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

AutoSamplingTheory.SALD.cycle55ForwardKlSkeletonDag

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 cycle55ForwardKlSkeletonDag : 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.forward_KL.cycle55_continuous_skeleton_route
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle-55 focused route: consume the cycle-54 five-backend re-check and cycle-50 forward-KL route, then wire main_body.tex:238-247 and appendix.tex:164-252 through derivative/Fokker-Planck, LSI/KL/FI, DV finite-log-mgf, Gronwall endpoint/exponent, and downstream EM-interface visibility without changing the theorem display.
    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.cycle55ForwardKlSkeletonUpperPacket
    2. SALD.cycle55ForwardKlSkeletonObligation
    3. SALD.cycle55ForwardKlSkeletonMiddleContract
    4. SALD.cycle55ForwardKlSkeletonMiddleObligation
    5. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
    6. SALD.cycle54MainSkeletonAnalyticMiddleObligation
    7. SALD.cycle50ForwardKlSkeletonObligation
    8. SALD.cycle50ForwardKlSkeletonMiddleObligation
    9. SALD.continuousForwardKlStatementContract
    10. SALD.forwardKlDerivativeCandidateContract
    11. SALD.forwardKlDerivativeSideConditionContract
    12. SALD.saldLsiKlFiDensityTestContract
    13. SALD.forwardKlDvFiniteLogMgfWitnessContract
    14. SALD.forwardKlGronwallInstantiationContract
    15. SALD.forwardKlGronwallSideConditionContract
    16. SALD.discreteForwardKlEmInterpolationSideConditionContract
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:forward-KL
    2. ASTIS-SALD-001 cycle 55
    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.forward_KL.cycle55_middle_route_audit
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle-55 middle audit: verify the upper continuous forward-KL route in source order, keep the theorem display and constants fixed, and select appendix.tex:168-228 sald.forward_kl.kl_derivative as the lower backend while LSI, DV, Gronwall, and EM interfaces remain separate obligations.
    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.cycle55ForwardKlSkeletonMiddleContract
    2. SALD.cycle55ForwardKlSkeletonMiddleObligation
    3. SALD.cycle55ForwardKlSkeletonObligation
    4. SALD.cycle54MainSkeletonAnalyticMiddleObligation
    5. SALD.cycle50ForwardKlSkeletonMiddleObligation
    6. SALD.cycle50ForwardKlDerivativeLowerObligation
    7. SALD.continuousForwardKlStatementContract
    8. SALD.forwardKlDerivativeCandidateContract
    9. SALD.forwardKlDerivativeSideConditionContract
    10. SALD.forwardKlDerivativeObligation
    11. sald.forward_kl.kl_derivative
    12. SALD.saldLsiKlFiDensityTestContract
    13. SALD.forwardKlDvFiniteLogMgfWitnessContract
    14. SALD.forwardKlGronwallInstantiationContract
    15. SALD.forwardKlGronwallSideConditionContract
    16. SALD.discreteForwardKlEmInterpolationSideConditionContract
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. thm:forward-KL
    2. cycle 55 lower derivative packet
    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.forward_KL.cycle55_lower_packet.kl_derivative
    interface : String (explicit)

    Text describing intended mathematical interface.

    Lower packet selected by cycle 55: keep proof-producing work on appendix.tex:168-228 for sald.forward_kl.kl_derivative, starting with mass conservation, KL differentiation, SALD Fokker-Planck substitution, integration by parts, and inverse-schedule calculus while LSI, DV, Gronwall, and EM backends stay separate.
    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.cycle55ForwardKlSkeletonObligation
    2. SALD.cycle55ForwardKlSkeletonMiddleObligation
    3. SALD.forwardKlDerivativeCandidateContract
    4. SALD.forwardKlDerivativeSideConditionContract
    5. SALD.forwardKlDerivativeObligation
    6. SALD.cycle55ForwardKlDerivativeMassLowerObligation
    7. SALD.forwardKlMassConservationDropScalar
    8. SALD.forwardKlMassConservationFirstTermFisherScalar
    9. SALD.forwardKlDensityBoundaryObligation
    10. SALD.forwardKlScheduleTimeChangeObligation
    11. sald.forward_kl.density_boundary_regular
    12. sald.forward_kl.schedule_time_change
    13. sald.forward_kl.kl_derivative
    14. SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar
    15. SALD.forwardKlDerivativeDvGronwallCoefficientOfKlFiVelocityScalingScalar
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.forward_kl.kl_derivative
    2. thm:forward-KL
    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.forward_KL.cycle55_derivative_mass_lower
    interface : String (explicit)

    Text describing intended mathematical interface.

    Cycle-55 lower proof-producing scalar slice for appendix.tex:168-185: drop the mass-conservation term from the raw KL derivative split, then compose with the supplied first-term=-FI identity to recover dK=-FI+targetTerm before the target-transport and LSI steps.
    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.cycle55ForwardKlDerivativeMassLowerObligation
    2. SALD.forwardKlMassConservationDropScalar
    3. SALD.forwardKlMassConservationFirstTermFisherScalar
    4. SALD.forwardKlFirstTermFisherSubstitutionScalar
    5. SALD.forwardKlDerivativeCandidateContract
    6. SALD.forwardKlDerivativeSideConditionContract
    7. SALD.forwardKlDerivativeObligation
    8. sald.forward_kl.density_boundary_regular
    9. sald.forward_kl.kl_derivative
    reusedBy : List String (explicit)

    Declared consumers as strings, default empty.

