Verification Pulses and the Cost of Escaping Wrong Consensus

A debate panel can become unanimous without becoming more correct. This is dangerous for downstream safeguards: a substituted verification ballot can change only narrow-margin votes, while richer arbiters lose disagreement as a natural targeting signal. We show that one debate round can erase that resource without requiring persuasion. Tracking a heterogeneous 7-judge panel through a blind round and three debate rounds on 600 code-correctness candidates, unanimity on a fixed cohort jumps from 39.5% to 95.2% in round 1 (93.1% of the total collapse), while accuracy moves by less than one point and 96.3% of verdict flips follow the displayed peer majority. An execution-based verification ballot corrects 8 of 2,037 pre-debate candidate-substitution instances but changes zero in every later round; by round 3 every wrong decision is unanimous, erasing dissent that had flagged two-thirds of the panel's errors. Identical-cohort controls explain why: no-peer reconsideration reproduces 79.6% of the collapse, real labels without reasoning reproduce 91.5%, and random labels steer flips toward whatever they display; the full-debate condition adds 4.3 percentage points over labels only (clustered 95% CI 0.7--8.1). The one-round collapse reproduces in two additional real runs and two fake-label seeds, remains under panel sizes 3--7, and appears in MATH-500. Parse failures concentrate on contested candidates ($p<0.001$), making attrition non-ignorable. The design implication is operational: verify before any second-pass evaluation or peer exposure, and never treat post-debate unanimity as independent evidence of reliability.

Test-time reasoning is increasingly used as a serving-time control knob, but extra reasoning is not uniformly valuable: it can repair failed attempts, waste compute on already-correct answers, or introduce harmful answer changes. We study this as a deployment allocation problem rather than a new-verifier problem. We introduce \sevra, Selective Verification for Reasoning Allocation, a serving-layer controller that decides whether to preserve a frozen solver's initial answer or invoke active verification. Using a frozen Qwen3-4B solver, we log intervention outcomes and train recoverability-aware gates from serving-visible attempt state. On \mathfive, selective verification reaches 76.3% accuracy, compared with 75.5% for always verifying, while reducing post-generation tokens by 26.8% and harmful flips from 2.2% to 1.0%. However, an 8,192-token initial solve reaches 76.0% accuracy with 28% fewer total model tokens, showing that selective recovery is useful but not the best tested cost frontier. In frozen transfer to \gsm, the selective policy verifies only 3.0% of examples, improves accuracy from 93.4% to 94.5%, and reduces verification tokens by 91.2% relative to always verifying; again, a longer initial solve matches its accuracy with fewer realized tokens. On CommonsenseQA, always-on verification hurts, while Self-Consistency@5 improves accuracy at about five times the realized token cost. The resulting deployment rule is: tune the initial budget first, then use selective recovery when explicit checks, bounded retries, auditability, or regression-risk control matter.

Sampling several answers and keeping the one a verifier scores highest is one of the simplest ways to buy accuracy at test time. Its effect is reported as a scaling curve: accuracy against the number $k$ of sampled answers. The curve is cheap to draw and expensive to trust. A budget read off it is chosen after looking at every point, so only a band that covers all budgets at once protects the choice, and on a 100-question benchmark a fixed exact-binomial design needs 192,000 generated answers to certify 64 budgets to within $\pm1/32$ at 95%. Most of that cost pays for the wrong uncertainty. A benchmark is a fixed list of questions; at budget 64, about three quarters of the variance of a selected answer's correctness lies between questions, and an audit that revisits every question need not pay for it. We derive the minimax cost of certifying the whole curve, up to logarithmic factors. It has three parts: calibrating the tail of the score distribution, telling the questions apart, and within-question noise summed along the curve. At a single benchmark the last part sharpens to the variance of one answer's influence under the best allocation of answers to questions, which every valid audit pays and an audit that learns the allocation attains, up to a logarithm, as the precision grows. A paired audit built on an exponential inequality for two independent draws at the same question needs no pilot. On 185 held-out score pools it uses 0.74 times the answers of the cheapest competing certified audit at 64 budgets and 0.53 times at 1,024, and on a newly generated MMLU-Pro study it certified the curve with 79,133 answers, within 0.6% of what a cost law fitted beforehand predicted from the study's within-question variance. The same paths certify pass@$k$ and majority voting, and the bands extend to populations of questions and to answers that depend on earlier ones.