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Equation 3 · Part 5 · Open-Weight AI in 2035: Scenarios and Falsifiers

Symbol W

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]
WW

What this part means

W is one factor in the product that computes the quantity on the left.

Its job in the formula

W is one factor in the product that computes the quantity on the left.

The passage around this formula

…jointly produce. Write O(t) for a stylised index of how close the strongest open-weight models sit to the closed frontier — Axis A’s own proxy, anchored in the Epoch and Artificial Analysis readings above [ 1 , 4 ] — and W(t) for the share of open-weight releases operating under standardized external governance: a regulatory regime that reviews them the way closed deployment is reviewed, or a licence that is genuinely OSI-compatible rather than bespoke [ 16 ] . Reaching and holding a position near the frontier…

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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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Sources cited in the surrounding passage

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