Kostochka–Stiebitz gap conjecture for oriented dicritical digraphs

Let $d_k(n)$ be the minimum number of arcs in a $k$-dicritical digraph of order $n$, and let $o_k(n)$ be the minimum number of arcs in a $k$-dicritical oriented graph of order $n$, with value $+\infty$ when no such oriented graph exists. Kostochka–Stiebitz gap conjecture. There exists $\varepsilon>0$ such that

$$o_k(n)\geq(1+\varepsilon)\cdot d_k(n)$$

for every $k\geq4$ and sufficiently large $n$. The conjecture asserts a uniform asymptotic density gap between arbitrary and oriented $k$-dicritical digraphs; the source notes that it is known for $k=3$ and $k=4$, but remains open for general $k$.