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

AutoSamplingTheory.SALD.cycle57GuidedGeneralSkeletonDag

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 cycle57GuidedGeneralSkeletonDag : 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.guided_general.cycle57_upper_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle-57 upper route check: after the clean cycle-56 discrete forward-KL recovery, recheck appendix.tex:619-951 and route prop:guided_path_residual plus thm:general-moving-target-SALD through the already named guided residual, KL derivative, LSI, residual-DV, Gronwall, pure-contraction, and downstream EM interfaces.
    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.cycle57GuidedGeneralSkeletonUpperPacket
    2. SALD.cycle57GuidedGeneralSkeletonObligation
    3. SALD.cycle56DiscreteForwardKlSkeletonObligation
    4. SALD.cycle52GuidedGeneralSkeletonObligation
    5. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
    6. SALD.guidedResidualIdentityContract
    7. SALD.generalMovingTargetStatementContract
    8. SALD.generalMovingTargetDerivativeCandidateContract
    9. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
    10. SALD.generalMovingTargetGronwallSideConditionContract
    11. SALD.saldLsiKlFiDensityTestContract
    12. dvVariationalFormulaInterface saldDvVariationSource
    13. SALD.saldGronwallEndpointCalculusContract
    14. SALD.discreteForwardKlEmInterpolationSideConditionContract
    15. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. prop:guided_path_residual
    2. thm:general-moving-target-SALD
    3. thm:unified-forward-KL
    4. ASTIS-SALD-001 cycle 57
    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_general.cycle57_middle_route_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle-57 middle audit: verify appendix.tex:619-951 in paper order, keep guided residual and continuous general theorem statements fixed, and route lower work to sald.general_moving_target.kl_derivative while guided residual, LSI, residual DV, Gronwall, pure contraction, unified specialization, and EM reuse remain separate 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.cycle57GuidedGeneralSkeletonMiddleContract
    2. SALD.cycle57GuidedGeneralSkeletonMiddleObligation
    3. SALD.cycle57GuidedGeneralSkeletonObligation
    4. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
    5. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
    6. SALD.guidedResidualIdentityContract
    7. SALD.generalMovingTargetStatementContract
    8. SALD.generalMovingTargetDerivativeCandidateContract
    9. SALD.generalMovingTargetDerivativeObligation
    10. sald.general_moving_target.kl_derivative
    11. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
    12. SALD.generalMovingTargetGronwallSideConditionContract
    13. SALD.saldLsiKlFiDensityTestContract
    14. SALD.saldGronwallEndpointCalculusContract
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. prop:guided_path_residual
    2. thm:general-moving-target-SALD
    3. cycle57 lower derivative packet
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

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

    Stable plan-node identifier.

    ASTIS.SALD.guided_general.cycle57_lower_packet.general_derivative
    interface : String (explicit)

    Text describing intended mathematical interface.

