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Equation 30 · Part 1 · The Token Tax of Giving a Model More Tools

Symbol σ

σ\sigma
σ\sigma

What this part means

σ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

σ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…— Anthropic’s Tool Search Tool, or a disciplined use of MCP’s own paginated listing — replaces the n in that formula with a much smaller m , the tools actually retrieved, at the cost of a small fixed search overhead σ\sigma . Separately, and not reducible to a token count at all, the choice the model makes over whatever shortlist it is shown carries its own error, decomposable into a retrieval gap that shrinks as the shortlist widens and a confusion gap that grows as it does, with namespacing removing one…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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