The Hurwitz ball quotient automorphism conjecture

Let $S$) be a smooth projective surface uniformized by the complex $2$-ball $\mathbb B^2$. Its Euler characteristic is denoted by $e(S)$, and $\operatorname{Aut}(S)$ is its automorphism group. The quotient $S / \operatorname{Aut}(S)$ is a complex hyperbolic $2$-orbifold.

Hurwitz ball quotient automorphism conjecture. Theorems concerning the bound $|\operatorname{Aut}(S)| \leq 288 e(S)$ and its equality case should hold without the arithmetic assumption. Equivalently,

$$|\operatorname{Aut}(S)| \leq 288 e(S),$$

with equality if and only if $S / \operatorname{Aut}(S)$ is the Deligne--Mostow orbifold associated with the ball tuple $\left(\frac{2}{12}, \frac{2}{12}, \frac{2}{12}, \frac{7}{12}, \frac{11}{12}\u000\right)$.

The conjecture extends the proved arithmetic result to all smooth projective ball quotients and identifies the extremal quotient. Its resolution is not given in the source.