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

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 {$[-8.2,18.5]$)}. A diagnostic sample reveals a distinct failure mode: 52 of 88 completed problems end in invalid proof construction without ever reaching a judge. Finally, external-LLM acceptance of rendered certified chains is 61.0-67.6\%, compared with 87.6\% answer-key match. {These audits lack human or formal-kernel ground truth.} Open-weight auditor pairs show near-zero chance-corrected agreement, which measures consistency rather than accuracy against proof truth. These results motivate separate reporting of execution failures, selected-answer precision, and independently assessed proof validity. We provide per-configuration results and evaluation details in the supplement.