The Cantor-set structure conjecture for entropy-maximizing primitive majors

Let $PM(d)$ be the space of primitive majors for degree $d$, and let $\Pi(s_1,\ldots,s_r)$ be a stratum other than $\Pi(d)$ and $\Pi(1,1,\ldots,1)$. Consider the set of primitive majors $M$ in this stratum satisfying $h(M)=\log(r+1)$. Cantor-set structure conjecture. This set is a Cantor set if $s_j>1$ for all $j$, and is a Cantor set union a finite number of isolated points otherwise. This conjectural description concerns the structure of the entropy-maximizing primitive majors in the remaining strata of $PM(d)$; the supplied text does not state whether the conjecture has been resolved.