Equation 8 · Part 1 · What Claude's Capability Evaluations Actually Measure
Symbol x
What this part means
then the duration at which the fitted curve crosses that threshold, i.
Its job in the formula
x is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol x→Article meaning
Where the article explains it
The reported time horizon at success level x is then the duration at which the fitted curve crosses that threshold, i.
The passage around this formula
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.
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value guide →
See this notation across published equations →
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 provide research context; check each source for the exact claim it supports.