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Equation 2 · Part 1 · What Claude's Capability Evaluations Actually Measure

Symbol p

p(t)=11+exp⁡(a+blog⁡t),p(t) = \frac{1}{1 + \exp\left(a + b \log t\right)},
pp

What this part means

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

Its job in the formula

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

The passage around this formula

…with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon TxT_x at success level x is then the duration at which the fitted curve crosses that threshold, i.e. the t solving p(t) = x . Two things follow directly from this formulation that a single reported number obscures: the curve, not the crossing point, is the actual result, and a different chosen threshold x produces a different headline number from the identical underlying data.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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