AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralDag

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 cycle68UnifiedDiscreteGeneralDag : 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.unified_discrete_general.cycle68_global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle-68 global judgment: cycle 67 passed and needs no recovery; Phase 1 is stable enough to finish the unified/discrete-general route before cited-theory backfill; select the discrete general theorem bridge as the single 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.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket
2. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
3. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. ASTIS-SALD-001 cycle 68
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.unified_discrete_general.cycle68_five_backend_check
interface : String (explicit)
Text describing intended mathematical interface.
Explicit cycle-68 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 for the unified specialization, and EM interpolation endpoint/conditional-law Fokker-Planck for the discrete general theorem.
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. SALD.generalMovingTargetGronwallSideConditionContract
3. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
4. dvVariationalFormulaInterface saldDvVariationSource
5. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
6. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
7. SALD.saldLsiKlFiDensityTestContract
8. SALD.generalMovingTargetDerivativeCandidateContract
9. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
10. 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
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.unified_discrete_general.cycle68_unified_route
interface : String (explicit)
Text describing intended mathematical interface.
Route main_body.tex:359-395 and appendix.tex:949-951 through guided residual, correction-field divergence, transport-velocity bridge, and the cycle-67 continuous general theorem specialization without changing thm:unified-forward-KL.
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.cycle68UnifiedDiscreteGeneralSkeletonObligation
2. SALD.guidedResidualIdentityContract
3. SALD.unifiedForwardKlSpecializationContract
4. sald.unified_forward_kl.transport_velocity_bridge
5. sald.unified_forward_kl.specialization
6. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
7. SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:unified-forward-KL
2. cycle 68 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.general_moving_target_discrete.cycle68_theorem_route
interface : String (explicit)
Text describing intended mathematical interface.
Route appendix.tex:1313-1603 through the fixed discrete general statement, general EM endpoint/conditional-FP, frozen-delta, KL derivative/LSI, residual DV, time change, and Gronwall/display interfaces without changing constants or labels.
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.cycle68UnifiedDiscreteGeneralSkeletonObligation
2. SALD.generalMovingTargetDiscreteStatementContract
3. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
4. sald.general_moving_target_discrete.em_interpolation_fp
5. sald.general_moving_target_discrete.frozen_delta_cross_lip
6. sald.general_moving_target_discrete.kl_derivative
7. sald.general_moving_target_discrete.dv_m_energy
8. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
9. sald.general_moving_target_discrete.gronwall_side_conditions
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:general-moving-target-SALD-discrete
2. cycle 68 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.unified_discrete_general.cycle68_middle_route_audit
interface : String (explicit)
Text describing intended mathematical interface.
Middle audit for cycle 68: verify the unified specialization and the discrete general theorem route in paper order, keep the theorem contracts fixed, and hand lower work to the source-cited discrete general bridge.
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.cycle68UnifiedDiscreteGeneralSkeletonMiddleContract
2. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
3. SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation
4. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation
5. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
6. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
7. SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation
8. SALD.unifiedForwardKlSpecializationContract
9. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
10. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
11. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
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. cycle 68 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.unified_discrete_general.cycle68_lower_packet.discrete_general_bridge
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: audit and sharpen the source-cited bridge from unified specialization and the discrete general EM/KL derivative route through residual DV and final Gronwall/display matching; the compiled lower wrapper only composes named Gronwall input with supplied Gronwall output and endpoint display rewrites.
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.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation
2. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
3. SALD.generalMovingTargetDiscreteGronwallDisplayBridgeScalar
4. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
5. SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation
6. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
7. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
8. SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation
9. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
10. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
11. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.unified_discrete_general.cycle68_discrete_general_bridge
2. thm:general-moving-target-SALD-discrete
3. cycle 68 middle/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 cycle68UnifiedDiscreteGeneralDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle68_global_phase_judgment"
      interface := "Cycle-68 global judgment: cycle 67 passed and needs no recovery; Phase 1 is stable enough to finish the unified/discrete-general route before cited-theory backfill; select the discrete general theorem bridge as the single lower packet."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation"
      ]
      reusedBy := ["ASTIS-SALD-001 cycle 68", "thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle68_five_backend_check"
      interface := "Explicit cycle-68 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 for the unified specialization, and EM interpolation endpoint/conditional-law Fokker-Planck for the discrete general theorem."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "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"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle68_unified_route"
      interface := "Route main_body.tex:359-395 and appendix.tex:949-951 through guided residual, correction-field divergence, transport-velocity bridge, and the cycle-67 continuous general theorem specialization without changing thm:unified-forward-KL."
      source := saldUnifiedForwardKlSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.unifiedForwardKlSpecializationContract",
        "sald.unified_forward_kl.transport_velocity_bridge",
        "sald.unified_forward_kl.specialization",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation"
      ]
      reusedBy := ["thm:unified-forward-KL", "cycle 68 lower handoff"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle68_theorem_route"
      interface := "Route appendix.tex:1313-1603 through the fixed discrete general statement, general EM endpoint/conditional-FP, frozen-delta, KL derivative/LSI, residual DV, time change, and Gronwall/display interfaces without changing constants or labels."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.generalMovingTargetDiscreteStatementContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.frozen_delta_cross_lip",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
        "sald.general_moving_target_discrete.gronwall_side_conditions"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "cycle 68 lower handoff"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle68_middle_route_audit"
      interface := "Middle audit for cycle 68: verify the unified specialization and the discrete general theorem route in paper order, keep the theorem contracts fixed, and hand lower work to the source-cited discrete general bridge."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleContract",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
        "SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation",
        "SALD.unifiedForwardKlSpecializationContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "cycle 68 lower handoff"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle68_lower_packet.discrete_general_bridge"
      interface := "Selected lower packet: audit and sharpen the source-cited bridge from unified specialization and the discrete general EM/KL derivative route through residual DV and final Gronwall/display matching; the compiled lower wrapper only composes named Gronwall input with supplied Gronwall output and endpoint display rewrites."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation",
        "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation",
        "SALD.generalMovingTargetDiscreteGronwallDisplayBridgeScalar",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation",
        "SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
        "SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract"
      ]
      reusedBy := ["sald.unified_discrete_general.cycle68_discrete_general_bridge", "thm:general-moving-target-SALD-discrete", "cycle 68 middle/lower handoff"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 69: post-route analytic interface ledger -/

/-- Cycle-69 upper ledger after the full theorem-route sprint.

This is source-to-Lean route data only.  It records the required upper phase
judgment, rechecks the five slow analytic interfaces after the cycle-68
unified/discrete-general pass, and chooses one lower packet for later narrow
backend work without promoting any theorem or analytic backend.
-/

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