AutoSamplingTheory.SALD.cycle52GuidedGeneralDerivativeDvLowerObligation

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 cycle52GuidedGeneralDerivativeDvLowerObligation : 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.general_moving_target.cycle52_derivative_dv_lower

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 lower compiles the source-shaped scalar handoff from appendix.tex lines 765-907: once the general Fokker--Planck/KL derivative backend, residual Young estimate, LSI half-Fisher comparison, inverse-schedule calculus, and selected residual DV estimate are supplied explicitly, SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar derives the pre-Gronwall differential inequality with coefficient (sigma_t^2/2)*dot{s}(t)*C_LSI(t)-sigma_t^(-2)*dot{s}(t)^(-1)*alpha^(-1) and residual sigma_t^(-2)*dot{s}(t)^(-1)*E_alpha(pi_t,m_t).

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDerivativeSource — 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.cycle52GuidedGeneralSkeletonMiddleContract
2. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
3. SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar
4. SALD.generalMovingTargetPreDvDerivativeBoundScalar
5. SALD.generalMovingTargetPostDvGronwallCoefficientScalar
6. SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar
7. SALD.generalMovingTargetDerivativeCandidateContract
8. SALD.generalMovingTargetDerivativeObligation
9. SALD.saldLsiKlFiDensityTestContract
10. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
11. SALD.generalMovingTargetDvPositiveAlphaScalingContract
12. sald.general_moving_target.kl_derivative
13. probability.lsi_to_kl_fi
14. sald.general_moving_target.dv_finite_log_mgf_witness
15. sald.general_moving_target.dv_positive_alpha_scaling
16. sald.general_moving_target.dv_m_energy
17. sald.forward_kl.schedule_time_change

note : String (explicit)

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

The scalar lemmas compile, but the Fokker--Planck/KL derivative identity, integration by parts, residual Young analytic estimate, LSI density-test theorem, schedule calculus, residual finite-log-mgf/common-space witnesses, source-cited DV, Gronwall, and thm:general-moving-target-SALD remain obligations. No theorem statement or source constant is changed.

def cycle52GuidedGeneralDerivativeDvLowerObligation : ProofObligation where
  id := "sald.general_moving_target.cycle52_derivative_dv_lower"
  statement := "Cycle 52 lower compiles the source-shaped scalar handoff from appendix.tex lines 765-907: once the general Fokker--Planck/KL derivative backend, residual Young estimate, LSI half-Fisher comparison, inverse-schedule calculus, and selected residual DV estimate are supplied explicitly, SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar derives the pre-Gronwall differential inequality with coefficient (sigma_t^2/2)*dot{s}(t)*C_LSI(t)-sigma_t^(-2)*dot{s}(t)^(-1)*alpha^(-1) and residual sigma_t^(-2)*dot{s}(t)^(-1)*E_alpha(pi_t,m_t)."
  source := saldGeneralMovingTargetDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle52GuidedGeneralSkeletonMiddleContract",
    "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
    "SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar",
    "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
    "SALD.generalMovingTargetPostDvGronwallCoefficientScalar",
    "SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
    "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
    "sald.general_moving_target.kl_derivative",
    "probability.lsi_to_kl_fi",
    "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.forward_kl.schedule_time_change"
  ]
  note := "The scalar lemmas compile, but the Fokker--Planck/KL derivative identity, integration by parts, residual Young analytic estimate, LSI density-test theorem, schedule calculus, residual finite-log-mgf/common-space witnesses, source-cited DV, Gronwall, and thm:general-moving-target-SALD remain obligations. No theorem statement or source constant is changed."

/-- Cycle-52 proof-DAG pane for the guided/general route closure check. -/