Symbol T
T 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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which, if schemas run at roughly a uniform average size , simplifies to T(n) + n . Nothing about this term depends on whether the model calls any tool at all; it is the price of the menu, not the price of the order. And critically, because a stateless inference API resends its full input on every request, T(n) is not paid once at the start of a session — it is paid again, in full, on every single turn for as long as tools remain attached to the request.
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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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Published contexts (2)
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Equation 7 · AI Infrastructure
The Token Tax of Giving a Model More Tools
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
which, if schemas run at roughly a uniform average size , simplifies to T(n) + n . Nothing about this term depends on whether the model calls any tool at all; it is the price of the menu, not the price of the order. And critically, because a stateless inference API resends its full input on every request, T(n) is not paid once at the start of a session — it is paid again, in full, on every single turn for as long as tools remain attached to the request.
Equation guide → · Article →Equation 9 · AI Infrastructure
The Token Tax of Giving a Model More Tools
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
That leaves the second meaning, and it is where the real cost lives. To discover what a server can do, a client still sends a tools/list request, and that response is the full tool catalogue — the same names, descriptions, and JSON Schemas that later get folded into T(n) on every inference call. The specification requires this operation to support pagination: “Pagination in MCP uses an opaque cursor-based approach, instead of numbered pages,” page size is “determined by the server,” and clients “ MUST NOT assume a fixed page size,” with the documentation naming the reason directly — pagination “is especially important when connecting to external services over the internet, but also useful…
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