Open. The site's label is OPEN (page last edited 23 March 2026). One partial claim is recorded: Graham, Witsenhausen and Spencer proved that the limit exists and equals $\frac13\sum_{k\in K}1/d_k$, a series over the $3$-smooth numbers $d_1<d_2<\cdots$ indexed by the set $K$ of $k$ at which the extremal count on $\{d_1,\ldots,d_k\}$ grows; the site's commentary credits the result and reports Eberhard's evaluation of the series as $0.800965\cdots$. The paper appeared in a collected volume not shown to be refereed, so the claim is pending. No closed form for the value and no answer to the irrationality question is claimed, so the problem stays open.