$$V(t)$$

Equation 2 · AI Safety

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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

Meanings in this article

• $V$: the field-wide growth rate of.

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Equation 7 · AI Safety

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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…

Meanings in this article

• $V$: the field-wide growth rate of.

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Equation 8 · AI Safety

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Mechanism. The same technical progress as scenario one occurs, but it stays inside the labs that develop it. Circuit-tracing-style tools and oversight procedures become routine internal practice at a small number of frontier labs, the way Circuit Tracing and weak-to-strong generalization already emerged from single-lab research programmes [ 6 , 3 ] , without an external certifier ever checking the method’s claims — Coggins and colleagues’ critique already shows that even a published framework’s actual guarantees can be narrower than its language suggests [ 11 ] , and nothing in this scenario changes who gets to look. V(t) rises for those labs specifically; the field-wide V(t) this article’s…

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Equation 9 · AI Safety

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Mechanism. The same technical progress as scenario one occurs, but it stays inside the labs that develop it. Circuit-tracing-style tools and oversight procedures become routine internal practice at a small number of frontier labs, the way Circuit Tracing and weak-to-strong generalization already emerged from single-lab research programmes [ 6 , 3 ] , without an external certifier ever checking the method’s claims — Coggins and colleagues’ critique already shows that even a published framework’s actual guarantees can be narrower than its language suggests [ 11 ] , and nothing in this scenario changes who gets to look. V(t) rises for those labs specifically; the field-wide V(t) this article’s…

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Equation 10 · AI Safety

AI Alignment and Safety in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Three things hold across every cell, and they are the safest things to build institutional practice on regardless of which one obtains. First, some form of behavioural testing survives in all four, including the certified-verification ones — even a fully trusted interpretability method would still need red-teaming to catch failure modes it was not built to look for, exactly as no technique in the debate-and-oversight family claims to replace evaluation outright [ 2 , 4 ] . Verification adds a floor; it does not remove the need to keep testing above it. Second, the split between scalable oversight and interpretability as two distinct techniques is a narrower, more separable engineering detail…

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