AutoSamplingTheory.SALD.cycle58UnifiedDiscreteGeneralMiddleObligation

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 cycle58UnifiedDiscreteGeneralMiddleObligation : 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.cycle58_middle_route_audit

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 58 middle audits the final unified/discrete general route after the upper refresh: thm:unified-forward-KL remains the paper specialization of the continuous general theorem through the correction-field transport bridge, thm:general-moving-target-SALD-discrete remains the source route through EM interpolation, frozen-delta, LSI, residual DV, and Gronwall, and the next lower target is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600 for endpoint stitching, constant-schedule coefficient rewrites, coefficient regularity, and exact theorem-display matching.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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.cycle58UnifiedDiscreteGeneralUpperPacket
2. SALD.cycle58UnifiedDiscreteGeneralSkeletonObligation
3. SALD.cycle58UnifiedDiscreteGeneralMiddleContract
4. SALD.cycle57GuidedGeneralSkeletonMiddleObligation
5. SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation
6. SALD.cycle53UnifiedDiscreteGeneralMiddleObligation
7. SALD.cycle53GeneralMovingTargetDiscreteDerivativeDvLowerObligation
8. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
9. SALD.unifiedForwardKlSpecializationContract
10. sald.unified_forward_kl.transport_velocity_bridge
11. sald.unified_forward_kl.specialization
12. SALD.generalMovingTargetStatementContract
13. SALD.generalVaSaldContract
14. sald.general_moving_target.kl_derivative
15. sald.general_moving_target.gronwall_side_conditions
16. SALD.generalMovingTargetDiscreteStatementContract
17. SALD.generalVaSaldDiscreteContract
18. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
19. sald.general_moving_target_discrete.em_interpolation_fp
20. sald.general_moving_target_discrete.kl_derivative
21. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
22. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
23. sald.general_moving_target_discrete.dv_m_energy
24. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
25. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
26. SALD.generalMovingTargetDiscreteGronwallSideConditionObligation
27. SALD.cycle20GeneralVaSaldDiscreteGronwallMiddleObligation
28. SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar
29. SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar
30. SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar
31. SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar
32. sald.general_moving_target_discrete.constant_schedule_stitching
33. sald.general_moving_target_discrete.gronwall_application
34. sald.general_moving_target_discrete.gronwall_side_conditions
35. lem:gronwall
36. lem:dv_variation
37. eq:LSI-KL-FI

note : String (explicit)

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

This is middle-role synchronization data and lower-packet selection, not a theorem proof. It adds no hidden endpoint, density, absolute-continuity, regular conditional law, finite-log-mgf, finite-KL/FI, schedule, sigma-positivity, coefficient-regularity, or Gronwall assumptions to the paper statements.

def cycle58UnifiedDiscreteGeneralMiddleObligation : ProofObligation where
  id := "sald.unified_discrete_general.cycle58_middle_route_audit"
  statement := "Cycle 58 middle audits the final unified/discrete general route after the upper refresh: thm:unified-forward-KL remains the paper specialization of the continuous general theorem through the correction-field transport bridge, thm:general-moving-target-SALD-discrete remains the source route through EM interpolation, frozen-delta, LSI, residual DV, and Gronwall, and the next lower target is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600 for endpoint stitching, constant-schedule coefficient rewrites, coefficient regularity, and exact theorem-display matching."
  source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle58UnifiedDiscreteGeneralUpperPacket",
    "SALD.cycle58UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle58UnifiedDiscreteGeneralMiddleContract",
    "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation",
    "SALD.cycle53UnifiedDiscreteGeneralMiddleObligation",
    "SALD.cycle53GeneralMovingTargetDiscreteDerivativeDvLowerObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.unified_forward_kl.transport_velocity_bridge",
    "sald.unified_forward_kl.specialization",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalVaSaldContract",
    "sald.general_moving_target.kl_derivative",
    "sald.general_moving_target.gronwall_side_conditions",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalVaSaldDiscreteContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "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.generalMovingTargetDiscreteGronwallInstantiationContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionObligation",
    "SALD.cycle20GeneralVaSaldDiscreteGronwallMiddleObligation",
    "SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar",
    "SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar",
    "sald.general_moving_target_discrete.constant_schedule_stitching",
    "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 middle-role synchronization data and lower-packet selection, not a theorem proof. It adds no hidden endpoint, density, absolute-continuity, regular conditional law, finite-log-mgf, finite-KL/FI, schedule, sigma-positivity, coefficient-regularity, or Gronwall assumptions to the paper statements."

/-- Cycle-58 proof-DAG pane for the final unified/discrete general route
refresh and selected lower packet. -/