The exact 3-partite path Ramsey conjecture

Let $K_{n,n,n}$ be the complete tripartite graph with three parts of size $n$, and let $P_m$ denote the path on $m$ vertices. For graphs $G_0,G_1,G_2$, write $G_0\mapsto(G_1,G_2)$ if every 2-coloring of the edges of $G_0$ contains a copy of $G_i$ whose edges all have color $i$ for some $i\in\{1,2\}$. Exact 3-partite path Ramsey conjecture. For every positive integer $n$,

$$K_{n,n,n}\mapsto(P_{2n+1},P_{2n+1}).$$

This conjecture asks for the exact strengthening of the previously known asymptotic bound $K_{n,n,n}\mapsto(P_{2n-o(n)},P_{2n-o(n)})$; its resolution is not indicated in the supplied source context.