Bensmail–Filasto–Hocquard–Marcille conjecture on mixed local irregularity

A sink-source path is an oriented path containing an arc directed into a vertex and an arc directed out of that vertex, as used in the source. For $a,b\in\{+,-\}$, define $(a,b)$-local irregularity by requiring $d^a(u)\neq d^b(v)$ on every arc $uv$, and let $\mathrm{lir}^{(+,-)}(D)$ be the corresponding chromatic index. Bensmail–Filasto–Hocquard–Marcille conjecture. Every digraph $D$ without a sink-source path satisfies

$$\mathrm{lir}^{(+,-)}(D)\leq 3.$$

The source gives a constant upper bound of seven for digraphs without a sink-source path, but does not report that the conjectured bound three has been attained.