AutoSamplingTheory.SALD.cycle52GuidedGeneralSkeletonObligation

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 cycle52GuidedGeneralSkeletonObligation : 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_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 52 upper verifies that the five slow analytic backends are explicit source-cited or obligation interfaces, then routes appendix.tex:619-951 through the named guided residual and continuous general moving-target interfaces: guided normalizer derivative and centered residual identity; general Fokker-Planck/KL derivative with residual m_t=v_t-c_t; eq:LSI-KL-FI; lem:dv_variation with the residual finite-log-mgf and positive-alpha scaling witnesses; lem:gronwall with sigma-weighted endpoint/exponent side conditions; and the pure-contraction residual-zero obligation. The proposition and theorem remain contractOnly.

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.cycle49MainSkeletonAnalyticReadinessObligation
2. SALD.cycle49MainSkeletonAnalyticMiddleObligation
3. SALD.cycle50ForwardKlSkeletonObligation
4. SALD.cycle51DiscreteForwardKlSkeletonObligation
5. SALD.cycle47GuidedGeneralSkeletonObligation
6. SALD.cycle47GuidedGeneralSkeletonMiddleObligation
7. SALD.cycle52GuidedGeneralSkeletonUpperPacket
8. SALD.guidedResidualIdentityContract
9. sald.guided_path_residual.normalizer_derivative
10. sald.guided_path_residual.identity
11. SALD.generalMovingTargetStatementContract
12. SALD.generalMovingTargetDerivativeCandidateContract
13. sald.general_moving_target.kl_derivative
14. SALD.saldGronwallCandidateContract
15. SALD.saldGronwallEndpointCalculusContract
16. SALD.saldGronwallExponentRewriteContract
17. SALD.gronwallAnalyticObligation
18. dvVariationalFormulaInterface saldDvVariationSource
19. SALD.saldDvFiniteLogMgfContract
20. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
21. SALD.generalMovingTargetDvPositiveAlphaScalingContract
22. sald.general_moving_target.dv_finite_log_mgf_witness
23. sald.general_moving_target.dv_positive_alpha_scaling
24. sald.general_moving_target.dv_m_energy
25. SALD.saldLsiKlFiDensityTestContract
26. SALD.lsiKlFiDensityTestObligation
27. probability.lsi_to_kl_fi
28. SALD.forwardKlDerivativeCandidateContract
29. sald.forward_kl.kl_derivative
30. SALD.generalMovingTargetGronwallInstantiationContract
31. SALD.generalMovingTargetGronwallSideConditionContract
32. sald.general_moving_target.gronwall_application
33. sald.general_moving_target.gronwall_side_conditions
34. sald.general_moving_target.pure_contraction
35. SALD.discreteForwardKlEmInterpolationSideConditionContract
36. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
37. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
38. sald.general_moving_target_discrete.em_interpolation_fp
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 route check. It does not add hidden assumptions, solve a backend, or mark Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, or EM interpolation as formalized.

def cycle52GuidedGeneralSkeletonObligation : ProofObligation where
  id := "sald.guided_general.cycle52_upper_route"
  statement := "Cycle 52 upper verifies that the five slow analytic backends are explicit source-cited or obligation interfaces, then routes appendix.tex:619-951 through the named guided residual and continuous general moving-target interfaces: guided normalizer derivative and centered residual identity; general Fokker-Planck/KL derivative with residual m_t=v_t-c_t; eq:LSI-KL-FI; lem:dv_variation with the residual finite-log-mgf and positive-alpha scaling witnesses; lem:gronwall with sigma-weighted endpoint/exponent side conditions; and the pure-contraction residual-zero obligation. The proposition and theorem remain contractOnly."
  source := saldGeneralMovingTargetSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle50ForwardKlSkeletonObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonObligation",
    "SALD.cycle47GuidedGeneralSkeletonObligation",
    "SALD.cycle47GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle52GuidedGeneralSkeletonUpperPacket",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.normalizer_derivative",
    "sald.guided_path_residual.identity",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "sald.general_moving_target.kl_derivative",
    "SALD.saldGronwallCandidateContract",
    "SALD.saldGronwallEndpointCalculusContract",
    "SALD.saldGronwallExponentRewriteContract",
    "SALD.gronwallAnalyticObligation",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "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.saldLsiKlFiDensityTestContract",
    "SALD.lsiKlFiDensityTestObligation",
    "probability.lsi_to_kl_fi",
    "SALD.forwardKlDerivativeCandidateContract",
    "sald.forward_kl.kl_derivative",
    "SALD.generalMovingTargetGronwallInstantiationContract",
    "SALD.generalMovingTargetGronwallSideConditionContract",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions",
    "sald.general_moving_target.pure_contraction",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is an upper workflow obligation and route check. It does not add hidden assumptions, solve a backend, or mark Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, or EM interpolation as formalized."

/-- Cycle-52 middle audit for the guided residual and continuous general
moving-target theorem route.

This synchronizes the cycle-52 upper route with the conversion window and
proof-obligation ledger.  It keeps the theorem-level target on
`appendix.tex:619-951`, selects the continuous general KL derivative as the
preferred lower backend, and preserves every slow analytic dependency as an
explicit source-cited interface or obligation.
-/