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

AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticInterfaceDag

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 cycle69MainSkeletonAnalyticInterfaceDag : 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.cycle69.global_phase_judgment
    interface : String (explicit)

    Text describing intended mathematical interface.

    Upper judgment for cycle 69: cycle 68 passed and needs no recovery; Phase 1 is stable enough for the post-route analytic-interface ledger but not broad backfill; select the shared EM interpolation conditional-law/Fokker-Planck backend as the one lower packet.
    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.cycle69MainSkeletonAnalyticInterfaceLedger
    2. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
    3. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. ASTIS-SALD-001 cycle 69
    2. sald.general_moving_target_discrete.em_interpolation_fp
    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.cycle69.five_backend_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Recheck Gronwall, DV, LSI/KL/FI, continuous forward-KL Fokker-Planck/KL derivative, and Euler-Maruyama interpolation Fokker-Planck interfaces after all six theorem-route skeletons are wired.
    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.saldGronwallEndpointCalculusContract
    2. dvVariationalFormulaInterface saldDvVariationSource
    3. SALD.saldLsiKlFiDensityTestContract
    4. SALD.forwardKlDerivativeSideConditionContract
    5. SALD.generalMovingTargetDerivativeCandidateContract
    6. SALD.discreteForwardKlEmInterpolationSideConditionContract
    7. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    8. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:forward-KL
    2. thm:forward-KL-discrete
    3. prop:guided_path_residual
    4. thm:general-moving-target-SALD
    5. thm:unified-forward-KL
    6. thm:general-moving-target-SALD-discrete
    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.cycle69.theorem_route_recheck
    interface : String (explicit)

    Text describing intended mathematical interface.

    Verify that the five analytic interfaces feed the six theorem skeletons in source order: forward-KL, discrete forward-KL, guided residual, continuous general moving target, unified forward-KL, and discrete general moving target.
    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.cycle69MainSkeletonAnalyticInterfaceObligation
    2. SALD.continuousSaldContract
    3. SALD.discreteSaldContract
    4. SALD.guidedResidualContract
    5. SALD.generalVaSaldContract
    6. SALD.unifiedForwardKlContract
    7. SALD.generalVaSaldDiscreteContract
    8. SALD.cycle65ForwardKlSkeletonMiddleObligation
    9. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
    10. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
    11. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:forward-KL
    2. thm:forward-KL-discrete
    3. prop:guided_path_residual
    4. thm:general-moving-target-SALD
    5. thm:unified-forward-KL
    6. 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.cycle69.middle_interface_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle audit for cycle 69: synchronize the post-route five-backend ledger with the six theorem skeletons, keep all theorem statements and statuses fixed, and hand lower work to the shared EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387.
    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.cycle69MainSkeletonAnalyticMiddleContract
    2. SALD.cycle69MainSkeletonAnalyticMiddleObligation
    3. SALD.cycle69MainSkeletonAnalyticInterfaceObligation
    4. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
    5. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
    6. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
    7. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
    8. SALD.cycle65ForwardKlSkeletonMiddleObligation
    9. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
    10. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    11. SALD.generalMovingTargetDiscreteConditionalDriftContract
    12. sald.general_moving_target_discrete.em_interpolation_fp
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:forward-KL
    2. thm:forward-KL-discrete
    3. prop:guided_path_residual
    4. thm:general-moving-target-SALD
    5. thm:unified-forward-KL
    6. thm:general-moving-target-SALD-discrete
    7. cycle 69 lower handoff
    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.cycle69.lower_packet.em_interpolation_fp
    interface : String (explicit)

    Text describing intended mathematical interface.

