Majority-vote self-consistency (SC) lowers per-problem accuracy on most GPQA Diamond problems for small instruction-tuned models: on 56.6% of problems for Qwen2.5-7B and 65.7% for Llama-3-8B. An obvious fix is a verifier-free confidence gate that decides which problems to vote on. We report that the most natural version of that fix also fails, and we separate three signal failures that v1 treated as one. The token-entropy gate fails for a measurement reason: averaged over a chain of 602 tokens, entropy mostly measures fluency. The chain average sits 0.0005 nats from the non-answer average and 0.1695 nats from the answer token. So we measure confidence at the answer token itself. On Qwen2.5-7B-Instruct-Turbo (198 problems, 64 samples each), a sample that disagrees with its problem's plurality still emits its answer at a median margin of at least 20.4 nats, and at least 75.5% of such samples exceed 10 nats. Both quantities were pre-registered and tested once on 69 problems that no exploratory analysis had seen; both passed. The unit matters. Pooled across the benchmark, the margin does separate correct from incorrect samples: the fraction above 10 nats differs by +0.0586 [+0.0160, +0.0994]. Within a problem, paired, it does not: -0.0142 [-0.0501, +0.0215]. Token log-probabilities do carry information, but not for the within-question choice that self-consistency makes. The agreement gate's failure has no mechanism we can identify, and we leave it open. The new claims rest on one model: a registered replication on a second model was sampled but could not be evaluated, and we report that instead. Separately, three reasoning models could not be evaluated on hosted serverless inference at a small budget, each for a different measured reason. All three are downloadable, so this is a limit of metered APIs, not of what can be known.

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