Kawarabayashi–Picasarri-Arrieta Reed-type conjecture for digraphs

Let $D$ be a digraph. Define its maximum geometric-mean degree by

$$\widetilde{\Delta}(D)=\max_{v\in V(D)}\sqrt{d^-(v)d^+(v)},$$

let $\overset{\leftrightarrow}{\omega}(D)$ be its biclique number, and let $\vec{\chi}(D)$ be its dichromatic number. Kawarabayashi–Picasarri-Arrieta conjecture.

$$\vec{\chi}(D) \leq \left\lceil \frac{1}{2}\big(\widetilde{\Delta}(D)+1+\overset{\leftrightarrow}{\omega}(D)\big)\right\rceil.$$

This is a directed analogue of Reed's conjecture. The source records an intermediate result with an error parameter, but does not state that the conjecture itself is resolved.