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The passage around this formula

which, if schemas run at roughly a uniform average size $\bar{s}$ , simplifies to T(n) $\approx$ $\tau_0$ + n$\bar{s}$ . 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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