Sedlar–Škrekovski local irregularity conjecture for colorable graphs

Let $B$ be the bow-tie cactus with $\mathrm{lir}(B)=4$. For a connected graph $G$ that is locally irregular colorable, let $\mathrm{lir}(G)$ denote the minimum number of colors in a locally irregular coloring. Local Irregularity Conjecture. Every connected graph $G\neq B$ that is locally irregular colorable satisfies

$$\mathrm{lir}(G)\leq 3.$$

The conjecture is presented as an improvement of the earlier universal bound after $B$ was found; the supplied text gives no resolution, so it remains open.