Blue path cover conjecture for the complete symmetric infinite digraph

Let $\vec{K}_{\mathbb{N}}$ be the complete symmetric digraph on the natural numbers, with each directed edge coloured red or blue. A red directed path of length $r$ is a directed path consisting of $r$ edges. Blue path cover conjecture. For every integer $r\geq 1$, if a 2-colouring of $\vec{K}_{\mathbb{N}}$ contains no red directed path of length $r$, then the vertices of $\vec{K}_{\mathbb{N}}$ can be covered by at most $r$ vertex-disjoint blue directed paths. The preceding discussion establishes an almost-cover by at most $r$ blue paths, and notes that the claim is known when $r<4$; the general case remains open.