AutoSamplingTheory.SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation

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 cycle53UnifiedDiscreteGeneralSkeletonObligation : 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.unified_discrete_general.cycle53_upper_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 53 upper wires thm:unified-forward-KL through the cycle-52 continuous general route, the guided residual/correction-field transport bridge, and the source specialization c_t=u_t, m_t=w_t; it wires thm:general-moving-target-SALD-discrete through the general EM endpoint/conditional-Fokker-Planck interface, frozen-delta side conditions, discrete KL derivative side conditions, eq:LSI-KL-FI, lem:dv_variation residual witness, and lem:gronwall side conditions. After that theorem-level route check, it backfills only the Measure.map a.e.-equality endpoint-law handoff for the discrete general EM interpolation.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteSource — 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.cycle49MainSkeletonAnalyticReadinessObligation
2. SALD.cycle49MainSkeletonAnalyticMiddleObligation
3. SALD.cycle52GuidedGeneralSkeletonObligation
4. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
5. SALD.cycle52GuidedGeneralDerivativeDvLowerObligation
6. SALD.cycle48UnifiedDiscreteSkeletonObligation
7. SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation
8. SALD.cycle53UnifiedDiscreteGeneralUpperPacket
9. SALD.unifiedForwardKlSpecializationContract
10. SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract
11. SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract
12. sald.unified_forward_kl.transport_velocity_bridge
13. sald.unified_forward_kl.specialization
14. SALD.generalMovingTargetStatementContract
15. SALD.generalMovingTargetDerivativeCandidateContract
16. SALD.generalMovingTargetDerivativeObligation
17. sald.general_moving_target.kl_derivative
18. sald.general_moving_target.dv_m_energy
19. sald.general_moving_target.gronwall_side_conditions
20. SALD.generalMovingTargetDiscreteStatementContract
21. SALD.generalVaSaldEulerMaruyamaContract
22. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
23. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
24. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
25. AutoSamplingTheory.lawMapEqOfAEEq
26. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
27. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
28. sald.general_moving_target_discrete.em_interpolation_fp
29. sald.general_moving_target_discrete.derivative_side_conditions
30. sald.general_moving_target_discrete.kl_derivative
31. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
32. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
33. sald.general_moving_target_discrete.dv_m_energy
34. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
35. sald.general_moving_target_discrete.gronwall_application
36. sald.general_moving_target_discrete.gronwall_side_conditions
37. lem:gronwall
38. lem:dv_variation
39. eq:LSI-KL-FI

note : String (explicit)

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

This is an upper route check plus one narrow compiled measure-level endpoint-law lemma. It does not prove the conditional drift, density/absolute-continuity, Fokker-Planck, KL derivative, LSI, DV, Gronwall, unified theorem, or discrete general theorem.

def cycle53UnifiedDiscreteGeneralSkeletonObligation : ProofObligation where
  id := "sald.unified_discrete_general.cycle53_upper_route"
  statement := "Cycle 53 upper wires thm:unified-forward-KL through the cycle-52 continuous general route, the guided residual/correction-field transport bridge, and the source specialization c_t=u_t, m_t=w_t; it wires thm:general-moving-target-SALD-discrete through the general EM endpoint/conditional-Fokker-Planck interface, frozen-delta side conditions, discrete KL derivative side conditions, eq:LSI-KL-FI, lem:dv_variation residual witness, and lem:gronwall side conditions. After that theorem-level route check, it backfills only the Measure.map a.e.-equality endpoint-law handoff for the discrete general EM interpolation."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle52GuidedGeneralSkeletonObligation",
    "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle52GuidedGeneralDerivativeDvLowerObligation",
    "SALD.cycle48UnifiedDiscreteSkeletonObligation",
    "SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation",
    "SALD.cycle53UnifiedDiscreteGeneralUpperPacket",
    "SALD.unifiedForwardKlSpecializationContract",
    "SALD.cycle16UnifiedForwardKlTransportBridgeMiddleContract",
    "SALD.cycle16UnifiedForwardKlTransportBridgeLowerContract",
    "sald.unified_forward_kl.transport_velocity_bridge",
    "sald.unified_forward_kl.specialization",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "sald.general_moving_target.kl_derivative",
    "sald.general_moving_target.dv_m_energy",
    "sald.general_moving_target.gronwall_side_conditions",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalVaSaldEulerMaruyamaContract",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "AutoSamplingTheory.lawMapEqOfAEEq",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.derivative_side_conditions",
    "sald.general_moving_target_discrete.kl_derivative",
    "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
    "sald.general_moving_target_discrete.dv_finite_log_mgf_witness",
    "sald.general_moving_target_discrete.dv_m_energy",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.gronwall_side_conditions",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI"
  ]
  note := "This is an upper route check plus one narrow compiled measure-level endpoint-law lemma. It does not prove the conditional drift, density/absolute-continuity, Fokker-Planck, KL derivative, LSI, DV, Gronwall, unified theorem, or discrete general theorem."

/-- Cycle-53 middle audit for the final unified/discrete general route.

This synchronizes the upper route packet with the conversion window and
proof-obligation ledger.  It keeps the source proof order fixed and leaves the
next lower target on the discrete general KL derivative backend over
`appendix.tex:1354-1387`.
-/