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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 GL 16 whose ABV-packet, as defined in [CFM + 21], 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 in [KS97]. 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.Date: Tuesday 9 th March, 2021. Clifton Cunningham gratefully acknowledges the support of NSERC Discovery Grant RGPIN-2020-05220.Andrew Fiori thanks and acknowledges the University of Lethbridge for their financial support as well as the support of NSERC Discovery Grant RGPIN-2020-05316.Nicole Kitt would like to thank and acknowledge support from the NSERC Undergraduate Summer Research Award (USRA) program and from the University of Calgary PURE program. 2 CLIFTON CUNNINGHAM, ANDREW FIORI, AND NICOLE KITT 2.4. A curious ABV-packet 18 3. The main geometric result 18 3.1. Evs CKS IC(½ CKS ) 19 3.2. Reduction of the problem 19 3.3. Overview of the calculations 21 3.4. Evs CKS IC(½ Cr ) 23 3.5. Evs CKS IC(½ Cm ) 26 3.6. Evs CKS IC(½ CR ) 28 3.7. Evs CKS IC(½ C ψ ) 30 3.8. A study of quadratic covers of the generic conormal bundle 34 3.9. Speculation on endoscopy for the Kashiwara-Saito representation 35 Appendix A. Macaulay2 instructions 36 A.1. General computations 36 A.2. Microlocal vanishing cycle calculations 38 A.3. Local Hessian Calculations 42 References 43