fraction

The passage around this formula

Whether the documented gap between capability and verified safety narrows or widens is not a third axis; it is what the other two jointly produce. Write C(t) for a stylised index of frontier capability — METR’s time-horizon trend is the best-measured available proxy [ 16 ] — and V(t) for an index of independently checkable verification coverage: the share of a system’s decision-relevant behaviour that something other than watching its output can vouch for. The gap is $G(t) = C(t) - V(t), \qquad \frac{\mathrm{d}G}{\mathrm{d}t} = \frac{\mathrm{d}C}{\mathrm{d}t} - \frac{\mathrm{d}V}{\mathrm{d}t}$. The gap narrows exactly when verification coverage grows faster than capability does. Axis A determines whether $\mathrm{d}$V/$\mathrm{d}$t can be large at all — whether there is a technique to scale in the…

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