AutoSamplingTheory.SALD.cycle61DiscreteForwardKlSkeletonObligation

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 cycle61DiscreteForwardKlSkeletonObligation : 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.cycle61_recovered_theorem_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 61 upper records that cycle 60 passed and recovers the interrupted cycle-56 thm:forward-KL-discrete route. It wires main_body.tex:299-323 and appendix.tex:260-592 through the explicit EM endpoint/conditional-Fokker-Planck interface, discrete KL derivative with frozen defect and LSI, DV velocity witness, cycle-56 t-time Gronwall input, and the linear-slowdown accumulated-error bridge. The selected lower packet is sald.discrete_forward_kl.accumulated_error_bridge over appendix.tex:557-590 and main_body.tex:309-323, with all theorem statuses and slow analytic interfaces kept below formalized.

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.cycle61DiscreteForwardKlSkeletonUpperPacket
2. SALD.cycle60ForwardKlSkeletonMiddleObligation
3. SALD.cycle60ForwardKlDerivativeRawLowerObligation
4. SALD.cycle59MainSkeletonAnalyticInterfaceObligation
5. SALD.cycle59MainSkeletonAnalyticMiddleObligation
6. SALD.cycle56DiscreteForwardKlSkeletonObligation
7. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
8. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
9. SALD.cycle51DiscreteForwardKlSkeletonObligation
10. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
11. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
12. SALD.discreteForwardKlStatementContract
13. SALD.discreteForwardKlEmInterpolationSideConditionContract
14. sald.discrete_forward_kl.em_endpoint_laws
15. sald.discrete_forward_kl.conditional_drift_density
16. sald.discrete_forward_kl.em_conditional_fokker_planck
17. sald.discrete_forward_kl.stitched_interval_regularity
18. sald.discrete_forward_kl.em_interpolation_fp
19. SALD.discreteForwardKlDerivativeCandidateContract
20. SALD.discreteForwardKlDerivativeObligation
21. sald.discrete_forward_kl.kl_derivative
22. SALD.frozenDeltaCrossLipSaldContract
23. sald.discrete_forward_kl.frozen_delta_cross_lip
24. SALD.saldLsiKlFiDensityTestContract
25. probability.lsi_to_kl_fi
26. dvVariationalFormulaInterface saldDvVariationSource
27. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
28. sald.discrete_forward_kl.dv_finite_log_mgf_witness
29. sald.discrete_forward_kl.dv_velocity_bound
30. SALD.saldGronwallEndpointCalculusContract
31. SALD.discreteForwardKlGronwallInstantiationContract
32. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
33. SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged
34. sald.discrete_forward_kl.gronwall_accumulation
35. SALD.discreteForwardKlAccumulatedErrorBridgeContract
36. SALD.discreteForwardKlAccumulatedErrorBridgeObligation
37. sald.discrete_forward_kl.linear_slowdown_specialization
38. sald.discrete_forward_kl.residual_exponent_bound
39. sald.discrete_forward_kl.accumulated_error_bridge
40. sald.discrete_forward_kl.coefficient_chain_audit
41. lem:gronwall
42. lem:dv_variation
43. eq:LSI-KL-FI
44. def:alpha-complexity
45. thm:forward-KL

note : String (explicit)

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

Upper workflow and source-to-Lean route data only. It adds no theorem hypotheses, changes no source constants, and does not promote EM/Fokker-Planck, frozen-delta, LSI/KL/FI, DV, Gronwall, accumulated-error, continuous derivative, SLT reuse, or thm:forward-KL-discrete.

def cycle61DiscreteForwardKlSkeletonObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle61_recovered_theorem_route"
  statement := "Cycle 61 upper records that cycle 60 passed and recovers the interrupted cycle-56 thm:forward-KL-discrete route. It wires main_body.tex:299-323 and appendix.tex:260-592 through the explicit EM endpoint/conditional-Fokker-Planck interface, discrete KL derivative with frozen defect and LSI, DV velocity witness, cycle-56 t-time Gronwall input, and the linear-slowdown accumulated-error bridge. The selected lower packet is sald.discrete_forward_kl.accumulated_error_bridge over appendix.tex:557-590 and main_body.tex:309-323, with all theorem statuses and slow analytic interfaces kept below formalized."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle61DiscreteForwardKlSkeletonUpperPacket",
    "SALD.cycle60ForwardKlSkeletonMiddleObligation",
    "SALD.cycle60ForwardKlDerivativeRawLowerObligation",
    "SALD.cycle59MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle59MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "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.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.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.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 and source-to-Lean route data only. It adds no theorem hypotheses, changes no source constants, and does not promote EM/Fokker-Planck, frozen-delta, LSI/KL/FI, DV, Gronwall, accumulated-error, continuous derivative, SLT reuse, or thm:forward-KL-discrete."

/-- Cycle-61 middle audit for the recovered discrete forward-KL route.

This synchronizes the upper packet with the source transcript and moves lower
work from the cycle-56 pointwise Gronwall input to the accumulated-error bridge
that matches the main-body linear-slowdown theorem display.
-/