Addario-Berry–Havet–Linhares Sales–Reed–Thomassé conjecture for antidirected trees

Let $D$ be a digraph, let $k$ be a positive integer, and let $T$ be an antidirected tree with $k$ arcs. Addario-Berry–Havet–Linhares Sales–Reed–Thomassé conjecture. If $D$ has more than

$$(k-1)|V(D)|$$

arcs, then $D$ contains $T$. This conjecture predicts the sharp linear arc threshold for containing every antidirected tree and would make the extremal construction described by Burr optimal. The supplied text does not state whether the conjecture is open or resolved; the paper proves it for broad classes of digraphs and for antidirected caterpillars.