Equation 8 · What Claude's Capability Evaluations Actually Measure
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then the duration at which the fitted curve crosses that threshold, i. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol x
then the duration at which the fitted curve crosses that threshold, i.
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What the article says around this equation
with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon 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.
Sources cited in the article section
- [7] Measuring AI Ability to Complete Long Tasks ↗
- [8] Task-Completion Time Horizons of Frontier AI Models ↗
These citations give research context. Read each source to check which claims it supports.
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