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

AutoSamplingTheory.SALD.cycle52GuidedGeneralSkeletonDag

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 cycle52GuidedGeneralSkeletonDag : 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.cycle52_upper_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle-52 upper route closure: after the forward-KL and discrete forward-KL route wrappers, verify the five analytic backends and connect prop:guided_path_residual plus thm:general-moving-target-SALD to their named guided residual, KL-derivative, LSI, residual-DV, Gronwall, and pure-contraction 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.cycle52GuidedGeneralSkeletonUpperPacket
    2. SALD.cycle52GuidedGeneralSkeletonObligation
    3. SALD.cycle52GuidedGeneralSkeletonMiddleContract
    4. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
    5. SALD.cycle49MainSkeletonAnalyticReadinessObligation
    6. SALD.cycle50ForwardKlSkeletonObligation
    7. SALD.cycle51DiscreteForwardKlSkeletonObligation
    8. SALD.cycle47GuidedGeneralSkeletonObligation
    9. SALD.cycle47GuidedGeneralSkeletonMiddleObligation
    10. SALD.guidedResidualIdentityContract
    11. SALD.generalMovingTargetDerivativeCandidateContract
    12. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
    13. SALD.generalMovingTargetDvEnergyCandidateContract
    14. SALD.generalMovingTargetGronwallSideConditionContract
    15. SALD.saldGronwallEndpointCalculusContract
    16. SALD.saldLsiKlFiDensityTestContract
    17. dvVariationalFormulaInterface saldDvVariationSource
    18. SALD.discreteForwardKlEmInterpolationSideConditionContract
    19. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
    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. main skeleton sprint 4 cycle 52
    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.cycle52_middle_route_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle source-to-Lean audit for cycle 52: verify appendix.tex:619-951 in paper order, keep the guided residual and general moving-target statements fixed, and select the continuous general KL derivative backend while guided residual, LSI, DV, Gronwall, pure contraction, and downstream EM interfaces remain explicit 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.cycle52GuidedGeneralSkeletonMiddleContract
    2. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
    3. SALD.cycle52GuidedGeneralSkeletonObligation
    4. SALD.cycle49MainSkeletonAnalyticMiddleObligation
    5. SALD.cycle50ForwardKlSkeletonMiddleObligation
    6. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
    7. SALD.cycle47GuidedGeneralSkeletonMiddleObligation
    8. SALD.guidedResidualIdentityContract
    9. sald.guided_path_residual.identity
    10. SALD.generalMovingTargetStatementContract
    11. SALD.generalMovingTargetDerivativeCandidateContract
    12. SALD.generalMovingTargetDerivativeObligation
    13. sald.general_moving_target.kl_derivative
    14. SALD.saldLsiKlFiDensityTestContract
    15. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
    16. SALD.generalMovingTargetDvPositiveAlphaScalingContract
    17. SALD.generalMovingTargetGronwallInstantiationContract
    18. SALD.generalMovingTargetGronwallSideConditionContract
    19. SALD.discreteForwardKlEmInterpolationSideConditionContract
    20. 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. cycle52 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.general_moving_target.cycle52_derivative_dv_lower
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower proof-producing scalar handoff for appendix.tex:765-907: compose the supplied general KL derivative/LSI pre-DV inequality with the residual DV estimate to obtain the exact sigma-weighted Gronwall coefficient and residual term.
    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.cycle52GuidedGeneralDerivativeDvLowerObligation
    2. SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar
    3. SALD.generalMovingTargetPreDvDerivativeBoundScalar
    4. SALD.generalMovingTargetPostDvGronwallCoefficientScalar
    5. SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar
    6. SALD.generalMovingTargetDerivativeCandidateContract
    7. SALD.generalMovingTargetDerivativeObligation
    8. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
    9. SALD.generalMovingTargetDvPositiveAlphaScalingContract
    10. sald.general_moving_target.kl_derivative
    11. probability.lsi_to_kl_fi
    12. sald.general_moving_target.dv_finite_log_mgf_witness
    13. sald.general_moving_target.dv_m_energy
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target.kl_derivative
    2. sald.general_moving_target.dv_m_energy
    3. thm:general-moving-target-SALD
    4. thm:unified-forward-KL
    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 cycle52GuidedGeneralSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.guided_general.cycle52_upper_route"
      interface := "Cycle-52 upper route closure: after the forward-KL and discrete forward-KL route wrappers, verify the five analytic backends and connect prop:guided_path_residual plus thm:general-moving-target-SALD to their named guided residual, KL-derivative, LSI, residual-DV, Gronwall, and pure-contraction obligations."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle52GuidedGeneralSkeletonUpperPacket",
        "SALD.cycle52GuidedGeneralSkeletonObligation",
        "SALD.cycle52GuidedGeneralSkeletonMiddleContract",
        "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
        "SALD.cycle50ForwardKlSkeletonObligation",
        "SALD.cycle51DiscreteForwardKlSkeletonObligation",
        "SALD.cycle47GuidedGeneralSkeletonObligation",
        "SALD.cycle47GuidedGeneralSkeletonMiddleObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDvEnergyCandidateContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation"
      ]
      reusedBy := ["prop:guided_path_residual", "thm:general-moving-target-SALD", "thm:unified-forward-KL", "main skeleton sprint 4 cycle 52"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_general.cycle52_middle_route_audit"
      interface := "Middle source-to-Lean audit for cycle 52: verify appendix.tex:619-951 in paper order, keep the guided residual and general moving-target statements fixed, and select the continuous general KL derivative backend while guided residual, LSI, DV, Gronwall, pure contraction, and downstream EM interfaces remain explicit obligations."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle52GuidedGeneralSkeletonMiddleContract",
        "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle52GuidedGeneralSkeletonObligation",
        "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle50ForwardKlSkeletonMiddleObligation",
        "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle47GuidedGeneralSkeletonMiddleObligation",
        "SALD.guidedResidualIdentityContract",
        "sald.guided_path_residual.identity",
        "SALD.generalMovingTargetStatementContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDerivativeObligation",
        "sald.general_moving_target.kl_derivative",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
        "SALD.generalMovingTargetGronwallInstantiationContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract"
      ]
      reusedBy := ["prop:guided_path_residual", "thm:general-moving-target-SALD", "cycle52 lower derivative packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target.cycle52_derivative_dv_lower"
      interface := "Lower proof-producing scalar handoff for appendix.tex:765-907: compose the supplied general KL derivative/LSI pre-DV inequality with the residual DV estimate to obtain the exact sigma-weighted Gronwall coefficient and residual term."
      source := saldGeneralMovingTargetDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle52GuidedGeneralDerivativeDvLowerObligation",
        "SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar",
        "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
        "SALD.generalMovingTargetPostDvGronwallCoefficientScalar",
        "SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDerivativeObligation",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
        "sald.general_moving_target.kl_derivative",
        "probability.lsi_to_kl_fi",
        "sald.general_moving_target.dv_finite_log_mgf_witness",
        "sald.general_moving_target.dv_m_energy"
      ]
      reusedBy := ["sald.general_moving_target.kl_derivative", "sald.general_moving_target.dv_m_energy", "thm:general-moving-target-SALD", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-57 upper packet returning to the guided residual and continuous
general moving-target theorem after the cycle-56 discrete forward-KL recovery.

This packet records the required upper phase judgment, rechecks the five slow
analytic interfaces, and keeps the current sprint on theorem-level route
closure for `appendix.tex:619-951`.  It is workflow data only: no theorem
statement, source label, source coefficient, or analytic backend status is
changed.
-/

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