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

AutoSamplingTheory.SALD.cycle64MainSkeletonAnalyticInterfaceDag

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 cycle64MainSkeletonAnalyticInterfaceDag : 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.cycle64.global_phase_judgment
    interface : String (explicit)

    Text describing intended mathematical interface.

    Upper judgment for cycle 64: cycle 63 passed; Phase 1 supports one narrow backend backfill only; the largest remaining proof risk is the 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.cycle64MainSkeletonAnalyticInterfaceLedger
    2. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
    3. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. ASTIS-SALD-001 cycle 64
    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.cycle64.five_backend_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Recheck the five slow analytic interfaces: endpoint-safe Gronwall, common-space DV with finite log-mgf, LSI/KL/FI density-test bridge, continuous Fokker-Planck/KL derivative, and EM endpoint/conditional-law Fokker-Planck.
    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.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.cycle64.theorem_route_rewire
    interface : String (explicit)

    Text describing intended mathematical interface.

    Wire the five analytic interfaces into the six faithful theorem skeletons in paper order without changing source statements, constants, labels, theorem statuses, or backend statuses.
    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.cycle64MainSkeletonAnalyticInterfaceObligation
    2. SALD.continuousSaldContract
    3. SALD.discreteSaldContract
    4. SALD.guidedResidualContract
    5. SALD.generalVaSaldContract
    6. SALD.unifiedForwardKlContract
    7. SALD.generalVaSaldDiscreteContract
    8. SALD.cycle60ForwardKlSkeletonMiddleObligation
    9. SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation
    10. SALD.cycle62GuidedGeneralSkeletonMiddleObligation
    11. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
    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.cycle64.middle_interface_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle audit for cycle 64: synchronize the five-backend analytic ledger with the source-to-Lean theorem route, keep cycle-63 endpoint-law helpers scoped to endpoint bookkeeping, and narrow lower work to appendix.tex:1358-1387 general EM conditional-law/Fokker-Planck prerequisites.
    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.cycle64MainSkeletonAnalyticMiddleContract
    2. SALD.cycle64MainSkeletonAnalyticMiddleObligation
    3. SALD.cycle64MainSkeletonAnalyticInterfaceObligation
    4. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
    5. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
    6. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
    7. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    8. SALD.generalMovingTargetDiscreteConditionalDriftContract
    9. sald.general_moving_target_discrete.cycle64_conditional_drift_lower
    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
    7. cycle64 lower conditional-FP packet
    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.cycle64.lower_packet.general_discrete_em_conditional_fp
    interface : String (explicit)

    Text describing intended mathematical interface.

    Selected lower packet for cycle 64: refine sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 after endpoint-law bookkeeping, exposing common-space/density assumptions, regular conditional drift, and the weak conditional Fokker-Planck equation with source signs.
    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.cycle64MainSkeletonAnalyticInterfaceObligation
    2. SALD.cycle64MainSkeletonAnalyticMiddleObligation
    3. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
    4. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    5. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
    6. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
    7. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
    8. SALD.generalMovingTargetDiscreteConditionalDriftContract
    9. SALD.generalMovingTargetDiscreteConditionalDriftLinearCombination
    10. SALD.generalMovingTargetDiscreteConditionalDriftFieldOfLinearCombination
    11. sald.general_moving_target_discrete.cycle64_conditional_drift_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 cycle64MainSkeletonAnalyticInterfaceDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle64.global_phase_judgment"
      interface := "Upper judgment for cycle 64: cycle 63 passed; Phase 1 supports one narrow backend backfill only; the largest remaining proof risk is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle64MainSkeletonAnalyticInterfaceLedger",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation"
      ]
      reusedBy := ["ASTIS-SALD-001 cycle 64", "sald.general_moving_target_discrete.em_interpolation_fp"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle64.five_backend_check"
      interface := "Recheck the five slow analytic interfaces: endpoint-safe Gronwall, common-space DV with finite log-mgf, LSI/KL/FI density-test bridge, continuous Fokker-Planck/KL derivative, and EM endpoint/conditional-law Fokker-Planck."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      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.cycle64.theorem_route_rewire"
      interface := "Wire the five analytic interfaces into the six faithful theorem skeletons in paper order without changing source statements, constants, labels, theorem statuses, or backend statuses."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle64MainSkeletonAnalyticInterfaceObligation",
        "SALD.continuousSaldContract",
        "SALD.discreteSaldContract",
        "SALD.guidedResidualContract",
        "SALD.generalVaSaldContract",
        "SALD.unifiedForwardKlContract",
        "SALD.generalVaSaldDiscreteContract",
        "SALD.cycle60ForwardKlSkeletonMiddleObligation",
        "SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle62GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation"
      ]
      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.cycle64.middle_interface_audit"
      interface := "Middle audit for cycle 64: synchronize the five-backend analytic ledger with the source-to-Lean theorem route, keep cycle-63 endpoint-law helpers scoped to endpoint bookkeeping, and narrow lower work to appendix.tex:1358-1387 general EM conditional-law/Fokker-Planck prerequisites."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle64MainSkeletonAnalyticMiddleContract",
        "SALD.cycle64MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle64MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract",
        "sald.general_moving_target_discrete.cycle64_conditional_drift_lower",
        "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",
        "cycle64 lower conditional-FP packet"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle64.lower_packet.general_discrete_em_conditional_fp"
      interface := "Selected lower packet for cycle 64: refine sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 after endpoint-law bookkeeping, exposing common-space/density assumptions, regular conditional drift, and the weak conditional Fokker-Planck equation with source signs."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle64MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle64MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteConditionalDriftContract",
        "SALD.generalMovingTargetDiscreteConditionalDriftLinearCombination",
        "SALD.generalMovingTargetDiscreteConditionalDriftFieldOfLinearCombination",
        "sald.general_moving_target_discrete.cycle64_conditional_drift_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
    }
  ]

/-! ### Cycle 65: continuous forward-KL post-cycle64 route -/

/-- Cycle-65 upper packet for the continuous forward-KL skeleton after the
accepted cycle-64 analytic-interface and conditional-drift pass.

This is upper-route data only.  It returns the main skeleton sprint to
`thm:forward-KL`, rechecks the five slow interfaces, and assigns the next
lower packet to the continuous Fokker--Planck/KL derivative backend without
changing the paper statement, constants, labels, or proof statuses.
-/

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