Equation 4 · How AI Models Learned to Use Tools: A Protocol History
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Symbol C_standardized
tandardized is part of the quantity the equation computes from the expression on the right.
Symbol N
both large and still growing, the gap between M N and M + N dominates every other consideration.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
separate integrations, because nothing built for one pair transfers to any other. A protocol that both sides implement exactly once instead collapses this to . The assumption a shared protocol is betting on is that the fixed cost of building and maintaining the standard itself is smaller than the integrations it removes, and that those removed integrations were genuinely redundant rather than differently necessary. When M and N are both large and still growing, the gap between M N and M + N dominates every other consideration; when either is small — a single application talking to a handful of tools it controls — a bespoke integration can still be cheaper than…
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separate integrations, because nothing built for one pair transfers to any other. A protocol that both sides implement exactly once instead collapses this to . The assumption a shared protocol is betting on is that the fixed cost of building and maintaining the standard itself is smaller than the integrations it removes, and that those removed integrations were genuinely redundant rather than differently necessary. When M and N are both large and still growing, the gap between M N and M + N dominates every other consideration; when either is small — a single application talking to a handful of tools it controls — a bespoke integration can still be cheaper than adopting a shared protocol at all, and treating standardization as free in that case would be cargo-culting rather than economizing.
Sources cited in the article section
- [10] Introducing the Model Context Protocol ↗
- [11] Specification ↗
- [12] JSON-RPC 2.0 Specification ↗
- [13] Language Server Protocol ↗
These citations give research context. Read each source to check which claims it supports.
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