AutoSamplingTheory.SALD.cycle48UnifiedDiscreteSkeletonObligation

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 cycle48UnifiedDiscreteSkeletonObligation : 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.cycle48_theorem_skeleton_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 48 upper wires the final two main-skeleton theorem nodes. thm:unified-forward-KL is routed through prop:guided_path_residual, eq:poisson-eq, the transport-velocity bridge, and thm:general-moving-target-SALD with c_t=u_t and m_t=w_t. thm:general-moving-target-SALD-discrete is routed through the general EM interpolation Fokker-Planck backend, frozen-delta lemma, discrete KL derivative side conditions, eq:LSI-KL-FI, lem:dv_variation with the residual m_t finite-log-mgf witness, lem:gronwall with constant-schedule stitching, and the discrete guided specialization. All slow analytic backends remain obligation or source-cited.

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.cycle44MainSkeletonAnalyticInterfaceObligation
2. SALD.cycle47GuidedGeneralSkeletonObligation
3. SALD.cycle47GuidedGeneralSkeletonMiddleObligation
4. SALD.cycle48UnifiedDiscreteSkeletonUpperPacket
5. SALD.guidedResidualIdentityContract
6. sald.guided_path_residual.identity
7. SALD.unifiedForwardKlSpecializationContract
8. sald.unified_forward_kl.transport_bridge_middle
9. sald.unified_forward_kl.transport_bridge_lower
10. sald.unified_forward_kl.transport_velocity_bridge
11. sald.unified_forward_kl.specialization
12. SALD.generalMovingTargetStatementContract
13. sald.general_moving_target.kl_derivative
14. sald.general_moving_target.dv_finite_log_mgf_witness
15. sald.general_moving_target.dv_m_energy
16. sald.general_moving_target.gronwall_application
17. sald.general_moving_target.gronwall_side_conditions
18. SALD.generalMovingTargetDiscreteStatementContract
19. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
20. sald.general_moving_target_discrete.em_interpolation_fp
21. sald.general_moving_target_discrete.frozen_delta_cross_lip
22. sald.general_moving_target_discrete.derivative_side_conditions
23. sald.general_moving_target_discrete.kl_derivative
24. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
25. sald.general_moving_target_discrete.dv_m_energy
26. sald.general_moving_target_discrete.gronwall_application
27. sald.general_moving_target_discrete.constant_schedule_stitching
28. sald.general_moving_target_discrete.gronwall_side_conditions
29. sald.general_moving_target_discrete.unified_specialization
30. probability.lsi_to_kl_fi
31. probability.dv_variational_formula
32. lem:gronwall
33. lem:dv_variation
34. eq:LSI-KL-FI
35. def:alpha-complexity

note : String (explicit)

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

This is an upper workflow obligation and theorem-route wrapper, not an analytic proof. It keeps the unified theorem as a specialization of the continuous general theorem and the discrete general theorem as the paper's EM/frozen-delta/DV/Gronwall route.

def cycle48UnifiedDiscreteSkeletonObligation : ProofObligation where
  id := "sald.unified_discrete_general.cycle48_theorem_skeleton_route"
  statement := "Cycle 48 upper wires the final two main-skeleton theorem nodes. thm:unified-forward-KL is routed through prop:guided_path_residual, eq:poisson-eq, the transport-velocity bridge, and thm:general-moving-target-SALD with c_t=u_t and m_t=w_t. thm:general-moving-target-SALD-discrete is routed through the general EM interpolation Fokker-Planck backend, frozen-delta lemma, discrete KL derivative side conditions, eq:LSI-KL-FI, lem:dv_variation with the residual m_t finite-log-mgf witness, lem:gronwall with constant-schedule stitching, and the discrete guided specialization. All slow analytic backends remain obligation or source-cited."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle47GuidedGeneralSkeletonObligation",
    "SALD.cycle47GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle48UnifiedDiscreteSkeletonUpperPacket",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.identity",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.unified_forward_kl.transport_bridge_middle",
    "sald.unified_forward_kl.transport_bridge_lower",
    "sald.unified_forward_kl.transport_velocity_bridge",
    "sald.unified_forward_kl.specialization",
    "SALD.generalMovingTargetStatementContract",
    "sald.general_moving_target.kl_derivative",
    "sald.general_moving_target.dv_finite_log_mgf_witness",
    "sald.general_moving_target.dv_m_energy",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.frozen_delta_cross_lip",
    "sald.general_moving_target_discrete.derivative_side_conditions",
    "sald.general_moving_target_discrete.kl_derivative",
    "sald.general_moving_target_discrete.dv_finite_log_mgf_witness",
    "sald.general_moving_target_discrete.dv_m_energy",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.constant_schedule_stitching",
    "sald.general_moving_target_discrete.gronwall_side_conditions",
    "sald.general_moving_target_discrete.unified_specialization",
    "probability.lsi_to_kl_fi",
    "probability.dv_variational_formula",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is an upper workflow obligation and theorem-route wrapper, not an analytic proof. It keeps the unified theorem as a specialization of the continuous general theorem and the discrete general theorem as the paper's EM/frozen-delta/DV/Gronwall route."

/-- Cycle-48 middle audit for the unified and discrete general theorem
route.

This source-to-Lean synchronization layer checks the upper route wrapper
against the exact TeX paragraphs and selects the next discrete KL-derivative
backend without changing the source theorem statements.
-/