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Published equation contexts

pmax⁡≈3kp_{\max} \approx \frac{3}{k}

Why this formula appears here

That bound has a name in elementary statistics, and it is worth stating plainly because it clarifies exactly what a clean red-team result can and cannot license. If k independent attempts are made against a fixed but unknown per-attempt bypass probability p , and all k fail, the standard “rule of three” approximation gives a roughly 95%-confidence upper bound on that probability of pmax⁡≈3kp_{\max} \approx \frac{3}{k}. Applied loosely to a red-team programme, this says a clean record is real evidence, and its strength depends entirely on k — the count of genuinely independent attempts, not the number of hours spent. The Constitutional Classifiers paper reports hours, not a count of independent attempts, so…

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pmax⁡p_{\max}

Symbol p_max

pmp_max is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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kk

Symbol k

k occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

pmax⁡≈3k.p_{\max} \approx \frac{3}{k}.

Equation 4 · AI Safety

How Do We Actually Know a Safety Measure Worked?

This equation gives an approximation: it relates the quantities while allowing an approximation.

That bound has a name in elementary statistics, and it is worth stating plainly because it clarifies exactly what a clean red-team result can and cannot license. If k independent attempts are made against a fixed but unknown per-attempt bypass probability p , and all k fail, the standard “rule of three” approximation gives a roughly 95%-confidence upper bound on that probability of pmax⁡≈3kp_{\max} \approx \frac{3}{k}. Applied loosely to a red-team programme, this says a clean record is real evidence, and its strength depends entirely on k — the count of genuinely independent attempts, not the number of hours spent. The Constitutional Classifiers paper reports hours, not a count of independent attempts, so…

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