AutoSamplingTheory.SALD.cycle66DiscreteForwardKlSkeletonObligation

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 cycle66DiscreteForwardKlSkeletonObligation : 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.cycle66_discrete_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 66 upper records the post-cycle-65 global phase judgment and wires thm:forward-KL-discrete through the five source-cited analytic interfaces in the paper order: appendix.tex:260-385 EM interpolation endpoint/conditional-Fokker-Planck setup, appendix.tex:388-491 discrete KL derivative with frozen defect and LSI, appendix.tex:493-523 DV velocity-energy, appendix.tex:526-553 time-changed Gronwall input, and appendix.tex:557-592 Gronwall output/accumulated-error collection to main_body.tex:309-323. The selected lower packet is sald.discrete_forward_kl.accumulated_error_bridge.

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.cycle66DiscreteForwardKlSkeletonUpperPacket
2. SALD.cycle65ForwardKlSkeletonMiddleObligation
3. SALD.cycle65ForwardKlDerivativePointwiseLowerObligation
4. SALD.cycle64MainSkeletonAnalyticInterfaceObligation
5. SALD.cycle64MainSkeletonAnalyticMiddleObligation
6. SALD.cycle61DiscreteForwardKlSkeletonObligation
7. SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation
8. SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation
9. SALD.cycle56DiscreteForwardKlSkeletonObligation
10. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
11. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
12. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
13. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
14. SALD.discreteForwardKlStatementContract
15. SALD.discreteForwardKlEmInterpolationSideConditionContract
16. sald.discrete_forward_kl.em_endpoint_laws
17. sald.discrete_forward_kl.conditional_drift_density
18. sald.discrete_forward_kl.em_conditional_fokker_planck
19. sald.discrete_forward_kl.stitched_interval_regularity
20. sald.discrete_forward_kl.em_interpolation_fp
21. SALD.discreteForwardKlDerivativeCandidateContract
22. SALD.discreteForwardKlDerivativeObligation
23. sald.discrete_forward_kl.kl_derivative
24. SALD.frozenDeltaCrossLipSaldContract
25. sald.discrete_forward_kl.frozen_delta_cross_lip
26. SALD.saldLsiKlFiDensityTestContract
27. probability.lsi_to_kl_fi
28. dvVariationalFormulaInterface saldDvVariationSource
29. SALD.saldDvFiniteLogMgfContract
30. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
31. sald.discrete_forward_kl.dv_finite_log_mgf_witness
32. sald.discrete_forward_kl.dv_velocity_bound
33. SALD.saldGronwallEndpointCalculusContract
34. SALD.discreteForwardKlGronwallInstantiationContract
35. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
36. SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged
37. sald.discrete_forward_kl.gronwall_accumulation
38. SALD.discreteForwardKlAccumulatedErrorBridgeContract
39. SALD.discreteForwardKlAccumulatedErrorBridgeObligation
40. SALD.discreteForwardKlGronwallCoeffIntervalIntegrable
41. SALD.discreteForwardKlGronwallCoeffIntegralSubSub
42. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
43. SALD.discreteForwardKlResidualExponentBoundScalar
44. SALD.discreteForwardKlResidualExpBoundScalar
45. SALD.discreteForwardKlAlphaComplexityCollectionScalar
46. SALD.discreteForwardKlDeltaAccumulationScalar
47. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
48. SALD.discreteForwardKlResidualIntegralDisplayBoundScalar
49. sald.discrete_forward_kl.linear_slowdown_specialization
50. sald.discrete_forward_kl.residual_exponent_bound
51. sald.discrete_forward_kl.accumulated_error_bridge
52. sald.discrete_forward_kl.coefficient_chain_audit
53. lem:gronwall
54. lem:dv_variation
55. eq:LSI-KL-FI
56. def:alpha-complexity
57. thm:forward-KL

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 EM/Fokker-Planck, frozen-delta, LSI/KL/FI, DV, Gronwall, accumulated-error collection, continuous derivative, theorem status, or SLT reuse status.

def cycle66DiscreteForwardKlSkeletonObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle66_discrete_route"
  statement := "Cycle 66 upper records the post-cycle-65 global phase judgment and wires thm:forward-KL-discrete through the five source-cited analytic interfaces in the paper order: appendix.tex:260-385 EM interpolation endpoint/conditional-Fokker-Planck setup, appendix.tex:388-491 discrete KL derivative with frozen defect and LSI, appendix.tex:493-523 DV velocity-energy, appendix.tex:526-553 time-changed Gronwall input, and appendix.tex:557-592 Gronwall output/accumulated-error collection to main_body.tex:309-323. The selected lower packet is sald.discrete_forward_kl.accumulated_error_bridge."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle66DiscreteForwardKlSkeletonUpperPacket",
    "SALD.cycle65ForwardKlSkeletonMiddleObligation",
    "SALD.cycle65ForwardKlDerivativePointwiseLowerObligation",
    "SALD.cycle64MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle64MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle61DiscreteForwardKlSkeletonObligation",
    "SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "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.discreteForwardKlDerivativeObligation",
    "sald.discrete_forward_kl.kl_derivative",
    "SALD.frozenDeltaCrossLipSaldContract",
    "sald.discrete_forward_kl.frozen_delta_cross_lip",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "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.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged",
    "sald.discrete_forward_kl.gronwall_accumulation",
    "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
    "SALD.discreteForwardKlAccumulatedErrorBridgeObligation",
    "SALD.discreteForwardKlGronwallCoeffIntervalIntegrable",
    "SALD.discreteForwardKlGronwallCoeffIntegralSubSub",
    "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
    "SALD.discreteForwardKlResidualExponentBoundScalar",
    "SALD.discreteForwardKlResidualExpBoundScalar",
    "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
    "SALD.discreteForwardKlDeltaAccumulationScalar",
    "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
    "SALD.discreteForwardKlResidualIntegralDisplayBoundScalar",
    "sald.discrete_forward_kl.linear_slowdown_specialization",
    "sald.discrete_forward_kl.residual_exponent_bound",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "sald.discrete_forward_kl.coefficient_chain_audit",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity",
    "thm:forward-KL"
  ]
  note := "Upper workflow obligation only. It adds no theorem hypotheses and does not promote EM/Fokker-Planck, frozen-delta, LSI/KL/FI, DV, Gronwall, accumulated-error collection, continuous derivative, theorem status, or SLT reuse status."

/-- Cycle-66 middle audit for the post-cycle-65 discrete forward-KL route.

This keeps the theorem-level transcript fixed while moving lower work to the
Gronwall output and accumulated-error bridge selected by the upper packet.
-/