Dependency Distance Audits Descendant Leakage in Lean Proving Benchmarks
Abstract
Lean proving benchmarks sometimes remove the target theorem from retrieval while importing the completed library. This protocol can still expose target-descendant declarations whose stored types or values transitively depend on the target. A proof using such a declaration is valid in the completed environment but does not establish that the target can be proved from its original environment. We introduce a dependency-distance audit over all project declarations and apply it to a 200-target case study with static and adaptive (agentic) retrieval. About one quarter of completed-valid proofs in each target-excluding BM25 condition use a detected descendant, usually through a direct dependency; extending a theorem-only graph to definitions also exposes a previously missed case. The audit describes the generated proof artifact and does not reconstruct source chronology. We therefore recommend reporting completed-environment validity and descendant-free validity separately, while reserving claims of historical availability for evaluations that recreate the target's source position.