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Equation 3 · Part 4 · AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

Symbol V

G(t)=C(t)−V(t),dGdt=dCdt−dVdt.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}.
VV

What this part means

the field-wide growth rate of.

Its job in the formula

V occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

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 .

The passage around this formula

…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),dGdt=dCdt−dVdtG(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.…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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