The regular-graph zero-sum 5-flow conjecture

Let $G$ be an $r$-regular graph, meaning every vertex of $G$ has degree $r$, with $r\geq 3$. A zero-sum $5$-flow is a zero-sum flow whose integer edge values satisfy $1\leq |f(e)|\leq 4$. Regular-graph zero-sum 5-flow conjecture. Every $r$-regular graph with $r\geq 3$ has a zero-sum $5$-flow. The claim extends known results for even regularity at least four and for cubic graphs. The source gives no resolution.