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

AutoSamplingTheory.SALD.cycle48UnifiedDiscreteSkeletonDag

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 cycle48UnifiedDiscreteSkeletonDag : List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

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.

Ordered data items

  1. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.unified_forward_KL.cycle48_theorem_skeleton_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Unified theorem-level route: combine the guided residual identity and correction-field equation to obtain the transport velocity u_t+w_t, then specialize thm:general-moving-target-SALD with c_t=u_t and m_t=w_t.
    source : AutoSamplingTheory.SourceAnchor (explicit)

    Source pointer.

    AutoSamplingTheory.SALD.saldUnifiedForwardKlSource — 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.cycle48UnifiedDiscreteSkeletonUpperPacket
    2. SALD.cycle48UnifiedDiscreteSkeletonObligation
    3. SALD.cycle48UnifiedDiscreteSkeletonMiddleContract
    4. SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation
    5. SALD.cycle47GuidedGeneralSkeletonObligation
    6. SALD.cycle47GuidedGeneralSkeletonMiddleObligation
    7. SALD.guidedResidualIdentityContract
    8. SALD.generalMovingTargetStatementContract
    9. SALD.unifiedForwardKlSpecializationContract
    10. sald.guided_path_residual.identity
    11. sald.unified_forward_kl.transport_velocity_bridge
    12. sald.unified_forward_kl.specialization
    13. sald.general_moving_target.kl_derivative
    14. sald.general_moving_target.dv_m_energy
    15. sald.general_moving_target.gronwall_side_conditions
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:unified-forward-KL
    2. main skeleton sprint 5
    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.general_moving_target_discrete.cycle48_theorem_skeleton_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Discrete general theorem-level route: compose the source statement, general EM endpoint/conditional-FP backend, frozen-delta bound, KL derivative/LSI block, residual DV witness, Gronwall/stitching side conditions, and discrete guided specialization without changing coefficients.
    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.cycle48UnifiedDiscreteSkeletonUpperPacket
    2. SALD.cycle48UnifiedDiscreteSkeletonObligation
    3. SALD.cycle48UnifiedDiscreteSkeletonMiddleContract
    4. SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation
    5. SALD.cycle44MainSkeletonAnalyticInterfaceObligation
    6. SALD.cycle47GuidedGeneralSkeletonObligation
    7. SALD.cycle28GeneralVaSaldUpperPacket
    8. SALD.cycle28GeneralVaSaldMiddleContract
    9. sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit
    10. SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff
    11. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
    12. SALD.cycle20GeneralVaSaldUpperPacket
    13. SALD.cycle20GeneralVaSaldMiddleContract
    14. SALD.generalMovingTargetDiscreteStatementContract
    15. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    16. SALD.generalFrozenDeltaCrossLipContract
    17. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
    18. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
    19. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
    20. sald.general_moving_target_discrete.em_interpolation_fp
    21. sald.general_moving_target_discrete.frozen_delta_cross_lip
    22. sald.general_moving_target_discrete.derivative_side_conditions
    23. sald.general_moving_target_discrete.kl_derivative
    24. probability.lsi_to_kl_fi
    25. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
    26. sald.general_moving_target_discrete.dv_m_energy
    27. sald.general_moving_target_discrete.gronwall_application
    28. sald.general_moving_target_discrete.gronwall_side_conditions
    29. 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-discrete
    2. main skeleton sprint 5
    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.unified_discrete_general.cycle48_middle_route_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle source-to-Lean audit for the final skeleton route: verify the unified specialization and discrete general EM/Fokker-Planck/frozen-delta/LSI/DV/Gronwall chain, then select the discrete KL derivative backend beginning with the endpoint and conditional-law interface.
    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.cycle48UnifiedDiscreteSkeletonMiddleContract
    2. SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation
    3. SALD.cycle48UnifiedDiscreteSkeletonObligation
    4. sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit
    5. SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff
    6. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
    7. SALD.unifiedForwardKlSpecializationContract
    8. sald.unified_forward_kl.transport_velocity_bridge
    9. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
    10. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    11. sald.general_moving_target_discrete.em_interpolation_fp
