← All parts of this equation

Equation 3 · Part 1 · How AI Models Learned to Use Tools: A Protocol History

Symbol C_bespoke

Cbespoke=M×NC_{\text{bespoke}} = M \times N
CbespokeC_{\text{bespoke}}

What this part means

CbC_bespoke is part of the quantity the equation computes from the expression on the right.

Its job in the formula

CbC_bespoke is part of the quantity the equation computes from the expression on the right.

The passage around this formula

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 Cbespoke=M×NC_{\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

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

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