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Published equation contexts

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]

Why this formula appears here

Whether the open-weight ecosystem consolidates around a handful of dominant families or stays fragmented across many providers is not a third axis; it is what the other two 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 takes…

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Published contexts (1)

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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]

Equation 3 · Open Models

Open-Weight AI in 2035: Scenarios and Falsifiers

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Whether the open-weight ecosystem consolidates around a handful of dominant families or stays fragmented across many providers is not a third axis; it is what the other two 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 takes…

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