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Equation 3 · Part 1 · Open-Weight AI in 2035: Scenarios and Falsifiers

Symbol K

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]
KK

What this part means

K is part of the quantity the equation computes from the expression on the right.

Its job in the formula

K is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…bar but sits well behind the frontier has little to sell. Durable consolidation around a few dominant, 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…

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

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