Makar-Limanov and J.-T. Yu's fractional-power conjecture

Let $K$ be a field of characteristic zero, let $g\in K\langle X\rangle$ generate its own centralizer, and suppose that the homogeneous component of maximal degree of $g$ is an $n$-th power of an element of $K\langle X\rangle$. For every $m>n$ not divisible by $n$, consider the formal power series $g^{m/n}\in K((X))$.

Makar-Limanov and J.-T. Yu's conjecture. The series $g^{m/n}$ has a monomial of positive degree containing a negative power of an indeterminate in $X$.

This is a fractional-power assertion for free associative polynomials and is presented as one of the two conjectures considered in the paper. The supplied text gives no resolution status.