Miasnikov–Ventura–Weil conjecture for free groups of rank greater than two

Let $F_Y$ be a free group on the set $Y$, with subgroups $H\leq K\leq F_Y$. For every basis $X$ of $F_Y$, consider the associated core-graph morphism $\Gamma_X(H)\to\Gamma_X(K)$. An extension $H\leq K$ is algebraic if it is not contained in any proper free factor of $K$.

Rank-greater-than-two conjecture. The original Miasnikov–Ventura–Weil conjecture holds for $H\leq K\leq F_Y$ whenever $|Y|>2$.

The assertion excludes the known counterexample in rank two, but the supplied text does not state whether it has been proved or disproved.