Symbol m

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…and a confusion gap , a roughly 10-percentage-point reduction in the theoretical best-case score that persists even when 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…

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