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

AutoSamplingTheory.SALD.cycle55ForwardKlSkeletonMiddleObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. 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 cycle55ForwardKlSkeletonMiddleObligation : ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

id : String (explicit)

Stable obligation identifier.

sald.forward_kl.cycle55_middle_route_audit
statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 55 middle audits the focused continuous thm:forward-KL skeleton after the upper route: main_body.tex:238-247 remains unchanged, appendix.tex:168-252 is routed through the named continuous KL derivative/Fokker--Planck, LSI/KL/FI, DV finite-log-mgf, and Gronwall endpoint/exponent interfaces in paper order, and the next lower target is sald.forward_kl.kl_derivative over appendix.tex:168-228. The downstream EM interpolation backend remains a visible sibling obligation for discrete reuse only.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlProofSource — audited data reference, not expanded and not a compiled dependency edge
status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

  1. SALD.cycle55ForwardKlSkeletonUpperPacket
  2. SALD.cycle55ForwardKlSkeletonObligation
  3. SALD.cycle55ForwardKlSkeletonMiddleContract
  4. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
  5. SALD.cycle54MainSkeletonAnalyticMiddleObligation
  6. SALD.cycle50ForwardKlSkeletonObligation
  7. SALD.cycle50ForwardKlSkeletonMiddleObligation
  8. SALD.cycle50ForwardKlDerivativeLowerObligation
  9. SALD.continuousForwardKlStatementContract
  10. SALD.forwardKlDerivativeCandidateContract
  11. SALD.forwardKlDerivativeSideConditionContract
  12. SALD.forwardKlDerivativeObligation
  13. SALD.forwardKlDensityBoundaryObligation
  14. SALD.forwardKlScheduleTimeChangeObligation
  15. sald.forward_kl.density_boundary_regular
  16. sald.forward_kl.schedule_time_change
  17. sald.forward_kl.kl_derivative
  18. SALD.saldLsiKlFiDensityTestContract
  19. probability.lsi_to_kl_fi
  20. dvVariationalFormulaInterface saldDvVariationSource
  21. SALD.saldDvFiniteLogMgfContract
  22. SALD.forwardKlDvFiniteLogMgfWitnessContract
  23. sald.forward_kl.dv_finite_log_mgf_witness
  24. sald.forward_kl.dv_energy_bound
  25. SALD.saldGronwallEndpointCalculusContract
  26. SALD.forwardKlGronwallInstantiationContract
  27. SALD.forwardKlGronwallSideConditionContract
  28. sald.forward_kl.gronwall_side_conditions
  29. sald.forward_kl.gronwall_application
  30. SALD.discreteForwardKlEmInterpolationSideConditionContract
  31. sald.discrete_forward_kl.em_interpolation_fp
note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It adds no hidden density, boundary, endpoint, absolute-continuity, finite-log-mgf, finite-KL/FI, schedule, or coefficient-regularity assumptions to thm:forward-KL.
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 cycle55ForwardKlSkeletonMiddleObligation : ProofObligation where
  id := "sald.forward_kl.cycle55_middle_route_audit"
  statement := "Cycle 55 middle audits the focused continuous thm:forward-KL skeleton after the upper route: main_body.tex:238-247 remains unchanged, appendix.tex:168-252 is routed through the named continuous KL derivative/Fokker--Planck, LSI/KL/FI, DV finite-log-mgf, and Gronwall endpoint/exponent interfaces in paper order, and the next lower target is sald.forward_kl.kl_derivative over appendix.tex:168-228. The downstream EM interpolation backend remains a visible sibling obligation for discrete reuse only."
  source := saldForwardKlProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle55ForwardKlSkeletonUpperPacket",
    "SALD.cycle55ForwardKlSkeletonObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleContract",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle50ForwardKlSkeletonObligation",
    "SALD.cycle50ForwardKlSkeletonMiddleObligation",
    "SALD.cycle50ForwardKlDerivativeLowerObligation",
    "SALD.continuousForwardKlStatementContract",
    "SALD.forwardKlDerivativeCandidateContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.forwardKlDerivativeObligation",
    "SALD.forwardKlDensityBoundaryObligation",
    "SALD.forwardKlScheduleTimeChangeObligation",
    "sald.forward_kl.density_boundary_regular",
    "sald.forward_kl.schedule_time_change",
    "sald.forward_kl.kl_derivative",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.forwardKlDvFiniteLogMgfWitnessContract",
    "sald.forward_kl.dv_finite_log_mgf_witness",
    "sald.forward_kl.dv_energy_bound",
    "SALD.saldGronwallEndpointCalculusContract",
    "SALD.forwardKlGronwallInstantiationContract",
    "SALD.forwardKlGronwallSideConditionContract",
    "sald.forward_kl.gronwall_side_conditions",
    "sald.forward_kl.gronwall_application",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It adds no hidden density, boundary, endpoint, absolute-continuity, finite-log-mgf, finite-KL/FI, schedule, or coefficient-regularity assumptions to thm:forward-KL."

/-- Cycle-55 lower obligation for the first continuous derivative scalar slice. -/

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