$$C_{\text{bespoke}} = M \times N$$

Equation 3 · AI Infrastructure

How AI Models Learned to Use Tools: A Protocol History

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

That parallel is precise enough to formalize, and doing so exposes the actual economic assumption both protocols are making rather than merely asserting it. Let M be the number of distinct hosts — editors, for LSP; agent frameworks and model-serving applications, for MCP — and N be the number of distinct targets — languages, for LSP; tools and data sources, for MCP. Wiring every host to every target independently, the way plugins and early framework wrappers did, requires $C_{\text{bespoke}} = M \times N$. separate integrations, because nothing built for one pair transfers to any other. A protocol that both sides implement exactly once instead collapses this to

Meanings in this article

• $M$: the number of distinct hosts — editors, for LSP.
• $N$: both large and still growing, the gap between M $\times$ N and M + N dominates every other consideration.

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