Packing coloring conjecture for (3,0)-saturated subcubic graphs

Let $G$ be a $(3,0)$-saturated subcubic graph, and let $g_3(G)$ denote its local girth parameter. Packing coloring conjecture. If

$$g_3(G)=3,$$

then $G$ is $(1,1,2)$-packing colorable. The paper proves $(1,1,2,4)$-packing colorability in this setting and reports no example that fails the stronger three-color assertion; it remains open.