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

AutoSamplingTheory.SALD.cycle63UnifiedDiscreteGeneralDag

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 cycle63UnifiedDiscreteGeneralDag : 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.unified_discrete_general.cycle63_global_phase_judgment
    interface : String (explicit)

    Text describing intended mathematical interface.

    Upper judgment for cycle 63: cycle 62 passed and needs no recovery; Phase 1 is stable enough for unified/discrete-general route wiring and one narrow endpoint-law backfill; the largest remaining proof risk is the discrete general EM endpoint/common-space layer before conditional-law and Fokker-Planck work.
    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.cycle63UnifiedDiscreteGeneralSkeletonUpperPacket
    2. SALD.cycle62GuidedGeneralSkeletonMiddleObligation
    3. SALD.cycle62GuidedGeneralScaledResidualLowerObligation
    4. SALD.cycle58UnifiedDiscreteGeneralMiddleObligation
    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. ASTIS-SALD-001 cycle 63
    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.unified_discrete_general.cycle63_five_backend_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Explicit cycle-63 check 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 EM endpoint/conditional-law Fokker-Planck all have named source-cited or obligation interfaces.
    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.forwardKlDerivativeCandidateContract
    9. SALD.generalMovingTargetDerivativeCandidateContract
    10. SALD.discreteForwardKlEmInterpolationSideConditionContract
    11. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    12. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
    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.unified_discrete_general.cycle63_upper_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Route thm:unified-forward-KL through guided residual, correction-field transport, and thm:general-moving-target-SALD; route thm:general-moving-target-SALD-discrete through general EM endpoint/conditional-FP, frozen delta, KL derivative/LSI, residual DV, Gronwall, and display stitching, with statements and constants unchanged.
    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.cycle63UnifiedDiscreteGeneralSkeletonObligation
    2. SALD.cycle62GuidedGeneralSkeletonMiddleObligation
    3. SALD.guidedResidualIdentityContract
    4. SALD.unifiedForwardKlSpecializationContract
    5. sald.unified_forward_kl.transport_velocity_bridge
    6. sald.unified_forward_kl.specialization
    7. SALD.generalMovingTargetDiscreteStatementContract
    8. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    9. sald.general_moving_target_discrete.em_interpolation_fp
    10. sald.general_moving_target_discrete.kl_derivative
    11. sald.general_moving_target_discrete.dv_m_energy
    12. sald.general_moving_target_discrete.gronwall_side_conditions
    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
    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.unified_discrete_general.cycle63_middle_route_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle route audit for cycle 63: check the unified specialization and discrete general EM/frozen-delta/LSI/DV/Gronwall chain against the source order, keep the paired Measure.map endpoint backfill scoped to endpoint laws, and hand off the 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.cycle63UnifiedDiscreteGeneralMiddleContract
    2. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
    3. SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation
    4. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
    5. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
    6. sald.unified_forward_kl.specialization
    7. sald.general_moving_target_discrete.em_interpolation_fp
    8. sald.general_moving_target_discrete.kl_derivative
    9. sald.general_moving_target_discrete.dv_m_energy
    10. sald.general_moving_target_discrete.gronwall_side_conditions
    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. cycle63 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.general_moving_target_discrete.cycle63_joint_endpoint_law_backfill
    interface : String (explicit)

    Text describing intended mathematical interface.

    Narrow measure-theory backfill: from componentwise a.e. endpoint identities, derive equality of paired Measure.map pushforward laws and project that joint law to each marginal endpoint law for common-space EM endpoint bookkeeping.
    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/Probability.lean
    dependsOn : List String (explicit)

    Declared input names as strings, default empty.

    Ordered data items

    1. AutoSamplingTheory.lawMapEqOfAEEq
    2. AutoSamplingTheory.lawMapProdEqOfAEEq
    3. AutoSamplingTheory.lawMapProdFst
    4. AutoSamplingTheory.lawMapProdSnd
    5. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
    6. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
    7. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
    8. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
    9. sald.general_moving_target_discrete.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. thm:general-moving-target-SALD-discrete
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.formalized — 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 cycle63UnifiedDiscreteGeneralDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle63_global_phase_judgment"
      interface := "Upper judgment for cycle 63: cycle 62 passed and needs no recovery; Phase 1 is stable enough for unified/discrete-general route wiring and one narrow endpoint-law backfill; the largest remaining proof risk is the discrete general EM endpoint/common-space layer before conditional-law and Fokker-Planck work."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle63UnifiedDiscreteGeneralSkeletonUpperPacket",
        "SALD.cycle62GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle62GuidedGeneralScaledResidualLowerObligation",
        "SALD.cycle58UnifiedDiscreteGeneralMiddleObligation"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "ASTIS-SALD-001 cycle 63"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle63_five_backend_check"
      interface := "Explicit cycle-63 check 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 EM endpoint/conditional-law Fokker-Planck all have named source-cited or obligation interfaces."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.generalMovingTargetGronwallSideConditionContract",
        "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
        "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.generalMovingTargetDerivativeCandidateContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation"
      ]
      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.cycle63_upper_route"
      interface := "Route thm:unified-forward-KL through guided residual, correction-field transport, and thm:general-moving-target-SALD; route thm:general-moving-target-SALD-discrete through general EM endpoint/conditional-FP, frozen delta, KL derivative/LSI, residual DV, Gronwall, and display stitching, with statements and constants unchanged."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.cycle62GuidedGeneralSkeletonMiddleObligation",
        "SALD.guidedResidualIdentityContract",
        "SALD.unifiedForwardKlSpecializationContract",
        "sald.unified_forward_kl.transport_velocity_bridge",
        "sald.unified_forward_kl.specialization",
        "SALD.generalMovingTargetDiscreteStatementContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.gronwall_side_conditions"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle63_middle_route_audit"
      interface := "Middle route audit for cycle 63: check the unified specialization and discrete general EM/frozen-delta/LSI/DV/Gronwall chain against the source order, keep the paired Measure.map endpoint backfill scoped to endpoint laws, and hand off the conditional-law/Fokker-Planck backend over appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle63UnifiedDiscreteGeneralMiddleContract",
        "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
        "SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation",
        "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
        "sald.unified_forward_kl.specialization",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.gronwall_side_conditions"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "cycle63 lower conditional-FP packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle63_joint_endpoint_law_backfill"
      interface := "Narrow measure-theory backfill: from componentwise a.e. endpoint identities, derive equality of paired Measure.map pushforward laws and project that joint law to each marginal endpoint law for common-space EM endpoint bookkeeping."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/Probability.lean"
      dependsOn := [
        "AutoSamplingTheory.lawMapEqOfAEEq",
        "AutoSamplingTheory.lawMapProdEqOfAEEq",
        "AutoSamplingTheory.lawMapProdFst",
        "AutoSamplingTheory.lawMapProdSnd",
        "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation",
        "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := ["sald.general_moving_target_discrete.em_interpolation_fp", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.formalized
    }
  ]

/-! ### Cycle 64: analytic interface ledger refresh -/

/-- Cycle-64 upper ledger for the analytic-interface sprint.

This is route data only.  It records the required upper phase judgment,
re-checks the five slow analytic backends, and routes them through the six
faithful theorem skeletons in paper order while keeping every unproved backend
below `formalized`.
-/

Existing module entry · Audited data-reader index · All teaching coverage