  In 1993 David Vogan proposed a basis for the vector space of stable
distributions on $p$-adic groups using the microlocal geometry of moduli spaces
of Langlands parameters. In the case of general linear groups, distribution
characters of irreducible admissible representations, taken up to equivalence,
form a basis for the vector space of stable distributions. In this paper we
show that these two bases, one putative, cannot be equal. Specifically, we use
the Kashiwara-Saito singularity to find a non-Arthur type irreducible
admissible representation of $p$-adic $\mathop{GL}_{16}$ whose ABV-packet, as
defined in earlier work, contains exactly one other representation; remarkably,
this other admissible representation is of Arthur type. In the course of this
study we strengthen the main result concerning the Kashiwara-Saito singularity.
The irreducible admissible representations in this paper illustrate a fact we
found surprising: for general linear groups, while all A-packets are
singletons, some ABV-packets are not.
