AutoSamplingTheory.SALD.cycle50ForwardKlSkeletonDag

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 cycle50ForwardKlSkeletonDag : 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.forward_KL.cycle50_theorem_skeleton_route
interface : String (explicit)
Text describing intended mathematical interface.
Post-readiness continuous forward-KL route: compose the cycle-49 five-backend check, the cycle-45 theorem wrapper, derivative/Fokker-Planck, LSI/KL/FI, DV finite-log-mgf, and Gronwall endpoint/exponent interfaces into the exact source 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.cycle50ForwardKlSkeletonUpperPacket
2. SALD.cycle50ForwardKlSkeletonObligation
3. SALD.cycle49MainSkeletonAnalyticReadinessObligation
4. SALD.cycle49MainSkeletonAnalyticMiddleObligation
5. SALD.cycle45ForwardKlSkeletonObligation
6. SALD.cycle45ForwardKlSkeletonMiddleObligation
7. SALD.cycle50ForwardKlSkeletonMiddleContract
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 50
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.forward_KL.cycle50_middle_route_audit
interface : String (explicit)
Text describing intended mathematical interface.
Middle audit after the cycle-50 post-readiness route: verify the exact source-order derivative -> LSI -> DV -> Gronwall map and select the continuous KL derivative/Fokker-Planck backend as the next lower 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.cycle50ForwardKlSkeletonMiddleContract
2. SALD.cycle50ForwardKlSkeletonMiddleObligation
3. SALD.cycle50ForwardKlSkeletonObligation
4. SALD.forwardKlDerivativeCandidateContract
5. SALD.forwardKlDerivativeSideConditionContract
6. SALD.forwardKlDerivativeObligation
7. sald.forward_kl.kl_derivative
8. SALD.saldLsiKlFiDensityTestContract
9. SALD.forwardKlDvFiniteLogMgfWitnessContract
10. SALD.forwardKlGronwallInstantiationContract
11. SALD.forwardKlGronwallSideConditionContract
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. cycle 50 lower derivative packet
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.forward_KL.cycle50_derivative_dv_lower
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing scalar handoff for appendix.tex:168-241: compose the selected KL derivative route, source KL/FI comparison, inverse-schedule velocity scaling, and selected-test DV input into the pre-Gronwall differential inequality with the paper's exact coefficient.
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.cycle50ForwardKlDerivativeLowerObligation
2. SALD.forwardKlDerivativeDvGronwallCoefficientOfKlFiVelocityScalingScalar
3. SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar
4. SALD.forwardKlPostDvGronwallCoefficientOfScheduleScalar
5. SALD.forwardKlDerivativeObligation
6. SALD.forwardKlDensityBoundaryObligation
7. SALD.forwardKlScheduleTimeChangeObligation
8. probability.lsi_to_kl_fi
9. sald.forward_kl.dv_finite_log_mgf_witness
10. sald.forward_kl.dv_energy_bound
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. sald.forward_kl.kl_derivative
3. sald.forward_kl.dv_energy_bound
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 cycle50ForwardKlSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.forward_KL.cycle50_theorem_skeleton_route"
      interface := "Post-readiness continuous forward-KL route: compose the cycle-49 five-backend check, the cycle-45 theorem wrapper, derivative/Fokker-Planck, LSI/KL/FI, DV finite-log-mgf, and Gronwall endpoint/exponent interfaces into the exact source theorem display."
      source := saldForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle50ForwardKlSkeletonUpperPacket",
        "SALD.cycle50ForwardKlSkeletonObligation",
        "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
        "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
        "SALD.cycle45ForwardKlSkeletonObligation",
        "SALD.cycle45ForwardKlSkeletonMiddleObligation",
        "SALD.cycle50ForwardKlSkeletonMiddleContract",
        "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 50"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL.cycle50_middle_route_audit"
      interface := "Middle audit after the cycle-50 post-readiness route: verify the exact source-order derivative -> LSI -> DV -> Gronwall map and select the continuous KL derivative/Fokker-Planck backend as the next lower target."
      source := saldForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle50ForwardKlSkeletonMiddleContract",
        "SALD.cycle50ForwardKlSkeletonMiddleObligation",
        "SALD.cycle50ForwardKlSkeletonObligation",
        "SALD.forwardKlDerivativeCandidateContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.forwardKlDerivativeObligation",
        "sald.forward_kl.kl_derivative",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDvFiniteLogMgfWitnessContract",
        "SALD.forwardKlGronwallInstantiationContract",
        "SALD.forwardKlGronwallSideConditionContract"
      ]
      reusedBy := ["thm:forward-KL", "cycle 50 lower derivative packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL.cycle50_derivative_dv_lower"
      interface := "Lower proof-producing scalar handoff for appendix.tex:168-241: compose the selected KL derivative route, source KL/FI comparison, inverse-schedule velocity scaling, and selected-test DV input into the pre-Gronwall differential inequality with the paper's exact coefficient."
      source := saldForwardKlProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle50ForwardKlDerivativeLowerObligation",
        "SALD.forwardKlDerivativeDvGronwallCoefficientOfKlFiVelocityScalingScalar",
        "SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar",
        "SALD.forwardKlPostDvGronwallCoefficientOfScheduleScalar",
        "SALD.forwardKlDerivativeObligation",
        "SALD.forwardKlDensityBoundaryObligation",
        "SALD.forwardKlScheduleTimeChangeObligation",
        "probability.lsi_to_kl_fi",
        "sald.forward_kl.dv_finite_log_mgf_witness",
        "sald.forward_kl.dv_energy_bound"
      ]
      reusedBy := ["thm:forward-KL", "sald.forward_kl.kl_derivative", "sald.forward_kl.dv_energy_bound"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-51 upper packet for the discrete forward-KL theorem skeleton.

This is the post-cycle-50 return to `thm:forward-KL-discrete`.  It checks the
five slow analytic interfaces again, then records the discrete theorem route
as a consumer of the already named EM/Fokker--Planck interfaces rather than a
request to prove those interfaces in this upper cycle.
-/

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