Gishboliner–Steiner–Szabó conjecture on subdivisions of the bidirected triangle

Let $F$ be a digraph, and let $\mathrm{mader}_{\vec{\chi}}(F)$ be the least integer $k$ such that every digraph $D$ with dichromatic number $\vec{\chi}(D)\geq k$ contains a subdivision of $F$. Write $\overleftrightarrow{K_3}$ for the digraph obtained from the complete graph $K_3$ by replacing each edge with both possible directed arcs. Gishboliner–Steiner–Szabó conjecture.

$$\mathrm{mader}_{\vec{\chi}}(\overleftrightarrow{K_3})=4.$$

The exact value of $\mathrm{mader}_{\vec{\chi}}(F)$ is known for only a few digraphs, and $\overleftrightarrow{K_3}$ is the smallest digraph for which the value was unknown in the source. The conjecture is presented as an open problem.