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Equation 3 · Part 4 · Open-Weight AI in 2035: Scenarios and Falsifiers

Symbol o^*

K(t)=1 ⁣[O(t)≥o∗]⋅1 ⁣[W(t)≥w∗]K(t) = \mathbb{1}\!\left[O(t) \ge o^{*}\right] \cdot \mathbb{1}\!\left[W(t) \ge w^{*}\right]
o∗o^{*}

What this part means

o∗o^* is one factor in the product that computes the quantity on the left.

Its job in the formula

o∗o^* is one factor in the product that computes the quantity on the left.

The passage around this formula

…well-capitalised families needs both conditions cleared at once, not an average of them: K(t)=1 ⁣[O(t)≥o∗]⋅1 ⁣[W(t)≥w∗]K(t) = \mathbb{1}\!\left[O(t) \ge o^{*}\right] \cdot \mathbb{1}\!\left[W(t) \ge w^{*}\right]. K(t) stays low however high either term climbs alone. Axis A determines whether O(t) can plausibly clear o∗o^{*} within this article’s horizon; Axis B determines whether W(t) can. Neither can be inferred from the other, which is why they are kept as two axes rather than folded into one — and why a narrowing capability gap sitting beside a licensing and regulatory picture that is still openly split, as…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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