AutoSamplingTheory.SALD.cycle67GuidedGeneralSkeletonDag

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 cycle67GuidedGeneralSkeletonDag : 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

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.guided_general.cycle67_global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle-67 global judgment: cycle 66 passed and needs no recovery; Phase 1 is not ready for cited-theory backfill until guided residual and continuous general moving-target route wiring is rechecked; select the residual-to-Gronwall bridge as the single lower packet.
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.cycle67GuidedGeneralSkeletonUpperPacket
2. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
3. SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. ASTIS-SALD-001 cycle 67
2. prop:guided_path_residual
3. thm:general-moving-target-SALD
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.guided_general.cycle67_five_backend_check
interface : String (explicit)
Text describing intended mathematical interface.
Explicit cycle-67 check of the five slow interfaces before lower work: endpoint-safe Gronwall, common-space DV with finite log-mgf, LSI/KL/FI density-test bridge, continuous Fokker-Planck/KL derivative, and downstream EM interpolation Fokker-Planck.
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.saldGronwallEndpointCalculusContract
2. SALD.generalMovingTargetGronwallInstantiationContract
3. dvVariationalFormulaInterface saldDvVariationSource
4. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
5. SALD.saldLsiKlFiDensityTestContract
6. SALD.generalMovingTargetDerivativeCandidateContract
7. SALD.generalMovingTargetDerivativeObligation
8. SALD.discreteForwardKlEmInterpolationSideConditionContract
9. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.guided_general.cycle67_guided_residual_route
interface : String (explicit)
Text describing intended mathematical interface.
Route appendix.tex:619-704 through the guided normalizer derivative, quotient/product differentiation, divergence cancellation, centered residual identity, and mean-zero residual obligations without changing prop:guided_path_residual.
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.cycle67GuidedGeneralSkeletonUpperPacket
2. SALD.cycle67GuidedGeneralSkeletonObligation
3. SALD.guidedResidualIdentityContract
4. sald.guided_path_residual.normalizer_derivative
5. sald.guided_path_residual.identity
6. TransportVelocityContract
7. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.guided_general.cycle67_general_moving_target_route
interface : String (explicit)
Text describing intended mathematical interface.
Route appendix.tex:724-945 through the fixed general moving-target statement, continuous KL derivative, residual LSI/DV, sigma-weighted Gronwall, and pure-contraction interfaces without changing constants or source labels.
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.cycle67GuidedGeneralSkeletonUpperPacket
2. SALD.cycle67GuidedGeneralSkeletonObligation
3. SALD.generalMovingTargetStatementContract
4. SALD.generalMovingTargetDerivativeCandidateContract
5. SALD.generalMovingTargetDerivativeObligation
6. sald.general_moving_target.kl_derivative
7. SALD.saldLsiKlFiDensityTestContract
8. sald.general_moving_target.dv_m_energy
9. SALD.generalMovingTargetGronwallInstantiationContract
10. SALD.generalMovingTargetGronwallSideConditionContract
11. sald.general_moving_target.gronwall_side_conditions
12. sald.general_moving_target.pure_contraction
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.guided_general.cycle67_middle_route_audit
interface : String (explicit)
Text describing intended mathematical interface.
Middle audit for cycle 67: verify appendix.tex:619-951 in paper order, keep guided residual calculus, continuous KL derivative, LSI/KL/FI, residual DV, Gronwall, pure contraction, unified specialization, and downstream EM interfaces explicit, and hand lower work to the residual-to-Gronwall bridge.
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.cycle67GuidedGeneralSkeletonMiddleContract
2. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
3. SALD.cycle67GuidedGeneralSkeletonObligation
4. SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation
5. SALD.guidedResidualIdentityContract
6. SALD.generalMovingTargetStatementContract
7. SALD.generalMovingTargetDerivativeCandidateContract
8. SALD.saldLsiKlFiDensityTestContract
9. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
10. SALD.generalMovingTargetDvPositiveAlphaScalingContract
11. SALD.generalMovingTargetGronwallInstantiationContract
12. SALD.generalMovingTargetGronwallSideConditionContract
13. SALD.unifiedForwardKlSpecializationContract
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. cycle 67 lower handoff
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.guided_general.cycle67_lower_packet.residual_to_gronwall_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: audit and sharpen the source-cited bridge from the residual KL derivative through LSI, DV with Z=alpha*||m_t||^2, sigma-weighted Gronwall, and pure contraction.
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.cycle67GuidedGeneralResidualGronwallBridgeObligation
2. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
3. SALD.cycle67GuidedGeneralSkeletonObligation
4. SALD.generalMovingTargetDerivativeObligation
5. SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation
6. SALD.cycle62GuidedGeneralScaledResidualLowerObligation
7. SALD.cycle67GuidedGeneralResidualGronwallLowerObligation
8. SALD.generalMovingTargetResidualToGronwallBridgeScalar
9. SALD.generalMovingTargetDvEnergyObligation
10. SALD.generalMovingTargetGronwallApplicationObligation
11. SALD.generalMovingTargetGronwallSideConditionObligation
12. SALD.generalMovingTargetPureContractionObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target.cycle67_residual_to_gronwall_lower
2. sald.general_moving_target.cycle67_residual_to_gronwall_bridge
3. thm:general-moving-target-SALD
4. cycle 67 lower handoff
