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The passage around this formula

There is a statistical floor underneath all of this worth making explicit, because it exposes an assumption a five-run smoke test quietly violates. A model’s behaviour on a given prompt is not deterministic across runs, so a single trial is one draw from a Bernoulli process with some true success probability p , and the uncertainty in an observed rate $\hat{p}$ from n independent trials shrinks only as $\sqrt{n}$ . To bound that uncertainty to a half-width e at a chosen confidence level z , the standard requirement is

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