Equation 4 · What Claude's Capability Evaluations Actually Measure
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
the reported time horizon. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
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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