Lee, Loh, and Sudakov's conjecture on judicious bipartitions of digraphs

Let $D$ be a digraph with $m$ arcs and minimum outdegree at least an integer $d\geq 2$. For a bipartition $V(D)=V_1\cup V_2$, write $e(V_i,V_j)$ for the number of arcs directed from $V_i$ to $V_j$. Lee, Loh, and Sudakov's conjecture. Every such digraph admits a bipartition $V(D)=V_1\cup V_2$ with

$$\min\{e(V_1,V_2),e(V_2,V_1)\}\geq \Big(\frac{d-1}{2(2d-1)}+o(1)\Big)m.$$

This conjecture addresses Scott's question about the largest constant guaranteeing a balanced directed cut in digraphs with prescribed minimum outdegree. The supplied source does not state whether the conjecture has been resolved.