When Is Proof-Step Verification Worth Its Cost? Operating Requirements of Certify-or-Decline Verification for Open-Weight Mathematical Reasoning

arXiv:2611.14794v1 Announce Type: new Abstract: Proof-step verification rewrites a solver's answer into typed steps and uses LLM judges to certify or decline. We evaluate this pipeline on open-weight models across GPQA, AIME-2025, and a MATH-500 subset. Certification raises answer-key-match precision by 31 percentage points on the strong GPQA configuration and 46 on AIME, while answering only 35% and 21% of attempts. On near-ceiling MATH-500, gains are at most 5 points at a loss of 13-27 points of coverage. An output-token-matched self-consistency selector obtains 82.9% precision at 35% coverage, compared with the verifier's pooled 87.6% (paired difference: +4.8 points, 95% interval [-8.2, 18.5]).