport_velocity_bridge", "thm:unified-forward-KL", "cycle16 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_forward_KL.transport_velocity_bridge"
      interface := "Combine the centered guided residual identity with eq:poisson-eq to show u_t+w_t transports pi_t, then record v_t=u_t+w_t and m_t=w_t."
      source := saldCorrectionFieldSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.unified_forward_kl.transport_bridge_middle",
        "sald.unified_forward_kl.transport_bridge_lower",
        "SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract",
        "prop:guided_path_residual",
        "eq:poisson-eq",
        "sald.guided_path_residual.identity",
        "TransportVelocityContract"
      ]
      reusedBy := ["thm:unified-forward-KL", "cycle16 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_forward_KL.specialization"
      interface := "Specialize the general moving-target theorem with c_t=u_t, use the correction equation to choose v_t=u_t+w_t, and identify m_t=w_t."
      source := saldUnifiedForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "prop:guided_path_residual",
        "eq:poisson-eq",
        "eq:SALD_Ito",
        "thm:general-moving-target-SALD",
        "sald.unified_forward_kl.transport_velocity_bridge",
        "sald.unified_forward_kl.specialization"
      ]
      reusedBy := ["thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_va_sald.guided_path_middle"
      interface := "Middle packet mapping the guided residual proposition, continuous general theorem, unified specialization, and discrete general theorem to explicit lower obligations."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "sald.guided_path_residual.identity",
        "sald.general_moving_target.kl_derivative",
        "sald.general_moving_target.dv_finite_log_mgf_witness",
        "sald.general_moving_target.dv_m_energy",
        "sald.general_moving_target.gronwall_application",
        "sald.general_moving_target.gronwall_side_conditions",
        "sald.unified_forward_kl.transport_bridge_middle",
        "sald.unified_forward_kl.transport_velocity_bridge",
        "sald.unified_forward_kl.specialization",
        "sald.general_moving_target_discrete.derivative_side_conditions",
        "sald.general_moving_target_discrete.dv_finite_log_mgf_witness",
        "sald.general_moving_target_discrete.gronwall_side_conditions",
        "sald.general_moving_target_discrete.unified_specialization"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "cycle12 lower packets"]
      status := ProofStatus.obligation
    }
  ]

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