Aboulker et al.'s directed cycle subdivision conjecture

Let $C_\ell$ be the undirected cycle of length $\ell$, and let $C$ be an orientation of $C_\ell$. For a digraph $F$, let $\operatorname{mader}_{\vec{\chi}}(F)$ be the smallest integer $k\ge1$ such that every digraph $D$ with dichromatic number $\vec{\chi}(D)\ge k$ contains a subdivision of $F$. Aboulker et al.'s conjecture. If $C$ is an orientation of $C_\ell$, then

$$\operatorname{mader}_{\vec{\chi}}(C)=\ell.$$

This conjecture concerns the threshold at which large dichromatic number forces subdivisions of directed cycles. The paper's abstract states that this conjecture is settled by proving the asserted equality.