§6, p. 470 — corrected count of requests served by a fixed run

Fix a run $a$ of $q$ accesses, a hand capacity $b$, and $t$ request rounds. The number of request sequences that this run legally satisfies is bounded by

This bounds the request sequences associated with a single hidden action history, retaining the paper's non-strict round-end indices.

Formalization Note The printed proof says $b^q$ and footnote 29 offers $\binom qt b^t$; both fail when round ends repeat. With $m=b=q=2$ and $t=7$, a run that takes both balls serves all $2^7$ request sequences, exceeding $b^q=4$ while $\binom qt=0$. The formal bound uses Nat.multichoose q t, equal to $\binom{q+t-1}{t}$ when $q\ge1$, and is the corrected statement needed for Theorem 6.1. No legality hypothesis is needed: an illegal run satisfies no requests.