The logarithmic multipermutation-level conjecture for square-free solutions

Suppose $(X,r)$ is a nondegenerate square-free multipermutation solution of finite order $n$, and let $\mathop{\mathrm{mpl}}(X)$ denote its multipermutation level.

Logarithmic multipermutation-level conjecture. One has

$$\mathop{\mathrm{mpl}}(X)<\log_2 n.$$

This conjecture gives a logarithmic upper bound on the multipermutation level in terms of the order of the solution, refining the expectation that finite square-free solutions have controlled retraction complexity. The source attributes it to the more recent conjecture cited as T08ini; no resolution is stated in the supplied text.