Symbol I_bespoke
espoke is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
That combinatorial framing is worth making explicit, as a stylized model rather than a measured cost curve. Call the number of distinct model-facing client applications M and the number of distinct external tools or data sources N . Absent any shared protocol, a connector is needed for each pairing that is actually wanted, so the number of bespoke integrations that must be built and separately kept current scales as . A protocol that both sides target once, instead, lets each side write a single adapter to the shared standard, so the count becomes
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Symbol N
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Its accuracy depends on the assumptions and range of use described in the article.
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Equation 3 · AI Infrastructure
Function Calling, MCP, and the Other Ways to Give a Model Tools
This equation gives an approximation: it relates the quantities while allowing an approximation.
That combinatorial framing is worth making explicit, as a stylized model rather than a measured cost curve. Call the number of distinct model-facing client applications M and the number of distinct external tools or data sources N . Absent any shared protocol, a connector is needed for each pairing that is actually wanted, so the number of bespoke integrations that must be built and separately kept current scales as . A protocol that both sides target once, instead, lets each side write a single adapter to the shared standard, so the count becomes