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

AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticInterfaceDag

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 cycle54MainSkeletonAnalyticInterfaceDag : 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.cycle54.analytic_interface_recheck
    interface : String (explicit)

    Text describing intended mathematical interface.

    Upper re-check of the five slow source-cited or obligation interfaces after the theorem skeleton route is wired: Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL derivative, and EM interpolation 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.cycle54MainSkeletonAnalyticInterfaceLedger
    2. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
    3. SALD.cycle49MainSkeletonAnalyticReadinessObligation
    4. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
    5. SALD.saldGronwallEndpointCalculusContract
    6. dvVariationalFormulaInterface saldDvVariationSource
    7. SALD.saldLsiKlFiDensityTestContract
    8. SALD.forwardKlDerivativeSideConditionContract
    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
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle54.middle_interface_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Middle audit of the upper cycle-54 analytic ledger against the six theorem consumers, with the lower packet narrowed to appendix.tex:1354-1387 EM conditional-law/Fokker-Planck and KL-derivative inputs.
    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.cycle54MainSkeletonAnalyticMiddleContract
    2. SALD.cycle54MainSkeletonAnalyticMiddleObligation
    3. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
    4. SALD.cycle49MainSkeletonAnalyticMiddleObligation
    5. SALD.cycle53UnifiedDiscreteGeneralMiddleObligation
    6. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
    7. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    8. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
    9. SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
    10. sald.general_moving_target_discrete.kl_derivative
    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.general_moving_target_discrete.cycle54_em_fp_sigma_split
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower proof-producing algebra for appendix.tex:1380-1387: under the supplied weak FP identity, Laplacian split, and abstract divergence linearity, regroup the sigma_eta^2/2 Laplacian contribution into the source conditional-FP divergence form.
    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.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
    2. SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation
    3. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    4. sald.general_moving_target_discrete.em_interpolation_fp
    5. sald.general_moving_target_discrete.kl_derivative
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.general_moving_target_discrete.em_interpolation_fp
    2. sald.general_moving_target_discrete.kl_derivative
    3. thm:general-moving-target-SALD-discrete
    status : AutoSamplingTheory.ProofStatus (explicit)

    Recorded workflow status, default planned.

    AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
  4. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle54.lower_packet.general_discrete_em_fp
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower packet remains on appendix.tex:1354-1387 for the discrete general EM conditional-law/Fokker-Planck and KL-derivative backend, using the cycle-53 Measure.map endpoint-law handoff only as endpoint bookkeeping and the cycle-54 sigma split only as divergence algebra.
    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.generalMovingTargetDiscreteDerivativeCandidateContract
    2. SALD.generalMovingTargetDiscreteDerivativeObligation
    3. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
    4. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
    5. SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
    6. SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation
    7. sald.general_moving_target_discrete.em_interpolation_fp
    8. sald.general_moving_target_discrete.kl_derivative
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:general-moving-target-SALD-discrete
    2. cycle54 lower work
    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 cycle54MainSkeletonAnalyticInterfaceDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle54.analytic_interface_recheck"
      interface := "Upper re-check of the five slow source-cited or obligation interfaces after the theorem skeleton route is wired: Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL derivative, and EM interpolation Fokker-Planck."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle54MainSkeletonAnalyticInterfaceLedger",
        "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
        "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.saldGronwallEndpointCalculusContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "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.cycle54.middle_interface_audit"
      interface := "Middle audit of the upper cycle-54 analytic ledger against the six theorem consumers, with the lower packet narrowed to appendix.tex:1354-1387 EM conditional-law/Fokker-Planck and KL-derivative inputs."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle54MainSkeletonAnalyticMiddleContract",
        "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle53UnifiedDiscreteGeneralMiddleObligation",
        "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      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.general_moving_target_discrete.cycle54_em_fp_sigma_split"
      interface := "Lower proof-producing algebra for appendix.tex:1380-1387: under the supplied weak FP identity, Laplacian split, and abstract divergence linearity, regroup the sigma_eta^2/2 Laplacian contribution into the source conditional-FP divergence form."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
        "SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      reusedBy := ["sald.general_moving_target_discrete.em_interpolation_fp", "sald.general_moving_target_discrete.kl_derivative", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle54.lower_packet.general_discrete_em_fp"
      interface := "Lower packet remains on appendix.tex:1354-1387 for the discrete general EM conditional-law/Fokker-Planck and KL-derivative backend, using the cycle-53 Measure.map endpoint-law handoff only as endpoint bookkeeping and the cycle-54 sigma split only as divergence algebra."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
        "SALD.generalMovingTargetDiscreteDerivativeObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
        "SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      reusedBy := ["thm:general-moving-target-SALD-discrete", "cycle54 lower work"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-55 upper packet for returning the global analytic-interface audit to
the continuous forward-KL skeleton.

The cycle focus is deliberately narrow: consume the cycle-54 five-backend
check, then re-wire `thm:forward-KL` through the already named source-cited
interfaces in the exact paper order.  No analytic backend or theorem statement
is promoted by this packet.
-/

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