Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticMiddleObligation

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 cycle69MainSkeletonAnalyticMiddleObligation : 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.main_skeleton.cycle69_middle_interface_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 69 middle synchronizes the upper analytic-interface ledger with the complete SALD theorem route: the five slow interfaces are consumed by thm:forward-KL, thm:forward-KL-discrete, prop:guided_path_residual, thm:general-moving-target-SALD, thm:unified-forward-KL, and thm:general-moving-target-SALD-discrete in paper order, and the selected lower packet remains the shared EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387. Theorem statuses and slow analytic interfaces remain below formalized.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.cycle69MainSkeletonAnalyticMiddleContract
  2. SALD.cycle69MainSkeletonAnalyticInterfaceObligation
  3. SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
  4. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
  5. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
  6. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
  7. SALD.cycle65ForwardKlSkeletonMiddleObligation
  8. SALD.cycle64MainSkeletonAnalyticMiddleObligation
  9. SALD.saldGronwallEndpointCalculusContract
  10. dvVariationalFormulaInterface saldDvVariationSource
  11. SALD.saldLsiKlFiDensityTestContract
  12. SALD.forwardKlDerivativeSideConditionContract
  13. SALD.generalMovingTargetDerivativeCandidateContract
  14. SALD.discreteForwardKlEmInterpolationSideConditionContract
  15. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
  16. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
  17. SALD.generalMovingTargetDiscreteConditionalDriftContract
  18. SALD.generalMovingTargetDiscreteConditionalDriftLinearCombination
  19. SALD.generalMovingTargetDiscreteConditionalDriftFieldOfLinearCombination
  20. sald.general_moving_target_discrete.em_interpolation_fp
  21. sald.discrete_forward_kl.em_interpolation_fp
  22. lem:gronwall
  23. lem:dv_variation
  24. eq:LSI-KL-FI
  25. thm:forward-KL
  26. thm:forward-KL-discrete
  27. prop:guided_path_residual
  28. thm:general-moving-target-SALD
  29. thm:unified-forward-KL
  30. thm:general-moving-target-SALD-discrete
note : String (explicit)

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

Middle workflow obligation only. It adds no hidden common-space, density, absolute-continuity, finite-KL/FI, finite-log-mgf, regular conditional law, weak Fokker-Planck, endpoint, schedule, sigma-positivity, coefficient-regularity, stitched-interval, or theorem-level assumption.
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 cycle69MainSkeletonAnalyticMiddleObligation : ProofObligation where
  id := "sald.main_skeleton.cycle69_middle_interface_audit"
  statement := "Cycle 69 middle synchronizes the upper analytic-interface ledger with the complete SALD theorem route: the five slow interfaces are consumed by thm:forward-KL, thm:forward-KL-discrete, prop:guided_path_residual, thm:general-moving-target-SALD, thm:unified-forward-KL, and thm:general-moving-target-SALD-discrete in paper order, and the selected lower packet remains the shared EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387. Theorem statuses and slow analytic interfaces remain below formalized."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle69MainSkeletonAnalyticMiddleContract",
    "SALD.cycle69MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation",
    "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation",
    "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle65ForwardKlSkeletonMiddleObligation",
    "SALD.cycle64MainSkeletonAnalyticMiddleObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftLinearCombination",
    "SALD.generalMovingTargetDiscreteConditionalDriftFieldOfLinearCombination",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "thm:forward-KL",
    "thm:forward-KL-discrete",
    "prop:guided_path_residual",
    "thm:general-moving-target-SALD",
    "thm:unified-forward-KL",
    "thm:general-moving-target-SALD-discrete"
  ]
  note := "Middle workflow obligation only. It adds no hidden common-space, density, absolute-continuity, finite-KL/FI, finite-log-mgf, regular conditional law, weak Fokker-Planck, endpoint, schedule, sigma-positivity, coefficient-regularity, stitched-interval, or theorem-level assumption."

/-- Cycle-69 lower obligation for the source-sign EM FP handoff. -/

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