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 cycle67GuidedGeneralSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.guided_general.cycle67_global_phase_judgment"
      interface := "Cycle-67 global judgment: cycle 66 passed and needs no recovery; Phase 1 is not ready for cited-theory backfill until guided residual and continuous general moving-target route wiring is rechecked; select the residual-to-Gronwall bridge as the single lower packet."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle67GuidedGeneralSkeletonUpperPacket",
        "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation"
      ]
      reusedBy := ["ASTIS-SALD-001 cycle 67", "prop:guided_path_residual", "thm:general-moving-target-SALD"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_general.cycle67_five_backend_check"
      interface := "Explicit cycle-67 check of the five slow interfaces before lower work: endpoint-safe Gronwall, common-space DV with finite log-mgf, LSI/KL/FI density-test bridge, continuous Fokker-Planck/KL derivative, and downstream EM interpolation Fokker-Planck."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.generalMovingTargetGronwallInstantiationContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDerivativeObligation",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract"
      ]
      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.guided_general.cycle67_guided_residual_route"
      interface := "Route appendix.tex:619-704 through the guided normalizer derivative, quotient/product differentiation, divergence cancellation, centered residual identity, and mean-zero residual obligations without changing prop:guided_path_residual."
      source := saldGuidedResidualSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle67GuidedGeneralSkeletonUpperPacket",
        "SALD.cycle67GuidedGeneralSkeletonObligation",
        "SALD.guidedResidualIdentityContract",
        "sald.guided_path_residual.normalizer_derivative",
        "sald.guided_path_residual.identity",
        "TransportVelocityContract",
        "GuidedTiltContract"
      ]
      reusedBy := ["prop:guided_path_residual", "thm:unified-forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_general.cycle67_general_moving_target_route"
      interface := "Route appendix.tex:724-945 through the fixed general moving-target statement, continuous KL derivative, residual LSI/DV, sigma-weighted Gronwall, and pure-contraction interfaces without changing constants or source labels."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle67GuidedGeneralSkeletonUpperPacket",
        "SALD.cycle67GuidedGeneralSkeletonObligation",
        "SALD.generalMovingTargetStatementContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDerivativeObligation",
        "sald.general_moving_target.kl_derivative",
        "SALD.saldLsiKlFiDensityTestContract",
        "sald.general_moving_target.dv_m_energy",
        "SALD.generalMovingTargetGronwallInstantiationContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "sald.general_moving_target.gronwall_side_conditions",
        "sald.general_moving_target.pure_contraction"
      ]
      reusedBy := ["thm:general-moving-target-SALD", "thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_general.cycle67_middle_route_audit"
      interface := "Middle audit for cycle 67: verify appendix.tex:619-951 in paper order, keep guided residual calculus, continuous KL derivative, LSI/KL/FI, residual DV, Gronwall, pure contraction, unified specialization, and downstream EM interfaces explicit, and hand lower work to the residual-to-Gronwall bridge."
      source := saldGeneralMovingTargetSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle67GuidedGeneralSkeletonMiddleContract",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle67GuidedGeneralSkeletonObligation",
        "SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.generalMovingTargetStatementContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
        "SALD.generalMovingTargetGronwallInstantiationContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.unifiedForwardKlSpecializationContract"
      ]
      reusedBy := ["prop:guided_path_residual", "thm:general-moving-target-SALD", "cycle 67 lower handoff"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.guided_general.cycle67_lower_packet.residual_to_gronwall_bridge"
      interface := "Selected lower packet: audit and sharpen the source-cited bridge from the residual KL derivative through LSI, DV with Z=alpha*||m_t||^2, sigma-weighted Gronwall, and pure contraction."
      source := saldGeneralMovingTargetDvGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle67GuidedGeneralSkeletonObligation",
        "SALD.generalMovingTargetDerivativeObligation",
        "SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation",
        "SALD.cycle62GuidedGeneralScaledResidualLowerObligation",
        "SALD.cycle67GuidedGeneralResidualGronwallLowerObligation",
        "SALD.generalMovingTargetResidualToGronwallBridgeScalar",
        "SALD.generalMovingTargetDvEnergyObligation",
        "SALD.generalMovingTargetGronwallApplicationObligation",
        "SALD.generalMovingTargetGronwallSideConditionObligation",
        "SALD.generalMovingTargetPureContractionObligation"
      ]
      reusedBy := ["sald.general_moving_target.cycle67_residual_to_gronwall_lower", "sald.general_moving_target.cycle67_residual_to_gronwall_bridge", "thm:general-moving-target-SALD", "cycle 67 lower handoff"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 68: unified and discrete general theorem route refresh -/

/-- Cycle-68 upper packet for the unified forward-KL theorem and the
discrete-time general moving-target theorem.

This is a theorem-skeleton route packet only.  It reuses the accepted
continuous guided/general route from cycle 67 and the earlier unified/discrete
general route, rechecks the five slow interfaces, and selects one lower packet
for the discrete general theorem bridge without changing theorem statements or
promoting analytic backends.
-/

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