Equation 3 · Part 6 · Open-Weight AI in 2035: Scenarios and Falsifiers

Symbol w^*

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

w^{*}

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.

Full expressionSymbol w^*Article meaning

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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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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