AutoSamplingTheory.SALD.cycle56DiscreteForwardKlSkeletonObligation

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.

def cycle56DiscreteForwardKlSkeletonObligation : 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_theorem_interface_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 56 upper wires thm:forward-KL-discrete at theorem level: main_body.tex:299-323 stays fixed; appendix.tex:260-385 is consumed through explicit EM endpoint, conditional-drift density, conditional-Fokker-Planck, Laplacian split, and stitched-interval interfaces; 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 remains the selected Gronwall/linear-slowdown accumulated-error backend. The EM/Fokker-Planck backend is source-cited obligation data, not a proof in this cycle.

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.cycle54MainSkeletonAnalyticInterfaceObligation
3. SALD.cycle54MainSkeletonAnalyticMiddleObligation
4. SALD.cycle55ForwardKlSkeletonObligation
5. SALD.cycle55ForwardKlSkeletonMiddleObligation
6. SALD.cycle51DiscreteForwardKlSkeletonObligation
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.discreteForwardKlPostLsiDerivativeBoundScalar
19. SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
20. SALD.frozenDeltaCrossLipSaldContract
21. sald.discrete_forward_kl.frozen_delta_cross_lip
22. SALD.saldLsiKlFiDensityTestContract
23. probability.lsi_to_kl_fi
24. dvVariationalFormulaInterface saldDvVariationSource
25. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
26. sald.discrete_forward_kl.dv_finite_log_mgf_witness
27. sald.discrete_forward_kl.dv_velocity_bound
28. SALD.saldGronwallEndpointCalculusContract
29. SALD.discreteForwardKlGronwallInstantiationContract
30. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
31. sald.discrete_forward_kl.gronwall_accumulation
32. SALD.discreteForwardKlAccumulatedErrorBridgeContract
33. sald.discrete_forward_kl.linear_slowdown_specialization
34. sald.discrete_forward_kl.residual_exponent_bound
35. sald.discrete_forward_kl.accumulated_error_bridge
36. lem:gronwall
37. lem:dv_variation
38. eq:LSI-KL-FI
39. thm:forward-KL

note : String (explicit)

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

This is an upper workflow obligation and route check. It adds no hidden assumptions, proves no EM/Fokker-Planck theorem, and does not promote Gronwall, DV, LSI/KL/FI, KL differentiation, endpoint stitching, accumulated-error collection, or thm:forward-KL-discrete.

def cycle56DiscreteForwardKlSkeletonObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle56_theorem_interface_route"
  statement := "Cycle 56 upper wires thm:forward-KL-discrete at theorem level: main_body.tex:299-323 stays fixed; appendix.tex:260-385 is consumed through explicit EM endpoint, conditional-drift density, conditional-Fokker-Planck, Laplacian split, and stitched-interval interfaces; 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 remains the selected Gronwall/linear-slowdown accumulated-error backend. The EM/Fokker-Planck backend is source-cited obligation data, not a proof in this cycle."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle56DiscreteForwardKlSkeletonUpperPacket",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle55ForwardKlSkeletonObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonObligation",
    "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.discreteForwardKlPostLsiDerivativeBoundScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
    "SALD.frozenDeltaCrossLipSaldContract",
    "sald.discrete_forward_kl.frozen_delta_cross_lip",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
    "sald.discrete_forward_kl.dv_finite_log_mgf_witness",
    "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.linear_slowdown_specialization",
    "sald.discrete_forward_kl.residual_exponent_bound",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "thm:forward-KL"
  ]
  note := "This is an upper workflow obligation and route check. It adds no hidden assumptions, proves no EM/Fokker-Planck theorem, and does not promote Gronwall, DV, LSI/KL/FI, KL differentiation, endpoint stitching, accumulated-error collection, or thm:forward-KL-discrete."

/-- Cycle-56 middle audit for the discrete forward-KL theorem route.

This synchronizes the upper cycle-56 route with the source-to-Lean ledger.  It
keeps the already wired derivative and DV interfaces as inputs and selects the
appendix Gronwall/accumulated-error backend as the next lower packet.
-/