Two-color conjecture for weak local irregularity of digraphs

For a digraph $D$, two adjacent vertices are weakly distinguished when their outdegree–indegree pairs differ. Let $\mathrm{lir}(D)$ be the minimum number of colors in an arc coloring such that every color class induces a digraph in which every arc has endpoints with different outdegree–indegree pairs. Weak local irregularity conjecture. Every digraph $D$ satisfies

$$\mathrm{lir}(D)\leq 2.$$

This conjecture asserts that the weakening from distinguishing outdegrees or indegrees separately to distinguishing ordered pairs always permits a two-color decomposition. The paper states that it is supported by several results but supplies no resolution.