What does this equation mean?

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 first place. Axis B determines how much of any technical gain is actually applied across the field rather than sitting inside one lab’s internal practice, acting as a multiplier on the effective, field-wide growth rate of V . A technique that works in one laboratory’s hands but is never externally audited or adopted elsewhere raises V for that laboratory alone; the field-wide V(t) this equation needs barely moves. That is why the gap is downstream of both axes rather than a genuinely independent third question: no combination of assumptions lets it move without one or both axes above having already moved first.