Samplinglib
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AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation

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 cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation :
    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_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 68 middle audits the upper unified/discrete-general route in paper order: thm:unified-forward-KL remains the source specialization of thm:general-moving-target-SALD through the guided residual and correction-field transport bridge, thm:general-moving-target-SALD-discrete remains the appendix route through EM endpoint/conditional-FP, frozen-delta, LSI, residual DV, time change, and Gronwall/display interfaces, and the selected lower packet remains sald.unified_discrete_general.cycle68_discrete_general_bridge. 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.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket
  2. SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation
  3. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleContract
  4. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation
  5. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
  6. SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation
  7. SALD.cycle67GuidedGeneralResidualGronwallLowerObligation
  8. SALD.cycle63UnifiedDiscreteGeneralSkeletonObligation
  9. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
  10. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
  11. SALD.cycle64MainSkeletonAnalyticMiddleObligation
  12. SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation
  13. SALD.guidedResidualIdentityContract
  14. sald.guided_path_residual.identity
  15. SALD.unifiedForwardKlSpecializationContract
  16. sald.unified_forward_kl.transport_velocity_bridge
  17. sald.unified_forward_kl.specialization
  18. SALD.generalMovingTargetStatementContract
  19. SALD.generalVaSaldContract
  20. SALD.generalMovingTargetDiscreteStatementContract
  21. SALD.generalVaSaldDiscreteContract
  22. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
  23. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
  24. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
  25. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
  26. SALD.generalMovingTargetDiscreteConditionalDriftContract
  27. sald.general_moving_target_discrete.em_interpolation_fp
  28. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
  29. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
  30. sald.general_moving_target_discrete.frozen_delta_cross_lip
  31. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
  32. SALD.generalMovingTargetDiscreteYoungFisherShareScalar
  33. SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar
  34. SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar
  35. sald.general_moving_target_discrete.kl_derivative
  36. SALD.saldLsiKlFiDensityTestContract
  37. SALD.lsiKlFiDensityTestObligation
  38. probability.lsi_to_kl_fi
  39. dvVariationalFormulaInterface saldDvVariationSource
  40. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
  41. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
  42. sald.general_moving_target_discrete.dv_m_energy
  43. SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar
  44. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
  45. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
  46. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
  47. SALD.generalMovingTargetDiscreteGronwallDisplayBridgeScalar
  48. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
  49. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
  50. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
  51. sald.general_moving_target_discrete.gronwall_application
  52. sald.general_moving_target_discrete.gronwall_side_conditions
  53. lem:gronwall
  54. lem:dv_variation
  55. eq:LSI-KL-FI
  56. def:alpha-complexity
note : String (explicit)

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

Middle workflow and source-to-Lean audit only. It adds no hidden common-space, density, absolute-continuity, finite-KL/FI, finite-log-mgf, regular conditional law, weak Fokker-Planck, schedule, sigma-positivity, endpoint, or coefficient-regularity assumptions to the paper 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 cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation :
    ProofObligation where
  id := "sald.unified_discrete_general.cycle68_middle_route_audit"
  statement := "Cycle 68 middle audits the upper unified/discrete-general route in paper order: thm:unified-forward-KL remains the source specialization of thm:general-moving-target-SALD through the guided residual and correction-field transport bridge, thm:general-moving-target-SALD-discrete remains the appendix route through EM endpoint/conditional-FP, frozen-delta, LSI, residual DV, time change, and Gronwall/display interfaces, and the selected lower packet remains sald.unified_discrete_general.cycle68_discrete_general_bridge. All theorem statuses and slow analytic interfaces remain below formalized."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket",
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleContract",
    "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation",
    "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.generalVaSaldDiscreteContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.frozen_delta_cross_lip",
    "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
    "SALD.generalMovingTargetDiscreteYoungFisherShareScalar",
    "SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar",
    "SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar",
    "sald.general_moving_target_discrete.kl_derivative",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.lsiKlFiDensityTestObligation",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
    "sald.general_moving_target_discrete.dv_finite_log_mgf_witness",
    "sald.general_moving_target_discrete.dv_m_energy",
    "SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar",
    "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
    "SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput",
    "SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar",
    "SALD.generalMovingTargetDiscreteGronwallDisplayBridgeScalar",
    "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation",
    "SALD.generalMovingTargetDiscreteGronwallInstantiationContract",
    "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",
    "def:alpha-complexity"
  ]
  note := "Middle workflow and source-to-Lean audit only. It adds no hidden common-space, density, absolute-continuity, finite-KL/FI, finite-log-mgf, regular conditional law, weak Fokker-Planck, schedule, sigma-positivity, endpoint, or coefficient-regularity assumptions to the paper theorem statements."

/-- Cycle-68 lower proof-producing obligation for the final discrete general
Gronwall/display bridge. -/

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