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Equation 2 · Part 5 · The Hardest Unsolved Problems in Meta, Llama, and Open-Weight AI

≤

L(u)={1,u≤7×108g,u>7×108L(u) = \begin{cases} 1, & u \le 7 \times 10^{8} \\ g, & u > 7 \times 10^{8} \end{cases}
≤

What this part means

Less than or equal to.

Its job in the formula

Less than or equal to.

The passage around this formula

A minimal formal statement of what this means is worth writing out, because it is easy to read past the word “sole discretion” in prose. Call u a licensee’s monthly active users at release, and define licence validity as L(u)={1,u≤7×108g,u>7×108L(u) = \begin{cases} 1, & u \le 7 \times 10^{8} \\ g, & u > 7 \times 10^{8} \end{cases}. where g ∈\in \{0, 1\} is not a fixed rule but a discretionary grant decided by the licensor after the fact. Below the threshold, “open” behaves like a normal permissive licence. Above it, the licence is not denied — it is converted into a negotiation whose outcome the model’s own publisher controls. That second regime has no counterpart in any license the Open Source Initiative recognises, and it is the specific, cited reason OSI has stated Llama’s…

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Learn the underlying idea

An inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.

Open the illustrated inequalities: bounds and allowed ranges guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.