  Sum-of-norms clustering is a method for assigning $n$ points in
$\mathbb{R}^d$ to $K$ clusters, $1\le K\le n$, using convex optimization.
Recently, Panahi et al.\ proved that sum-of-norms clustering is guaranteed to
recover a mixture of Gaussians under the restriction that the number of samples
is not too large. The purpose of this note is to lift this restriction, i.e.,
show that sum-of-norms clustering with equal weights can recover a mixture of
Gaussians even as the number of samples tends to infinity. Our proof relies on
an interesting characterization of clusters computed by sum-of-norms clustering
that was developed inside a proof of the agglomeration conjecture by Chiquet et
al. Because we believe this theorem has independent interest, we restate and
reprove the Chiquet et al.\ result herein.
