Girã o, Snyder, and Popielarz's linear minimum out-degree conjecture for linked tournaments

Let $k$ be an integer. A tournament is a digraph obtained by orienting each edge of a complete graph in exactly one direction, and a tournament is $r$-connected when deletion of any set of at most $r-1$ vertices leaves a strongly connected digraph. A digraph is $k$-linked if, for every $2k$ distinct vertices $x_1,\ldots,x_k,y_1,\ldots,y_k$, it contains pairwise vertex-disjoint paths from $x_i$ to $y_i$ for all $i\in[k]$. The minimum out-degree is the minimum out-degree among its vertices.

Girã o, Snyder, and Popielarz's conjecture. There exists a constant $C>0$ such that every $(2k+1)$-connected tournament with minimum out-degree at least $Ck$ is $k$-linked.

This conjecture asks whether the connectivity bound in the cited theorem can be reduced to $2k+1$ while retaining a linear minimum out-degree condition. The supplied text gives no evidence that it has been resolved.