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

AutoSamplingTheory.SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation

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 cycle56DiscreteForwardKlSkeletonMiddleObligation : 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.discrete_forward_kl.cycle56_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 56 middle audits the discrete thm:forward-KL-discrete route after the upper wrapper: main_body.tex:299-323 remains unchanged; appendix.tex:260-385 EM endpoint/conditional-Fokker-Planck interfaces are consumed only as named obligations; appendix.tex:388-491 uses the cycle-51 derivative/LSI scalar handoff; appendix.tex:493-523 uses the discrete DV velocity witness; and appendix.tex:526-592 is selected as the next lower Gronwall accumulation backend. The accumulated-error bridge stays downstream and all slow analytic backends remain obligation or source-cited.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — 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.cycle56DiscreteForwardKlSkeletonUpperPacket
  2. SALD.cycle56DiscreteForwardKlSkeletonObligation
  3. SALD.cycle56DiscreteForwardKlSkeletonMiddleContract
  4. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
  5. SALD.cycle54MainSkeletonAnalyticMiddleObligation
  6. SALD.cycle55ForwardKlSkeletonMiddleObligation
  7. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
  8. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
  9. SALD.discreteForwardKlStatementContract
  10. SALD.discreteForwardKlEmInterpolationSideConditionContract
  11. sald.discrete_forward_kl.em_endpoint_laws
  12. sald.discrete_forward_kl.conditional_drift_density
  13. sald.discrete_forward_kl.em_conditional_fokker_planck
  14. sald.discrete_forward_kl.stitched_interval_regularity
  15. sald.discrete_forward_kl.em_interpolation_fp
  16. SALD.discreteForwardKlDerivativeCandidateContract
  17. sald.discrete_forward_kl.kl_derivative
  18. SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
  19. SALD.frozenDeltaCrossLipSaldContract
  20. SALD.saldLsiKlFiDensityTestContract
  21. probability.lsi_to_kl_fi
  22. dvVariationalFormulaInterface saldDvVariationSource
  23. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
  24. sald.discrete_forward_kl.dv_velocity_bound
  25. SALD.saldGronwallEndpointCalculusContract
  26. SALD.discreteForwardKlGronwallInstantiationContract
  27. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
  28. sald.discrete_forward_kl.gronwall_accumulation
  29. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  30. sald.discrete_forward_kl.accumulated_error_bridge
  31. lem:gronwall
  32. lem:dv_variation
  33. eq:LSI-KL-FI
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 endpoint, density, absolute-continuity, finite-log-mgf, conditional-law, boundary, stitched-interval, or coefficient assumptions to thm:forward-KL-discrete.
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 cycle56DiscreteForwardKlSkeletonMiddleObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle56_middle_route_audit"
  statement := "Cycle 56 middle audits the discrete thm:forward-KL-discrete route after the upper wrapper: main_body.tex:299-323 remains unchanged; appendix.tex:260-385 EM endpoint/conditional-Fokker-Planck interfaces are consumed only as named obligations; appendix.tex:388-491 uses the cycle-51 derivative/LSI scalar handoff; appendix.tex:493-523 uses the discrete DV velocity witness; and appendix.tex:526-592 is selected as the next lower Gronwall accumulation backend. The accumulated-error bridge stays downstream and all slow analytic backends remain obligation or source-cited."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle56DiscreteForwardKlSkeletonUpperPacket",
    "SALD.cycle56DiscreteForwardKlSkeletonObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleContract",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
    "SALD.discreteForwardKlStatementContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.conditional_drift_density",
    "sald.discrete_forward_kl.em_conditional_fokker_planck",
    "sald.discrete_forward_kl.stitched_interval_regularity",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "SALD.discreteForwardKlDerivativeCandidateContract",
    "sald.discrete_forward_kl.kl_derivative",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
    "SALD.frozenDeltaCrossLipSaldContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
    "sald.discrete_forward_kl.dv_velocity_bound",
    "SALD.saldGronwallEndpointCalculusContract",
    "SALD.discreteForwardKlGronwallInstantiationContract",
    "SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar",
    "sald.discrete_forward_kl.gronwall_accumulation",
    "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI"
  ]
  note := "This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It adds no hidden endpoint, density, absolute-continuity, finite-log-mgf, conditional-law, boundary, stitched-interval, or coefficient assumptions to thm:forward-KL-discrete."

/-- Cycle-56 lower obligation for the discrete Gronwall accumulation backend. -/

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