Isaacs–Keller–Meierfrankenfeld–Moreto's primitive character divisibility conjecture

Let $G$ be a finite group, and let $\chi$ be an irreducible primitive character of $G$. For $g\in G$, write $cl_G(g)$ for the conjugacy class of $g$ in $G$.

Primitive character divisibility conjecture. The character degree $\chi(1)$ divides the size of some conjugacy class:

$$\chi(1)\mid \lvert cl_G(g)\rvert$$

for some element $g\in G$.

The conjecture concerns the arithmetic relationship between irreducible primitive character degrees and conjugacy-class sizes. The supplied status evidence says that it was proved in the cited work, so the conjecture is solved.