    Selected lower packet for cycle 57: refine sald.general_moving_target.kl_derivative over appendix.tex:765-884, starting with law regularity, mass conservation, Fokker-Planck substitution, KL differentiation, integration by parts, target transport, residual Young, LSI, and schedule side conditions. The first scalar split now compiles through SALD.generalMovingTargetKlDerivativeResidualSplitScalar and SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar.
    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. SALD.cycle57GuidedGeneralSkeletonObligation
    2. SALD.cycle57GuidedGeneralSkeletonMiddleObligation
    3. SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation
    4. SALD.generalMovingTargetDerivativeCandidateContract
    5. SALD.generalMovingTargetDerivativeObligation
    6. sald.general_moving_target.kl_derivative
    7. SALD.generalMovingTargetKlDerivativeResidualSplitScalar
    8. SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar
    9. SALD.generalMovingTargetPostYoungDerivativeBoundScalar
    10. SALD.generalMovingTargetLsiDerivativeBoundScalar
    11. SALD.generalMovingTargetTimeChangedDerivativeBoundScalar
    12. SALD.generalMovingTargetPreDvDerivativeBoundScalar
    13. SALD.saldLsiKlFiDensityTestContract
    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.kl_derivative
    2. thm:general-moving-target-SALD
    3. thm:unified-forward-KL
    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.cycle57_derivative_split_lower
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower proof-producing scalar handoff for appendix.tex:765-884: consume the supplied mass-conservation drop, general Fokker-Planck first-term evaluation, target-transport term, residual identification, Young, LSI, and schedule inputs to reach the existing pre-DV derivative inequality.
    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. SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation
    2. SALD.generalMovingTargetKlDerivativeResidualSplitScalar
    3. SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar
    4. SALD.generalMovingTargetDerivativeCandidateContract
    5. SALD.generalMovingTargetDerivativeObligation
    6. sald.general_moving_target.kl_derivative
    7. probability.lsi_to_kl_fi
    8. sald.forward_kl.schedule_time_change
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target.kl_derivative
    2. thm:general-moving-target-SALD
    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 cycle57GuidedGeneralSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.guided_general.cycle57_upper_route"
      interface := "Cycle-57 upper route check: after the clean cycle-56 discrete forward-KL recovery, recheck appendix.tex:619-951 and route prop:guided_path_residual plus thm:general-moving-target-SALD through the already named guided residual, KL derivative, LSI, residual-DV, Gronwall, pure-contraction, and downstream EM interfaces."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle57GuidedGeneralSkeletonUpperPacket",
        "SALD.cycle57GuidedGeneralSkeletonObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonObligation",
        "SALD.cycle52GuidedGeneralSkeletonObligation",
        "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.generalMovingTargetStatementContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract"
      ]
      reusedBy := ["prop:guided_path_residual", "thm:general-moving-target-SALD", "thm:unified-forward-KL", "ASTIS-SALD-001 cycle 57"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_general.cycle57_middle_route_audit"
      interface := "Cycle-57 middle audit: verify appendix.tex:619-951 in paper order, keep guided residual and continuous general theorem statements fixed, and route lower work to sald.general_moving_target.kl_derivative while guided residual, LSI, residual DV, Gronwall, pure contraction, unified specialization, and EM reuse remain separate obligations."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle57GuidedGeneralSkeletonMiddleContract",
        "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle57GuidedGeneralSkeletonObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.generalMovingTargetStatementContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDerivativeObligation",
        "sald.general_moving_target.kl_derivative",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.saldGronwallEndpointCalculusContract"
      ]
      reusedBy := ["prop:guided_path_residual", "thm:general-moving-target-SALD", "cycle57 lower derivative packet"]
      status := ProofStatus.obligation
    },
      {
        id := "ASTIS.SALD.guided_general.cycle57_lower_packet.general_derivative"
        interface := "Selected lower packet for cycle 57: refine sald.general_moving_target.kl_derivative over appendix.tex:765-884, starting with law regularity, mass conservation, Fokker-Planck substitution, KL differentiation, integration by parts, target transport, residual Young, LSI, and schedule side conditions. The first scalar split now compiles through SALD.generalMovingTargetKlDerivativeResidualSplitScalar and SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar."
        source := saldGeneralMovingTargetDerivativeSource
        targetLean := "AutoSamplingTheory/SALD.lean"
        dependsOn := [
          "SALD.cycle57GuidedGeneralSkeletonObligation",
          "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
          "SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation",
          "SALD.generalMovingTargetDerivativeCandidateContract",
          "SALD.generalMovingTargetDerivativeObligation",
          "sald.general_moving_target.kl_derivative",
          "SALD.generalMovingTargetKlDerivativeResidualSplitScalar",
          "SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar",
          "SALD.generalMovingTargetPostYoungDerivativeBoundScalar",
          "SALD.generalMovingTargetLsiDerivativeBoundScalar",
          "SALD.generalMovingTargetTimeChangedDerivativeBoundScalar",
          "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
          "SALD.saldLsiKlFiDensityTestContract",
          "sald.forward_kl.schedule_time_change"
        ]
        reusedBy := ["sald.general_moving_target.kl_derivative", "thm:general-moving-target-SALD", "thm:unified-forward-KL"]
        status := ProofStatus.obligation
      },
      {
        id := "ASTIS.SALD.general_moving_target.cycle57_derivative_split_lower"
        interface := "Lower proof-producing scalar handoff for appendix.tex:765-884: consume the supplied mass-conservation drop, general Fokker-Planck first-term evaluation, target-transport term, residual identification, Young, LSI, and schedule inputs to reach the existing pre-DV derivative inequality."
        source := saldGeneralMovingTargetDerivativeSource
        targetLean := "AutoSamplingTheory/SALD.lean"
        dependsOn := [
          "SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation",
          "SALD.generalMovingTargetKlDerivativeResidualSplitScalar",
          "SALD.generalMovingTargetKlDerivativePreDvBoundOfSplitScalar",
          "SALD.generalMovingTargetDerivativeCandidateContract",
          "SALD.generalMovingTargetDerivativeObligation",
          "sald.general_moving_target.kl_derivative",
          "probability.lsi_to_kl_fi",
          "sald.forward_kl.schedule_time_change"
        ]
        reusedBy := ["sald.general_moving_target.kl_derivative", "thm:general-moving-target-SALD"]
        status := ProofStatus.obligation
      }
    ]

/-- Cycle-48 upper packet for closing the unified and discrete general theorem
skeleton route.

This keeps the cycle-44 slow analytic backend ledger in force and wires the
last two theorem-level nodes requested by the task contract:
`thm:unified-forward-KL` and `thm:general-moving-target-SALD-discrete`.
It is workflow data only.  The source proof still goes through the guided
residual, the continuous general theorem, and the general EM interpolation
interfaces; no theorem statement or analytic backend is promoted.
-/

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