AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation

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 cycle68UnifiedDiscreteGeneralSkeletonObligation : 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.cycle68_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 68 upper records that cycle 67 passed, then rewires thm:unified-forward-KL through prop:guided_path_residual, eq:poisson-eq, the transport-velocity bridge, and thm:general-moving-target-SALD; it also rewires thm:general-moving-target-SALD-discrete through the general EM endpoint/conditional-law interface, frozen-delta lemma, discrete KL derivative/LSI route, residual DV, constant-schedule time change, and final Gronwall/display side conditions over appendix.tex:1313-1603. The selected lower packet is sald.unified_discrete_general.cycle68_discrete_general_bridge. Both theorem contracts remain contractOnly.

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.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket
2. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
3. SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation
4. SALD.cycle67GuidedGeneralResidualGronwallLowerObligation
5. SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation
6. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
7. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
8. SALD.cycle64MainSkeletonAnalyticMiddleObligation
9. SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation
10. SALD.guidedResidualIdentityContract
11. sald.guided_path_residual.identity
12. SALD.unifiedForwardKlSpecializationContract
13. sald.unified_forward_kl.transport_velocity_bridge
14. sald.unified_forward_kl.specialization
15. SALD.generalMovingTargetStatementContract
16. SALD.generalVaSaldContract
17. SALD.generalMovingTargetDiscreteStatementContract
18. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
19. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
20. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
21. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
22. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
23. SALD.generalMovingTargetDiscreteConditionalDriftContract
24. sald.general_moving_target_discrete.em_interpolation_fp
25. sald.general_moving_target_discrete.frozen_delta_cross_lip
26. sald.general_moving_target_discrete.kl_derivative
27. SALD.saldLsiKlFiDensityTestContract
28. probability.lsi_to_kl_fi
29. dvVariationalFormulaInterface saldDvVariationSource
30. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
31. sald.general_moving_target_discrete.dv_m_energy
32. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
33. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
34. sald.general_moving_target_discrete.gronwall_application
35. sald.general_moving_target_discrete.gronwall_side_conditions
36. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation
37. lem:gronwall
38. lem:dv_variation
39. eq:LSI-KL-FI
40. def:alpha-complexity

note : String (explicit)

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

Upper workflow obligation only. It adds no hidden hypotheses, direct VA-SALD proof replacement, analytic proof closure, or status promotion.

def cycle68UnifiedDiscreteGeneralSkeletonObligation : ProofObligation where
  id := "sald.unified_discrete_general.cycle68_upper_route"
  statement := "Cycle 68 upper records that cycle 67 passed, then rewires thm:unified-forward-KL through prop:guided_path_residual, eq:poisson-eq, the transport-velocity bridge, and thm:general-moving-target-SALD; it also rewires thm:general-moving-target-SALD-discrete through the general EM endpoint/conditional-law interface, frozen-delta lemma, discrete KL derivative/LSI route, residual DV, constant-schedule time change, and final Gronwall/display side conditions over appendix.tex:1313-1603. The selected lower packet is sald.unified_discrete_general.cycle68_discrete_general_bridge. Both theorem contracts remain contractOnly."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket",
    "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation",
    "SALD.cycle67GuidedGeneralResidualGronwallLowerObligation",
    "SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
    "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation",
    "SALD.cycle64MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.identity",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.unified_forward_kl.transport_velocity_bridge",
    "sald.unified_forward_kl.specialization",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalVaSaldContract",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.frozen_delta_cross_lip",
    "sald.general_moving_target_discrete.kl_derivative",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
    "sald.general_moving_target_discrete.dv_m_energy",
    "SALD.generalMovingTargetDiscreteGronwallInstantiationContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.gronwall_side_conditions",
    "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "Upper workflow obligation only. It adds no hidden hypotheses, direct VA-SALD proof replacement, analytic proof closure, or status promotion."

/-- Cycle-68 source-cited bridge for the final unified/discrete general
theorem route. -/