AutoSamplingTheory.SALD.cycle47GuidedGeneralSkeletonObligation

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 cycle47GuidedGeneralSkeletonObligation : 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.cycle47_theorem_skeleton_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 47 upper wires appendix.tex:619-951 into the faithful guided/general theorem skeleton: prop:guided_path_residual uses the guided normalizer derivative and centered residual identity obligations; thm:general-moving-target-SALD uses the general Fokker-Planck/KL derivative interface, eq:LSI-KL-FI, lem:dv_variation with the residual m_t finite-log-mgf witness, lem:gronwall with sigma-weighted endpoint/exponent side conditions, and the pure-contraction residual-zero obligation. All slow analytic interfaces remain obligation or source-cited.

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.cycle44MainSkeletonAnalyticInterfaceObligation
2. SALD.cycle47GuidedGeneralSkeletonUpperPacket
3. SALD.guidedResidualIdentityContract
4. sald.guided_path_residual.normalizer_derivative
5. sald.guided_path_residual.identity
6. SALD.generalMovingTargetStatementContract
7. SALD.generalMovingTargetDerivativeCandidateContract
8. sald.general_moving_target.kl_derivative
9. SALD.saldLsiKlFiDensityTestContract
10. probability.lsi_to_kl_fi
11. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
12. sald.general_moving_target.dv_finite_log_mgf_witness
13. sald.general_moving_target.dv_positive_alpha_scaling
14. sald.general_moving_target.dv_m_energy
15. SALD.generalMovingTargetGronwallInstantiationContract
16. sald.general_moving_target.gronwall_application
17. sald.general_moving_target.gronwall_side_conditions
18. sald.general_moving_target.pure_contraction
19. lem:gronwall
20. lem:dv_variation
21. eq:LSI-KL-FI
22. def:alpha-complexity

note : String (explicit)

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

This is a theorem-route wrapper for main skeleton sprint 4. It does not add hidden smoothness, density, endpoint, absolute-continuity, finite-log-mgf, sigma-positivity, or interval-integrability assumptions to prop:guided_path_residual or thm:general-moving-target-SALD.

def cycle47GuidedGeneralSkeletonObligation : ProofObligation where
  id := "sald.guided_general.cycle47_theorem_skeleton_route"
  statement := "Cycle 47 upper wires appendix.tex:619-951 into the faithful guided/general theorem skeleton: prop:guided_path_residual uses the guided normalizer derivative and centered residual identity obligations; thm:general-moving-target-SALD uses the general Fokker-Planck/KL derivative interface, eq:LSI-KL-FI, lem:dv_variation with the residual m_t finite-log-mgf witness, lem:gronwall with sigma-weighted endpoint/exponent side conditions, and the pure-contraction residual-zero obligation. All slow analytic interfaces remain obligation or source-cited."
  source := saldGeneralMovingTargetSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle47GuidedGeneralSkeletonUpperPacket",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.normalizer_derivative",
    "sald.guided_path_residual.identity",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "sald.general_moving_target.kl_derivative",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
    "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.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions",
    "sald.general_moving_target.pure_contraction",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is a theorem-route wrapper for main skeleton sprint 4. It does not add hidden smoothness, density, endpoint, absolute-continuity, finite-log-mgf, sigma-positivity, or interval-integrability assumptions to prop:guided_path_residual or thm:general-moving-target-SALD."

/-- Cycle-47 middle audit for the guided residual and continuous general
moving-target theorem skeleton.

This is the source-to-Lean synchronization layer for the upper route wrapper.
It checks the exact appendix proof order, keeps all slow analysis in named
interfaces, and selects a lower-ready backend without changing the source
proposition or theorem display.
-/