Beyond Correctness: Toward Automated Novelty Verification with Lean 4
Ayrton Porto
Abstract
Artificial intelligence systems applied to mathematics verify correctness but not novelty: an automatically generated theorem can compile in Lean without errors and yet be an already known result. This article presents AViD Journal, a pipeline that receives a LaTeX article, formalizes its statements in Lean 4, and issues a novelty verdict through a decision tree over three dimensions: prior existence in a formal corpus (Mathlib) and an informal one (TheoremSearch and Matlas, with temporal filter and LLM judge), non-triviality via automatic tactics, and structural distance between proofs measured as Jaccard distance over premise sets. Evaluation on papers withdrawn from arXiv due to declared duplication produced a result more informative than any performance measure: the identification of three obstacles that limit the approach regardless of this implementation. First, successful compilation of a Lean file does not guarantee semantic fidelity. Second, the recall ceiling is imposed by the coverage of theorem indices, not by the similarity metric. Third, arXiv removes the source code of articles upon withdrawal, compromising the reproducibility of any benchmark built upon them.
Topics
Classified with taxonomy v2 on Sat, 5 Sept 2026.