The bowtie three-in-or-three-out conjecture

Let $B=F_{2,3}$ be the bowtie graph, with a distinguished center vertex, and let $\vec{B}$ be an orientation of $B$ having exactly three edges directed toward the center vertex or exactly three edges directed away from it. The bowtie three-in-or-three-out conjecture. Then

$$D(n,\vec{B})=2^{\mathrm{ex}(n,B)}.$$

This is the remaining unresolved orientation case after the other bowtie orientations were shown to have more than $2^{\mathrm{ex}(n,B)}$ orientations; whether the displayed equality holds remains open.