    Selected lower packet: sharpen sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, exposing common-space/density prerequisites, regular conditional drift, and the weak conditional Fokker-Planck equation with source signs while leaving KL differentiation, LSI, DV, and Gronwall separate.
    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.cycle69MainSkeletonAnalyticInterfaceObligation
    2. SALD.cycle69MainSkeletonAnalyticMiddleObligation
    3. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
    4. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    5. SALD.generalMovingTargetDiscreteConditionalDriftContract
    6. SALD.generalMovingTargetDiscreteConditionalDriftLinearCombination
    7. SALD.generalMovingTargetDiscreteConditionalDriftFieldOfLinearCombination
    8. SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff
    9. SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation
    10. sald.general_moving_target_discrete.cycle64_conditional_drift_lower
    11. sald.general_moving_target_discrete.cycle69_em_fp_source_signs_lower
    12. sald.general_moving_target_discrete.em_interpolation_fp
    13. sald.discrete_forward_kl.em_interpolation_fp
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.discrete_forward_kl.em_interpolation_fp
    3. thm:forward-KL-discrete
    4. thm:general-moving-target-SALD-discrete
    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 cycle69MainSkeletonAnalyticInterfaceDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle69.global_phase_judgment"
      interface := "Upper judgment for cycle 69: cycle 68 passed and needs no recovery; Phase 1 is stable enough for the post-route analytic-interface ledger but not broad backfill; select the shared EM interpolation conditional-law/Fokker-Planck backend as the one lower packet."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle69MainSkeletonAnalyticInterfaceLedger",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation",
        "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation"
      ]
      reusedBy := ["ASTIS-SALD-001 cycle 69", "sald.general_moving_target_discrete.em_interpolation_fp"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle69.five_backend_check"
      interface := "Recheck Gronwall, DV, LSI/KL/FI, continuous forward-KL Fokker-Planck/KL derivative, and Euler-Maruyama interpolation Fokker-Planck interfaces after all six theorem-route skeletons are wired."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.saldGronwallEndpointCalculusContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation"
      ]
      reusedBy := [
        "thm:forward-KL",
        "thm:forward-KL-discrete",
        "prop:guided_path_residual",
        "thm:general-moving-target-SALD",
        "thm:unified-forward-KL",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle69.theorem_route_recheck"
      interface := "Verify that the five analytic interfaces feed the six theorem skeletons in source order: forward-KL, discrete forward-KL, guided residual, continuous general moving target, unified forward-KL, and discrete general moving target."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle69MainSkeletonAnalyticInterfaceObligation",
        "SALD.continuousSaldContract",
        "SALD.discreteSaldContract",
        "SALD.guidedResidualContract",
        "SALD.generalVaSaldContract",
        "SALD.unifiedForwardKlContract",
        "SALD.generalVaSaldDiscreteContract",
        "SALD.cycle65ForwardKlSkeletonMiddleObligation",
        "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation"
      ]
      reusedBy := [
        "thm:forward-KL",
        "thm:forward-KL-discrete",
        "prop:guided_path_residual",
        "thm:general-moving-target-SALD",
        "thm:unified-forward-KL",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle69.middle_interface_audit"
      interface := "Middle audit for cycle 69: synchronize the post-route five-backend ledger with the six theorem skeletons, keep all theorem statements and statuses fixed, and hand lower work to the shared EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle69MainSkeletonAnalyticMiddleContract",
        "SALD.cycle69MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle69MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation",
        "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle65ForwardKlSkeletonMiddleObligation",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL",
        "thm:forward-KL-discrete",
        "prop:guided_path_residual",
        "thm:general-moving-target-SALD",
        "thm:unified-forward-KL",
        "thm:general-moving-target-SALD-discrete",
        "cycle 69 lower handoff"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle69.lower_packet.em_interpolation_fp"
      interface := "Selected lower packet: sharpen sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, exposing common-space/density prerequisites, regular conditional drift, and the weak conditional Fokker-Planck equation with source signs while leaving KL differentiation, LSI, DV, and Gronwall separate."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle69MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle69MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftLinearCombination",
        "SALD.generalMovingTargetDiscreteConditionalDriftFieldOfLinearCombination",
        "SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff",
        "SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation",
        "sald.general_moving_target_discrete.cycle64_conditional_drift_lower",
        "sald.general_moving_target_discrete.cycle69_em_fp_source_signs_lower",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

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