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The passage around this formula

If a real number belongs in the audit-trail conversation, it is a threshold, not a measurement, and it should be written as a model rather than asserted as fact. A deployer setting an acceptance gate on a generative system’s confabulation rate might define a simple pass condition against a sampled evaluation set of size n , tolerance $\varepsilon$ , and observed error rate $\hat{p}$ : $\hat{p} + z_{0.95}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \le \varepsilon$. This is a standard one-sided Wald confidence bound, included here only because it exposes a real assumption practitioners often skip: a raw sampled error rate without its confidence interval says nothing about whether the true rate is actually below a threshold, especially at the sample sizes (…

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