Las Vergnas's simplicial vertex conjecture for oriented matroids

Let $G$ be the tope graph of an oriented matroid (OM), and let $r(G)$ be its rank. A vertex $v$ is simplicial if $\deg(v)=r(G)$. Las Vergnas's conjecture. Every OM has a simplicial vertex. This is known for realizable oriented matroids, for rank at most $3$, and for several additional classes, but remains open in general.