Jackson's Hamiltonicity conjecture for regular oriented graphs

Let $G$ be an oriented graph, meaning a directed graph with at most one directed edge between each pair of vertices. It is $d$-regular when every vertex has $d$ in-neighbours and $d$ out-neighbours.

Jackson's conjecture. For each $d>2$, every $d$-regular oriented graph on $n\leq 4d+1$ vertices has a Hamilton cycle.

The conjecture asserts that regularity substantially lowers the degree threshold for Hamiltonicity in oriented graphs. The paper proves it for sufficiently large $n$ as a consequence of a stronger dense cycle-cover theorem, but the stated conjecture is not presented as completely resolved here.