AutoSamplingTheory.SALD.generalMovingTargetDiscreteConstantScheduleObligation

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 generalMovingTargetDiscreteConstantScheduleObligation : 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.constant_schedule_stitching

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Formalize the constant inverse-schedule and stitched-interval interface used in appendix lines 1315 and 1573-1600: dot{t}(s)=dot{s}(t)^(-1) is constant, endpoint laws identify K(T) with KL(rho_K^eta||pi_T), and interval-wise derivative inequalities are admissible for the final Gronwall step.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteSource — 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.general_moving_target_discrete.em_interpolation_fp
2. sald.forward_kl.schedule_time_change
3. sald.gronwall.integrating_factor

note : String (explicit)

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

The paper states the constant-schedule condition but does not spell out the closed-interval regularity needed for a global Gronwall application.

def generalMovingTargetDiscreteConstantScheduleObligation : ProofObligation where
  id := "sald.general_moving_target_discrete.constant_schedule_stitching"
  statement := "Formalize the constant inverse-schedule and stitched-interval interface used in appendix lines 1315 and 1573-1600: dot{t}(s)=dot{s}(t)^(-1) is constant, endpoint laws identify K(T) with KL(rho_K^eta||pi_T), and interval-wise derivative inequalities are admissible for the final Gronwall step."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := ["sald.general_moving_target_discrete.em_interpolation_fp", "sald.forward_kl.schedule_time_change", "sald.gronwall.integrating_factor"]
  note := "The paper states the constant-schedule condition but does not spell out the closed-interval regularity needed for a global Gronwall application."