The $K_{4,6}$ extremal-number conjecture

Let $\operatorname{ex}(n,K_{4,6})$ be the maximum number of edges in an $n$-vertex graph containing no copy of $K_{4,6}$. $K_{4,6}$ extremal-number conjecture.

$$\operatorname{ex}(n,K_{4,6})=o(n^{7/4}).$$

The conjecture reflects the authors' belief that the geometric restrictions in the projective norm graph represent the limit of what algebraic constructions can offer, despite the occurrence of $K_{4,6}$ in $\operatorname{NG}(q,4)$; proving the asserted little-oh improvement remains open.