The Strong Anick conjecture on wild coordinates

Let $K\langle x,y,z\rangle$ be the free associative algebra over a field $K$. A coordinate is called wild if it is the image of a generator under a wild automorphism and no tame automorphism, possibly one not fixing $z$, sends that generator to the same element. Strong Anick conjecture. There exist wild coordinates in $K\langle x,y,z\rangle$. In particular, the two nontrivial coordinates of the Anick automorphism are both wild. The conjecture strengthens the question of whether wild automorphisms must have wild coordinates; the source presents it as open, with no resolution supplied there.