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

AutoSamplingTheory.SALD.cycle60ForwardKlSkeletonObligation

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 cycle60ForwardKlSkeletonObligation : 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.cycle60_post_cycle59_route
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 60 upper records the post-cycle-59 global phase judgment and wires thm:forward-KL through the source-cited analytic interfaces in the paper order: appendix.tex:168-228 continuous KL derivative/Fokker-Planck plus LSI/time change, appendix.tex:230-241 DV velocity-energy with finite-log-mgf witness, and appendix.tex:244-252 Gronwall endpoint/exponent display matching. main_body.tex:238-247 remains the unchanged theorem statement, and the next lower packet is sald.forward_kl.kl_derivative over appendix.tex:168-228.
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.cycle60ForwardKlSkeletonUpperPacket
  2. SALD.cycle59MainSkeletonAnalyticInterfaceObligation
  3. SALD.cycle59MainSkeletonAnalyticMiddleObligation
  4. SALD.cycle55ForwardKlSkeletonObligation
  5. SALD.cycle55ForwardKlSkeletonMiddleObligation
  6. SALD.cycle55ForwardKlDerivativeMassLowerObligation
  7. SALD.cycle50ForwardKlSkeletonObligation
  8. SALD.cycle50ForwardKlSkeletonMiddleObligation
  9. SALD.cycle50ForwardKlDerivativeLowerObligation
  10. SALD.continuousForwardKlStatementContract
  11. SALD.forwardKlDerivativeCandidateContract
  12. SALD.forwardKlDerivativeSideConditionContract
  13. SALD.forwardKlDerivativeObligation
  14. SALD.forwardKlDensityBoundaryObligation
  15. SALD.forwardKlScheduleTimeChangeObligation
  16. sald.forward_kl.density_boundary_regular
  17. sald.forward_kl.schedule_time_change
  18. sald.forward_kl.kl_derivative
  19. SALD.saldLsiKlFiDensityTestContract
  20. probability.lsi_to_kl_fi
  21. dvVariationalFormulaInterface saldDvVariationSource
  22. SALD.saldDvFiniteLogMgfContract
  23. SALD.forwardKlDvFiniteLogMgfWitnessContract
  24. sald.forward_kl.dv_finite_log_mgf_witness
  25. sald.forward_kl.dv_energy_bound
  26. SALD.saldGronwallEndpointCalculusContract
  27. SALD.forwardKlGronwallInstantiationContract
  28. SALD.forwardKlGronwallSideConditionContract
  29. sald.forward_kl.endpoint_schedule_identities
  30. sald.forward_kl.gronwall_side_conditions
  31. sald.forward_kl.gronwall_application
  32. SALD.discreteForwardKlEmInterpolationSideConditionContract
  33. sald.discrete_forward_kl.em_interpolation_fp
  34. lem:gronwall
  35. lem:dv_variation
  36. eq:LSI-KL-FI
  37. def:alpha-complexity
note : String (explicit)

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

Upper workflow obligation only. It adds no theorem hypotheses and does not promote Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL differentiation, EM interpolation, SLT reuse, or 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 cycle60ForwardKlSkeletonObligation : ProofObligation where
  id := "sald.forward_kl.cycle60_post_cycle59_route"
  statement := "Cycle 60 upper records the post-cycle-59 global phase judgment and wires thm:forward-KL through the source-cited analytic interfaces in the paper order: appendix.tex:168-228 continuous KL derivative/Fokker-Planck plus LSI/time change, appendix.tex:230-241 DV velocity-energy with finite-log-mgf witness, and appendix.tex:244-252 Gronwall endpoint/exponent display matching. main_body.tex:238-247 remains the unchanged theorem statement, and the next lower packet is sald.forward_kl.kl_derivative over appendix.tex:168-228."
  source := saldForwardKlProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle60ForwardKlSkeletonUpperPacket",
    "SALD.cycle59MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle59MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle55ForwardKlSkeletonObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle55ForwardKlDerivativeMassLowerObligation",
    "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.endpoint_schedule_identities",
    "sald.forward_kl.gronwall_side_conditions",
    "sald.forward_kl.gronwall_application",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "Upper workflow obligation only. It adds no theorem hypotheses and does not promote Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL differentiation, EM interpolation, SLT reuse, or thm:forward-KL."

/-- Cycle-60 middle audit for the post-cycle-59 continuous forward-KL route.

This source-to-Lean synchronization layer checks that the upper cycle-60 route
is consumed by the continuous theorem contract in the same order as
`appendix.tex:164-252`, while keeping the lower packet on the continuous KL
derivative/Fokker--Planck backend.
-/

Existing module entry · Audited data-reader index · All teaching coverage