AutoSamplingTheory.SALD.cycle52GuidedGeneralSkeletonMiddleObligation

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 cycle52GuidedGeneralSkeletonMiddleObligation : 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.guided_general.cycle52_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 52 middle audits appendix.tex:619-951 after the upper route check: prop:guided_path_residual and thm:general-moving-target-SALD remain unchanged, the proof route consumes the named guided residual, general KL derivative, LSI/KL/FI, residual DV, Gronwall, and pure-contraction interfaces in paper order, and the next lower target is sald.general_moving_target.kl_derivative over appendix.tex:765-884. EM interpolation remains only a downstream source-cited obligation interface.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetSource — 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.cycle52GuidedGeneralSkeletonUpperPacket
2. SALD.cycle52GuidedGeneralSkeletonObligation
3. SALD.cycle52GuidedGeneralSkeletonMiddleContract
4. SALD.cycle49MainSkeletonAnalyticReadinessObligation
5. SALD.cycle49MainSkeletonAnalyticMiddleObligation
6. SALD.cycle50ForwardKlSkeletonMiddleObligation
7. SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation
8. SALD.cycle47GuidedGeneralSkeletonMiddleObligation
9. SALD.guidedResidualIdentityContract
10. sald.guided_path_residual.normalizer_derivative
11. sald.guided_path_residual.identity
12. SALD.generalMovingTargetStatementContract
13. SALD.generalMovingTargetDerivativeCandidateContract
14. SALD.generalMovingTargetDerivativeObligation
15. sald.general_moving_target.kl_derivative
16. SALD.generalMovingTargetPostYoungDerivativeBoundScalar
17. SALD.generalMovingTargetLsiDerivativeBoundScalar
18. SALD.generalMovingTargetTimeChangedDerivativeBoundScalar
19. SALD.generalMovingTargetPreDvDerivativeBoundScalar
20. SALD.generalMovingTargetPostDvGronwallCoefficientScalar
21. SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar
22. SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar
23. SALD.saldLsiKlFiDensityTestContract
24. SALD.lsiKlFiDensityTestObligation
25. probability.lsi_to_kl_fi
26. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
27. SALD.generalMovingTargetDvPositiveAlphaScalingContract
28. sald.general_moving_target.dv_finite_log_mgf_witness
29. sald.general_moving_target.dv_positive_alpha_scaling
30. sald.general_moving_target.dv_m_energy
31. SALD.generalMovingTargetGronwallInstantiationContract
32. SALD.generalMovingTargetGronwallSideConditionContract
33. sald.general_moving_target.gronwall_application
34. sald.general_moving_target.gronwall_side_conditions
35. sald.general_moving_target.pure_contraction
36. SALD.unifiedForwardKlSpecializationContract
37. SALD.discreteForwardKlEmInterpolationSideConditionContract
38. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
39. sald.general_moving_target_discrete.em_interpolation_fp
40. lem:gronwall
41. lem:dv_variation
42. eq:LSI-KL-FI
43. def:alpha-complexity

note : String (explicit)

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

This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It adds no hidden density, boundary, endpoint, absolute-continuity, finite-log-mgf, finite-KL/FI, sigma-positivity, schedule, or coefficient-regularity assumptions to the guided residual proposition or continuous general theorem.

def cycle52GuidedGeneralSkeletonMiddleObligation : ProofObligation where
  id := "sald.guided_general.cycle52_middle_route_audit"
  statement := "Cycle 52 middle audits appendix.tex:619-951 after the upper route check: prop:guided_path_residual and thm:general-moving-target-SALD remain unchanged, the proof route consumes the named guided residual, general KL derivative, LSI/KL/FI, residual DV, Gronwall, and pure-contraction interfaces in paper order, and the next lower target is sald.general_moving_target.kl_derivative over appendix.tex:765-884. EM interpolation remains only a downstream source-cited obligation interface."
  source := saldGeneralMovingTargetSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle52GuidedGeneralSkeletonUpperPacket",
    "SALD.cycle52GuidedGeneralSkeletonObligation",
    "SALD.cycle52GuidedGeneralSkeletonMiddleContract",
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle50ForwardKlSkeletonMiddleObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle47GuidedGeneralSkeletonMiddleObligation",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.normalizer_derivative",
    "sald.guided_path_residual.identity",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "sald.general_moving_target.kl_derivative",
    "SALD.generalMovingTargetPostYoungDerivativeBoundScalar",
    "SALD.generalMovingTargetLsiDerivativeBoundScalar",
    "SALD.generalMovingTargetTimeChangedDerivativeBoundScalar",
    "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
    "SALD.generalMovingTargetPostDvGronwallCoefficientScalar",
    "SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar",
    "SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.lsiKlFiDensityTestObligation",
    "probability.lsi_to_kl_fi",
    "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
    "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
    "sald.general_moving_target.dv_finite_log_mgf_witness",
    "sald.general_moving_target.dv_positive_alpha_scaling",
    "sald.general_moving_target.dv_m_energy",
    "SALD.generalMovingTargetGronwallInstantiationContract",
    "SALD.generalMovingTargetGronwallSideConditionContract",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions",
    "sald.general_moving_target.pure_contraction",
    "SALD.unifiedForwardKlSpecializationContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It adds no hidden density, boundary, endpoint, absolute-continuity, finite-log-mgf, finite-KL/FI, sigma-positivity, schedule, or coefficient-regularity assumptions to the guided residual proposition or continuous general theorem."

/-- Cycle-52 lower obligation for the general moving-target derivative/DV scalar
handoff. -/