Multi-agent LLM pipelines increasingly assign roles, including execution and verification, to models of different capability tiers. This is done because running a flagship model at every stage is expensive. Previous literature has established that verification stages are not always beneficial, but holds reviewer capability roughly fixed relative to the executor. We vary it. We replace the reviewer with models spanning a capability range down to one that cannot solve the problems at all, and measure the outcome of every individual rejection. This is done across a constant set of 100 olympiad mathematics problems. A cross-family mid-tier reviewer improves final accuracy by 12 percentage points, from 52 to 64 percent (p = 0.0005), with zero damaged answers. Same-model self-review attains the highest error-detection rate of any condition (0.85 recall) yet yields no significant gain: it rejects 2.1 times as often for a third the repair rate (15 against 43 percent, p = 0.0074) and falsely rejects 35 percent of its own correct answers against 2 percent for the cross-family reviewer (paired p = 0.000015). The low damage rate of self-review proves to be an artifact of revision inertia rather than reviewer quality: of 18 falsely rejected correct answers, the three where the executor complied all became wrong, while the fifteen it ignored survived unchanged. Below a capability floor the role becomes inert: our weakest reviewer changed zero of 100 final answers while doubling token cost. These findings describe a single executor-reviewer configuration on 100 problems and should be read as a controlled pilot rather than a general claim about verification stages.

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