Samplinglib
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AutoSamplingTheory.SALD.cycle58UnifiedDiscreteGeneralSkeletonObligation

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 cycle58UnifiedDiscreteGeneralSkeletonObligation : 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_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 58 upper records that cycle 57 needs no recovery, rechecks the five slow analytic backends, wires thm:unified-forward-KL through prop:guided_path_residual, the correction-field transport bridge, and thm:general-moving-target-SALD, and wires thm:general-moving-target-SALD-discrete through the general EM endpoint/conditional-Fokker-Planck interface, frozen-delta side conditions, discrete KL derivative/DV handoff, eq:LSI-KL-FI, lem:dv_variation, and lem:gronwall. The selected lower packet is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600; 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.cycle58UnifiedDiscreteGeneralUpperPacket
  2. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
  3. SALD.cycle54MainSkeletonAnalyticMiddleObligation
  4. SALD.cycle55ForwardKlSkeletonMiddleObligation
  5. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
  6. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
  7. SALD.cycle57GuidedGeneralSkeletonObligation
  8. SALD.cycle57GuidedGeneralSkeletonMiddleObligation
  9. SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation
  10. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
  11. SALD.cycle53UnifiedDiscreteGeneralMiddleObligation
  12. SALD.unifiedForwardKlSpecializationContract
  13. sald.unified_forward_kl.transport_velocity_bridge
  14. sald.unified_forward_kl.specialization
  15. SALD.generalMovingTargetStatementContract
  16. sald.general_moving_target.kl_derivative
  17. sald.general_moving_target.dv_m_energy
  18. sald.general_moving_target.gronwall_application
  19. sald.general_moving_target.gronwall_side_conditions
  20. SALD.generalMovingTargetDiscreteStatementContract
  21. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
  22. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
  23. sald.general_moving_target_discrete.em_interpolation_fp
  24. sald.general_moving_target_discrete.derivative_side_conditions
  25. sald.general_moving_target_discrete.kl_derivative
  26. sald.general_moving_target_discrete.dv_finite_log_mgf_witness
  27. sald.general_moving_target_discrete.dv_m_energy
  28. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
  29. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
  30. sald.general_moving_target_discrete.gronwall_application
  31. sald.general_moving_target_discrete.constant_schedule_stitching
  32. sald.general_moving_target_discrete.cycle20_gronwall_middle
  33. sald.general_moving_target_discrete.gronwall_side_conditions
  34. SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar
  35. SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar
  36. SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar
  37. SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar
  38. sald.general_moving_target_discrete.unified_specialization
  39. lem:gronwall
  40. lem:dv_variation
  41. eq:LSI-KL-FI
  42. 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, not an analytic proof. It adds no hidden endpoint, density, absolute-continuity, finite-log-mgf, finite-KL/FI, 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 cycle58UnifiedDiscreteGeneralSkeletonObligation : ProofObligation where
  id := "sald.unified_discrete_general.cycle58_upper_route"
  statement := "Cycle 58 upper records that cycle 57 needs no recovery, rechecks the five slow analytic backends, wires thm:unified-forward-KL through prop:guided_path_residual, the correction-field transport bridge, and thm:general-moving-target-SALD, and wires thm:general-moving-target-SALD-discrete through the general EM endpoint/conditional-Fokker-Planck interface, frozen-delta side conditions, discrete KL derivative/DV handoff, eq:LSI-KL-FI, lem:dv_variation, and lem:gronwall. The selected lower packet is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600; all theorem statuses and slow analytic interfaces remain below formalized."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle58UnifiedDiscreteGeneralUpperPacket",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "SALD.cycle57GuidedGeneralSkeletonObligation",
    "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle57GuidedGeneralDerivativeSplitLowerObligation",
    "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle53UnifiedDiscreteGeneralMiddleObligation",
    "SALD.unifiedForwardKlSpecializationContract",
    "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_m_energy",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "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.generalMovingTargetDiscreteGronwallInstantiationContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.constant_schedule_stitching",
    "sald.general_moving_target_discrete.cycle20_gronwall_middle",
    "sald.general_moving_target_discrete.gronwall_side_conditions",
    "SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar",
    "SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar",
    "sald.general_moving_target_discrete.unified_specialization",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is an upper workflow obligation and theorem-route refresh, not an analytic proof. It adds no hidden endpoint, density, absolute-continuity, finite-log-mgf, finite-KL/FI, conditional-law, schedule, sigma-positivity, or coefficient-regularity assumptions to the source theorem statements."

/-- Cycle-58 middle audit for the unified/discrete general route.

This source-to-Lean synchronization layer checks the upper route against the
paper order and hands lower work to the discrete general Gronwall/display
backend over `appendix.tex:1573-1600`.
-/

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