    Ordered data items

    1. sald.forward_kl.kl_derivative
    2. thm:forward-KL
    3. cycle 55 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 cycle55ForwardKlSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.forward_KL.cycle55_continuous_skeleton_route"
      interface := "Cycle-55 focused route: consume the cycle-54 five-backend re-check and cycle-50 forward-KL route, then wire main_body.tex:238-247 and appendix.tex:164-252 through derivative/Fokker-Planck, LSI/KL/FI, DV finite-log-mgf, Gronwall endpoint/exponent, and downstream EM-interface visibility without changing the theorem display."
      source := saldForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle55ForwardKlSkeletonUpperPacket",
        "SALD.cycle55ForwardKlSkeletonObligation",
        "SALD.cycle55ForwardKlSkeletonMiddleContract",
        "SALD.cycle55ForwardKlSkeletonMiddleObligation",
        "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
        "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle50ForwardKlSkeletonObligation",
        "SALD.cycle50ForwardKlSkeletonMiddleObligation",
        "SALD.continuousForwardKlStatementContract",
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDvFiniteLogMgfWitnessContract",
        "SALD.forwardKlGronwallInstantiationContract",
        "SALD.forwardKlGronwallSideConditionContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract"
      ]
      reusedBy := ["thm:forward-KL", "ASTIS-SALD-001 cycle 55"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL.cycle55_middle_route_audit"
      interface := "Cycle-55 middle audit: verify the upper continuous forward-KL route in source order, keep the theorem display and constants fixed, and select appendix.tex:168-228 sald.forward_kl.kl_derivative as the lower backend while LSI, DV, Gronwall, and EM interfaces remain separate obligations."
      source := saldForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle55ForwardKlSkeletonMiddleContract",
        "SALD.cycle55ForwardKlSkeletonMiddleObligation",
        "SALD.cycle55ForwardKlSkeletonObligation",
        "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle50ForwardKlSkeletonMiddleObligation",
        "SALD.cycle50ForwardKlDerivativeLowerObligation",
        "SALD.continuousForwardKlStatementContract",
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.forwardKlDerivativeObligation",
        "sald.forward_kl.kl_derivative",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDvFiniteLogMgfWitnessContract",
        "SALD.forwardKlGronwallInstantiationContract",
        "SALD.forwardKlGronwallSideConditionContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract"
      ]
      reusedBy := ["thm:forward-KL", "cycle 55 lower derivative packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL.cycle55_lower_packet.kl_derivative"
      interface := "Lower packet selected by cycle 55: keep proof-producing work on appendix.tex:168-228 for sald.forward_kl.kl_derivative, starting with mass conservation, KL differentiation, SALD Fokker-Planck substitution, integration by parts, and inverse-schedule calculus while LSI, DV, Gronwall, and EM backends stay separate."
      source := saldForwardKlDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle55ForwardKlSkeletonObligation",
        "SALD.cycle55ForwardKlSkeletonMiddleObligation",
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.forwardKlDerivativeObligation",
        "SALD.cycle55ForwardKlDerivativeMassLowerObligation",
        "SALD.forwardKlMassConservationDropScalar",
        "SALD.forwardKlMassConservationFirstTermFisherScalar",
        "SALD.forwardKlDensityBoundaryObligation",
        "SALD.forwardKlScheduleTimeChangeObligation",
        "sald.forward_kl.density_boundary_regular",
        "sald.forward_kl.schedule_time_change",
        "sald.forward_kl.kl_derivative",
        "SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar",
        "SALD.forwardKlDerivativeDvGronwallCoefficientOfKlFiVelocityScalingScalar"
      ]
      reusedBy := ["sald.forward_kl.kl_derivative", "thm:forward-KL"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL.cycle55_derivative_mass_lower"
      interface := "Cycle-55 lower proof-producing scalar slice for appendix.tex:168-185: drop the mass-conservation term from the raw KL derivative split, then compose with the supplied first-term=-FI identity to recover dK=-FI+targetTerm before the target-transport and LSI steps."
      source := saldForwardKlDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle55ForwardKlDerivativeMassLowerObligation",
        "SALD.forwardKlMassConservationDropScalar",
        "SALD.forwardKlMassConservationFirstTermFisherScalar",
        "SALD.forwardKlFirstTermFisherSubstitutionScalar",
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.forwardKlDerivativeObligation",
        "sald.forward_kl.density_boundary_regular",
        "sald.forward_kl.kl_derivative"
      ]
      reusedBy := ["sald.forward_kl.kl_derivative", "thm:forward-KL", "cycle 55 lower handoff"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-56 upper packet for returning the main skeleton sprint to the
discrete forward-KL theorem.

The focus is the theorem route, not a new analytic proof: consume the existing
source-cited EM/Fokker-Planck interfaces, the cycle-51 derivative scalar handoff,
and the cycle-55 continuous forward-KL rewire, then keep the discrete
Gronwall/accumulated-error bridge as the next lower theorem-level backend.
-/

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