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Equation 4 · Part 3 · The Token Tax of Giving a Model More Tools

Symbol tau_0

T(n)=τ0+∑i=1nsiT(n) = \tau_0 + \sum_{i=1}^{n} s_i
τ0\tau_0

What this part means

the tool-independent charge.

Its job in the formula

tau0u_0 is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

Call this fixed, tool-independent charge τ0\tau_0 .

The passage around this formula

Call this fixed, tool-independent charge τ0\tau_0 . On top of it sits the actual content of the catalogue: for n tools attached to a request, each with a schema costing sis_i tokens for its name, description, and JSON Schema of parameters, the tool-visibility component of a single request’s input is T(n)=τ0+∑i=1nsiT(n) = \tau_0 + \sum_{i=1}^{n} s_i. which, if schemas run…

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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 →

See this notation across published equations →

Sources cited in the article section

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