Shi's recognition-by-spectrum conjecture for finite simple groups

Let $G$ be a simple group and let $H$ be a group. Write $|G|$ for the order of $G$ and let $\omega(G)$ denote the set of element orders of $G$. Shi's conjecture. $H\cong G$ if and only if

$$|H|=|G|\quad\text{and}\quad\omega(H)=\omega(G).$$

This conjecture asserts that a finite simple group is determined up to isomorphism by its order and spectrum. The supplied text does not state whether it has been resolved.