AutoSamplingTheory.SALD.cycle111GeneralMovingTargetDiscreteTargetTimeDerivativeMiddleObligation

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 cycle111GeneralMovingTargetDiscreteTargetTimeDerivativeMiddleObligation :
    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_discrete.cycle111_target_time_derivative_middle

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 111 keeps the active KL/log-ratio packet on appendix.tex:1358-1366 and narrows ASTIS.SALD.cycle105.remaining_pure_raw_kl_boundary. Classification: narrows-source-cited-boundary. The exact missing theorem is now the target-time subterm inside SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr: prove targetTimeTermIntegrable and targetTimeDerivativeFormula for - int (hat rho_s / tilde pi_s) * partial_s tilde pi_s dx from finite-KL llr regularity, a concrete density-ratio representative, pointwise HasDerivAt for the target density, and a local dominated parametric-integral hypothesis. The packet adds no sample-space P, hatX, massTerm, mapped-law mass derivative, hbarB, weak-FP source-sign, LSI, DV, or Gronwall field.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr
2. SALD.generalMovingTargetDiscretePureRawKlTargetTimeFieldsOfDominated
3. SALD.generalMovingTargetDiscreteTargetTimeDerivativeOfDominated
4. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
5. Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le
6. Mathlib.InformationTheory.KullbackLeibler.Basic
7. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
8. Mathlib.MeasureTheory.Integral.Bochner.Basic
9. eq:general_KL_derivative_0_discrete
10. appendix.tex:1358-1366

note : String (explicit)

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

Middle synchronization plus a lower-ready target-time theorem. It rejects broad hkl/hlog/hmass wrappers, route audits, source-index rebaselines, theorem-status promotion, SLT import, Lake dependency changes, and sald_version_2 use.

def cycle111GeneralMovingTargetDiscreteTargetTimeDerivativeMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle111_target_time_derivative_middle"
  statement := "Cycle 111 keeps the active KL/log-ratio packet on appendix.tex:1358-1366 and narrows ASTIS.SALD.cycle105.remaining_pure_raw_kl_boundary. Classification: narrows-source-cited-boundary. The exact missing theorem is now the target-time subterm inside SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr: prove targetTimeTermIntegrable and targetTimeDerivativeFormula for - int (hat rho_s / tilde pi_s) * partial_s tilde pi_s dx from finite-KL llr regularity, a concrete density-ratio representative, pointwise HasDerivAt for the target density, and a local dominated parametric-integral hypothesis. The packet adds no sample-space P, hatX, massTerm, mapped-law mass derivative, hbarB, weak-FP source-sign, LSI, DV, or Gronwall field."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.GeneralMovingTargetDiscretePureRawKlDerivativeNoMassAtFiniteKlLlr",
    "SALD.generalMovingTargetDiscretePureRawKlTargetTimeFieldsOfDominated",
    "SALD.generalMovingTargetDiscreteTargetTimeDerivativeOfDominated",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "eq:general_KL_derivative_0_discrete",
    "appendix.tex:1358-1366"
  ]
  note := "Middle synchronization plus a lower-ready target-time theorem. It rejects broad hkl/hlog/hmass wrappers, route audits, source-index rebaselines, theorem-status promotion, SLT import, Lake dependency changes, and sald_version_2 use."

/-- Cycle-111 lower obligation for the dominated target-time theorem. -/