The local antimagic chromatic number of joins of disjoint paths with a universal vertex

Let $P_n$ be the path on $n$ vertices, let $mP_n$ denote the disjoint union of $m$ copies of $P_n$, let $K_1$ be a single vertex, and let $\chi_{la}(G)$ denote the local antimagic chromatic number of a graph $G$. The conjecture. For $m\ge 2$ and $n\ge 2$,

$$\chi_{la}(mP_n \vee K_1)=3.$$

This claim concerns a broad family of joins of disjoint paths with a universal vertex. The supplied text presents it as a statement in the conclusion and open-problems discussion, without indicating whether it has been proved or disproved.