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Equation 2 · Part 4 · 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

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

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 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.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

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