The $C_8$ extremal-number conjecture

Let $C_8$ be the cycle on eight vertices, and let $\operatorname{ex}(n,H)$ denote the maximum number of edges in an $H$-free graph on $n$ vertices. $C_8$ extremal-number conjecture.

$$\operatorname{ex}(n,C_8)=\Theta\left(n^{5/4}\right).$$

The asymptotic order of $\operatorname{ex}(n,C_8)$ was open in the source; the conjecture is part of the broader even-cycle extremal problem.