Symbol S_m

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…retrieval is assumed perfect [ 11 ] . Written as a decomposition of the error a shortlist of size m drawn from a full catalogue of n tools produces, where $\mathrm{tool}^\star$ is the one the request actually calls for and $S_m$ is the shortlist shown to the model: $\mathrm{error}(m) \;=\; \underbrace{\Pr[\mathrm{tool}^\star \notin S_m]}_{\text{retrieval gap, shrinks as } m \text{ grows}} \;+\; \underbrace{\Pr[\text{miscall} \mid \mathrm{tool}^\star \in S_m]}_{\text{confusion gap, grows as } m \text{ grows}}$. Widening the shortlist drives the first term toward zero and the second term upward; narrowing it does the reverse. There is no value of m that eliminates both terms at once, which is exactly why the paper reports a design fix rather…

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