Charney--Davis conjecture for spherical Deligne complexes of braid groups

Let $G$ be a braid group, and let its spherical Deligne complex be the complex associated to the spherical standard parabolic subgroups of $G$, equipped with its natural piecewise spherical metric. Charney--Davis conjecture. The spherical Deligne complex of $G$ is CAT$(1)$. Charney and Davis proposed this as a guiding approach to the $K(\pi,1)$-conjecture and showed that it would imply that conjecture for a substantial portion of Artin groups. Its general status is not established in the supplied text.