    12. sald.general_moving_target_discrete.derivative_side_conditions
    13. sald.general_moving_target_discrete.kl_derivative
    14. sald.general_moving_target_discrete.dv_m_energy
    15. sald.general_moving_target_discrete.gronwall_side_conditions
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:unified-forward-KL
    2. thm:general-moving-target-SALD-discrete
    3. cycle48 lower packet
    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 cycle48UnifiedDiscreteSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.unified_forward_KL.cycle48_theorem_skeleton_route"
      interface := "Unified theorem-level route: combine the guided residual identity and correction-field equation to obtain the transport velocity u_t+w_t, then specialize thm:general-moving-target-SALD with c_t=u_t and m_t=w_t."
      source := saldUnifiedForwardKlSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle48UnifiedDiscreteSkeletonUpperPacket",
        "SALD.cycle48UnifiedDiscreteSkeletonObligation",
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleContract",
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation",
        "SALD.cycle47GuidedGeneralSkeletonObligation",
        "SALD.cycle47GuidedGeneralSkeletonMiddleObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.generalMovingTargetStatementContract",
        "SALD.unifiedForwardKlSpecializationContract",
        "sald.guided_path_residual.identity",
        "sald.unified_forward_kl.transport_velocity_bridge",
        "sald.unified_forward_kl.specialization",
        "sald.general_moving_target.kl_derivative",
        "sald.general_moving_target.dv_m_energy",
        "sald.general_moving_target.gronwall_side_conditions"
      ]
      reusedBy := ["thm:unified-forward-KL", "main skeleton sprint 5"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle48_theorem_skeleton_route"
      interface := "Discrete general theorem-level route: compose the source statement, general EM endpoint/conditional-FP backend, frozen-delta bound, KL derivative/LSI block, residual DV witness, Gronwall/stitching side conditions, and discrete guided specialization without changing coefficients."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle48UnifiedDiscreteSkeletonUpperPacket",
        "SALD.cycle48UnifiedDiscreteSkeletonObligation",
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleContract",
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation",
        "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle47GuidedGeneralSkeletonObligation",
        "SALD.cycle28GeneralVaSaldUpperPacket",
        "SALD.cycle28GeneralVaSaldMiddleContract",
        "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
        "SALD.cycle20GeneralVaSaldUpperPacket",
        "SALD.cycle20GeneralVaSaldMiddleContract",
        "SALD.generalMovingTargetDiscreteStatementContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalFrozenDeltaCrossLipContract",
        "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDiscreteGronwallInstantiationContract",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "sald.general_moving_target_discrete.derivative_side_conditions",
        "sald.general_moving_target_discrete.kl_derivative",
        "probability.lsi_to_kl_fi",
        "sald.general_moving_target_discrete.dv_finite_log_mgf_witness",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.gronwall_application",
        "sald.general_moving_target_discrete.gronwall_side_conditions",
        "sald.general_moving_target_discrete.unified_specialization"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "main skeleton sprint 5"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle48_middle_route_audit"
      interface := "Middle source-to-Lean audit for the final skeleton route: verify the unified specialization and discrete general EM/Fokker-Planck/frozen-delta/LSI/DV/Gronwall chain, then select the discrete KL derivative backend beginning with the endpoint and conditional-law interface."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleContract",
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation",
        "SALD.cycle48UnifiedDiscreteSkeletonObligation",
        "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
        "SALD.unifiedForwardKlSpecializationContract",
        "sald.unified_forward_kl.transport_velocity_bridge",
        "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.derivative_side_conditions",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.gronwall_side_conditions"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "cycle48 lower packet"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-53 upper packet for the unified and discrete general theorem route.

This consumes the cycle-52 continuous guided/general route and the cycle-48
unified/discrete route, then records the first narrow measure-level backfill
for EM endpoint laws.  It remains an upper workflow packet: the source
theorems stay fixed and all slow analytic backends stay below formalized.
-/

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