The dichromatic Mader bound for oriented cycles

Let $C$ be an oriented cycle, and let $\vec\chi(D)$ be the dichromatic number of a digraph $D$. Dichromatic-cycle conjecture. Every oriented cycle $C$ satisfies $\operatorname{mader}_{\vec\chi}(C)\leq |C|$. The surrounding text gives a weaker established bound for oriented cycles, so this stronger inequality is presented as an open conjecture.