AutoSamplingTheory.SALD.cycle44MainSkeletonAnalyticInterfaceDag

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 cycle44MainSkeletonAnalyticInterfaceDag : 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.cycle44.gronwall_interface
interface : String (explicit)
Text describing intended mathematical interface.
Endpoint-safe Gronwall interface: continuous coefficients, differentiable or absolutely continuous K, FTC/order integration, endpoint evaluation, and exponent rewrite with source signs unchanged.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGronwallSource — 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.saldGronwallCandidateContract
2. SALD.saldGronwallEndpointCalculusContract
3. SALD.saldGronwallExponentRewriteContract
4. SALD.cycle41GronwallMiddleObligation
5. SALD.cycle41GronwallLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. thm:forward-KL-discrete
3. thm:general-moving-target-SALD
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle44.dv_interface
interface : String (explicit)
Text describing intended mathematical interface.
Donsker-Varadhan interface: same probability space, absolute continuity, finite KL/log-likelihood, measurable selected tests, finite log-mgf, and selected-test one-sided consequences; full Boucheron supremum equality stays cited.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldDvVariationSource — 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. dvVariationalFormulaInterface saldDvVariationSource
2. probability.dv_variational_formula
3. SALD.saldDvFiniteLogMgfContract
4. SALD.cycle42DvVariationMiddleObligation
5. SALD.cycle42DvVariationLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. thm:forward-KL-discrete
3. thm:general-moving-target-SALD
4. thm:general-moving-target-SALD-discrete
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.sourceCited — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle44.lsi_kl_fi_interface
interface : String (explicit)
Text describing intended mathematical interface.
LSI-to-KL/FI interface: Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, Fisher chain rule, and finite KL/FI assumptions.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldKlFiLsiSource — 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. SALD.saldLsiKlFiDensityTestContract
2. SALD.lsiKlFiDensityTestObligation
3. SALD.cycle43LsiKlFiMiddleObligation
4. SALD.cycle43LsiKlFiLowerObligation
5. probability.lsi_to_kl_fi
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. thm:forward-KL-discrete
3. thm:general-moving-target-SALD
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle44.continuous_forward_kl_derivative_interface
interface : String (explicit)
Text describing intended mathematical interface.
Continuous forward-KL Fokker--Planck/KL derivative backend: law/density regularity, SALD Fokker--Planck, integration by parts, target transport, LSI handoff, and inverse-schedule time change.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDerivativeSource — 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.forwardKlDerivativeCandidateContract
2. SALD.forwardKlDerivativeSideConditionContract
3. SALD.forwardKlDensityBoundaryObligation
4. SALD.forwardKlScheduleTimeChangeObligation
5. SALD.cycle39ForwardKlDerivativeUpperObligation
6. SALD.cycle39ForwardKlDerivativeMiddleObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. 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.cycle44.em_interpolation_fp_interface
interface : String (explicit)
Text describing intended mathematical interface.
Euler--Maruyama interpolation Fokker--Planck backend: endpoint laws, conditional drift, conditional-law density, interpolation Fokker--Planck equation, Laplacian split, and stitched interval regularity.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — 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.discreteForwardKlEmInterpolationSideConditionContract
2. SALD.discreteForwardKlEmEndpointObligation
3. SALD.discreteForwardKlEmConditionalFpObligation
4. SALD.discreteForwardKlEmInterpolationObligation
5. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
6. SALD.generalMovingTargetDiscreteEmInterpolationObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle44.theorem_skeleton_route
interface : String (explicit)
Text describing intended mathematical interface.
Wire the five analytic interfaces into the faithful theorem order: forward-KL, discrete forward-KL, guided residual, continuous general moving target, unified forward-KL, and discrete general moving target.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlProofSource — 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.cycle44MainSkeletonAnalyticInterfaceLedger
2. SALD.cycle44MainSkeletonAnalyticInterfaceObligation
3. SALD.continuousSaldContract
4. SALD.discreteSaldContract
5. SALD.guidedResidualContract
6. SALD.generalVaSaldContract
7. SALD.unifiedForwardKlContract
8. SALD.generalVaSaldDiscreteContract
