Samplinglib
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AutoSamplingTheory.SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle63UnifiedDiscreteGeneralSkeletonObligation :
    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.cycle63_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 63 upper records that cycle 62 passed and needs no recovery, that Phase 1 theorem-skeleton translation is stable enough for one narrow endpoint-law backfill after route wiring, and that thm:unified-forward-KL and thm:general-moving-target-SALD-discrete remain wired through the accepted continuous/general skeletons and explicit source-cited interfaces. The route consumes prop:guided_path_residual, the correction-field transport bridge, thm:general-moving-target-SALD, general EM endpoint/conditional-Fokker-Planck interfaces, frozen-delta side conditions, discrete KL derivative/LSI, residual DV, lem:gronwall, and theorem-display stitching. All theorem statuses and slow analytic interfaces remain below formalized.
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.cycle63UnifiedDiscreteGeneralSkeletonUpperPacket
  2. SALD.cycle62GuidedGeneralSkeletonObligation
  3. SALD.cycle62GuidedGeneralSkeletonMiddleObligation
  4. SALD.cycle62GuidedGeneralScaledResidualLowerObligation
  5. SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation
  6. SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation
  7. SALD.cycle60ForwardKlSkeletonMiddleObligation
  8. SALD.cycle59MainSkeletonAnalyticInterfaceObligation
  9. SALD.cycle59MainSkeletonAnalyticMiddleObligation
  10. SALD.cycle58UnifiedDiscreteGeneralSkeletonObligation
  11. SALD.cycle58UnifiedDiscreteGeneralMiddleObligation
  12. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
  13. SALD.cycle53UnifiedDiscreteGeneralMiddleObligation
  14. SALD.guidedResidualIdentityContract
  15. sald.guided_path_residual.identity
  16. SALD.generalMovingTargetStatementContract
  17. SALD.generalMovingTargetDerivativeCandidateContract
  18. sald.general_moving_target.kl_derivative
  19. sald.general_moving_target.dv_m_energy
  20. sald.general_moving_target.gronwall_side_conditions
  21. SALD.unifiedForwardKlSpecializationContract
  22. sald.unified_forward_kl.transport_velocity_bridge
  23. sald.unified_forward_kl.specialization
  24. SALD.generalMovingTargetDiscreteStatementContract
  25. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
  26. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
  27. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
  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.general_moving_target_discrete.dv_finite_log_mgf_witness
  32. sald.general_moving_target_discrete.dv_m_energy
  33. sald.general_moving_target_discrete.gronwall_application
  34. sald.general_moving_target_discrete.gronwall_side_conditions
  35. AutoSamplingTheory.lawMapEqOfAEEq
  36. AutoSamplingTheory.lawMapProdEqOfAEEq
  37. AutoSamplingTheory.lawMapProdFst
  38. AutoSamplingTheory.lawMapProdSnd
  39. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
  40. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
  41. lem:gronwall
  42. lem:dv_variation
  43. eq:LSI-KL-FI
  44. 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 refresh. It does not add hidden endpoint, common-space, density, absolute-continuity, finite-KL/FI, finite-log-mgf, conditional-law, schedule, sigma-positivity, or coefficient-regularity assumptions to the source theorem statements.
Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle63UnifiedDiscreteGeneralSkeletonObligation :
    ProofObligation where
  id := "sald.unified_discrete_general.cycle63_upper_route"
  statement := "Cycle 63 upper records that cycle 62 passed and needs no recovery, that Phase 1 theorem-skeleton translation is stable enough for one narrow endpoint-law backfill after route wiring, and that thm:unified-forward-KL and thm:general-moving-target-SALD-discrete remain wired through the accepted continuous/general skeletons and explicit source-cited interfaces. The route consumes prop:guided_path_residual, the correction-field transport bridge, thm:general-moving-target-SALD, general EM endpoint/conditional-Fokker-Planck interfaces, frozen-delta side conditions, discrete KL derivative/LSI, residual DV, lem:gronwall, and theorem-display stitching. All theorem statuses and slow analytic interfaces remain below formalized."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle63UnifiedDiscreteGeneralSkeletonUpperPacket",
    "SALD.cycle62GuidedGeneralSkeletonObligation",
    "SALD.cycle62GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle62GuidedGeneralScaledResidualLowerObligation",
    "SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation",
    "SALD.cycle60ForwardKlSkeletonMiddleObligation",
    "SALD.cycle59MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle59MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle58UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle58UnifiedDiscreteGeneralMiddleObligation",
    "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle53UnifiedDiscreteGeneralMiddleObligation",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.identity",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "sald.general_moving_target.kl_derivative",
    "sald.general_moving_target.dv_m_energy",
    "sald.general_moving_target.gronwall_side_conditions",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.unified_forward_kl.transport_velocity_bridge",
    "sald.unified_forward_kl.specialization",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "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.gronwall_side_conditions",
    "AutoSamplingTheory.lawMapEqOfAEEq",
    "AutoSamplingTheory.lawMapProdEqOfAEEq",
    "AutoSamplingTheory.lawMapProdFst",
    "AutoSamplingTheory.lawMapProdSnd",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is an upper workflow obligation and theorem-route refresh. It does not add hidden endpoint, common-space, density, absolute-continuity, finite-KL/FI, finite-log-mgf, conditional-law, schedule, sigma-positivity, or coefficient-regularity assumptions to the source theorem statements."

/-- Cycle-63 narrow measure-theory backfill below the discrete general EM
endpoint-law interface. -/

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