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Equation 2 · Part 6 · The Hardest Unsolved Problems in Meta, Llama, and Open-Weight AI

multiplication

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}
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

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

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

Open the illustrated multiplication: combining factors guide →

Sources cited in the surrounding passage

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