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. ASTIS-SALD-001 main skeleton closure
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 cycle44MainSkeletonAnalyticInterfaceDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle44.gronwall_interface"
      interface := "Endpoint-safe Gronwall interface: continuous coefficients, differentiable or absolutely continuous K, FTC/order integration, endpoint evaluation, and exponent rewrite with source signs unchanged."
      source := saldGronwallSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.saldGronwallCandidateContract",
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.saldGronwallExponentRewriteContract",
        "SALD.cycle41GronwallMiddleObligation",
        "SALD.cycle41GronwallLowerObligation"
      ]
      reusedBy := ["thm:forward-KL", "thm:forward-KL-discrete", "thm:general-moving-target-SALD", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle44.dv_interface"
      interface := "Donsker-Varadhan interface: same probability space, absolute continuity, finite KL/log-likelihood, measurable selected tests, finite log-mgf, and selected-test one-sided consequences; full Boucheron supremum equality stays cited."
      source := saldDvVariationSource
      targetLean := "AutoSamplingTheory/Probability.lean"
      dependsOn := [
        "dvVariationalFormulaInterface saldDvVariationSource",
        "probability.dv_variational_formula",
        "SALD.saldDvFiniteLogMgfContract",
        "SALD.cycle42DvVariationMiddleObligation",
        "SALD.cycle42DvVariationLowerObligation"
      ]
      reusedBy := ["thm:forward-KL", "thm:forward-KL-discrete", "thm:general-moving-target-SALD", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.sourceCited
    },
    {
      id := "ASTIS.SALD.cycle44.lsi_kl_fi_interface"
      interface := "LSI-to-KL/FI interface: Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, Fisher chain rule, and finite KL/FI assumptions."
      source := saldKlFiLsiSource
      targetLean := "AutoSamplingTheory/Probability.lean"
      dependsOn := [
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.lsiKlFiDensityTestObligation",
        "SALD.cycle43LsiKlFiMiddleObligation",
        "SALD.cycle43LsiKlFiLowerObligation",
        "probability.lsi_to_kl_fi"
      ]
      reusedBy := ["thm:forward-KL", "thm:forward-KL-discrete", "thm:general-moving-target-SALD", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle44.continuous_forward_kl_derivative_interface"
      interface := "Continuous forward-KL Fokker--Planck/KL derivative backend: law/density regularity, SALD Fokker--Planck, integration by parts, target transport, LSI handoff, and inverse-schedule time change."
      source := saldForwardKlDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.forwardKlDensityBoundaryObligation",
        "SALD.forwardKlScheduleTimeChangeObligation",
        "SALD.cycle39ForwardKlDerivativeUpperObligation",
        "SALD.cycle39ForwardKlDerivativeMiddleObligation"
      ]
      reusedBy := ["thm:forward-KL", "thm:general-moving-target-SALD"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle44.em_interpolation_fp_interface"
      interface := "Euler--Maruyama interpolation Fokker--Planck backend: endpoint laws, conditional drift, conditional-law density, interpolation Fokker--Planck equation, Laplacian split, and stitched interval regularity."
      source := saldForwardKlDiscreteConditionalFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "SALD.discreteForwardKlEmEndpointObligation",
        "SALD.discreteForwardKlEmConditionalFpObligation",
        "SALD.discreteForwardKlEmInterpolationObligation",
        "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
        "SALD.generalMovingTargetDiscreteEmInterpolationObligation"
      ]
      reusedBy := ["thm:forward-KL-discrete", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle44.theorem_skeleton_route"
      interface := "Wire the five analytic interfaces into the faithful theorem order: forward-KL, discrete forward-KL, guided residual, continuous general moving target, unified forward-KL, and discrete general moving target."
      source := saldForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle44MainSkeletonAnalyticInterfaceLedger",
        "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
        "SALD.continuousSaldContract",
        "SALD.discreteSaldContract",
        "SALD.guidedResidualContract",
        "SALD.generalVaSaldContract",
        "SALD.unifiedForwardKlContract",
        "SALD.generalVaSaldDiscreteContract"
      ]
      reusedBy := ["ASTIS-SALD-001 main skeleton closure"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-49 upper readiness check for the five slow analytic interfaces.

This sharpens the cycle-44 ledger after the theorem-level route wrappers from
cycles 45--48 are in place.  It is intentionally route data: the unresolved
analytic backends stay as obligations or source-cited facts.
-/

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