Found first: a primary source the press has not covered yet.
A new dataset called LeanPRM provides 152,000 labeled proof steps across 10,634 proofs with no human annotation, by pairing natural-language proofs with formal Lean proofs and using Lean's checker to assign correctness labels at each step automatically. A Qwen3-4B verifier trained on this data reaches 74.7% exact step-label accuracy on LeanPRM-Bench, a held-out set of 200 proofs, compared to 60.3% for a model trained on the existing PRM800K dataset and 48.2% for the no-training baseline.
What the source says
The paper is by Lafuente-Mercado, Rahman, Shen, Shiffer, Gabriel, and Izmailov, submitted October 13, 2026. The method generates proofs in natural language and Lean in lockstep, then applies Lean's formal checker to label each step. A secondary filter discards syntax-only failures so negative labels capture genuine mathematical errors rather than formatting problems. The resulting verifier generalizes across model sizes from 0.6B to 8B parameters, and outperforms PRM800K-trained baselines on three of four external benchmarks, including IMO-level problems.
Why it matters
Training a process reward model for AI-generated math proofs requires a correctness label on every individual proof step. Until now that has meant paying human mathematicians to assess each one, which caps how large any training set can grow. LeanPRM moves that constraint: the supply of labeled steps is now bounded by the availability of formal Lean problem statements, not by annotator hours. This matters most right now because step-level verification of AI math is actively disputed, with Lean passage rates in question and institutions reassessing how they evaluate math AI systems. A scalable, annotation-free source of step labels changes what is practical to build.