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Equation 3 · Part 6 · Function Calling, MCP, and the Other Ways to Give a Model Tools

subscript

Ibespoke≈M×N.I_{\mathrm{bespoke}} \approx M \times N.
subscript

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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 Ibespoke≈M×NI_{\mathrm{bespoke}} \approx M \times N. 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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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 →

Sources cited in the article section

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