Large-digirth dichromatic subdivision bound by maximum degree

Let $F$ be a digraph with maximum degree $\Delta$. For an integer $g$, let $\mathrm{mader}_{\vec{\chi}}^{(g)}(F)$ be the least integer $k$, if it exists, such that every digraph $D$ with dichromatic number $\vec{\chi}(D)\geq k$ and digirth at least $g$ contains a subdivision of $F$. Large-digirth dichromatic subdivision conjecture. There is a function $f$ such that, for every digraph $F$ with maximum degree $\Delta$, there is an integer $g$ satisfying

$$\mathrm{mader}_{\vec{\chi}}^{(g)}(F)\leq f(\Delta).$$

This asserts that sufficiently large digirth permits a subdivision threshold controlled only by the maximum degree. The source says that this bound is believed to hold, but gives no resolution, so the conjecture remains open.