Mihalik's path-connectivity conjecture for right-angled Artin group boundaries

Let $A_\Gamma$ be the right-angled Artin group defined by a finite graph $\Gamma$, and let $S_\Gamma$ be the universal cover of its Salvetti complex. The visual boundary of $S_\Gamma$ is denoted by $\partial S_\Gamma$.

Mihalik's conjecture. The boundary $\partial S_\Gamma$ is path connected if and only if $\Gamma$ is a join.

The preceding results establish non-path-connectedness for important classes of right-angled Artin groups, including groups whose defining graph is an $n$-cycle for $n\geq 5$. The conjecture proposes that being a join exactly characterizes path connectivity of the visual boundary.