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Equation 3 · Part 7 · Open-Weight AI in 2035: Scenarios and Falsifiers

=

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]
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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