The ordinary diversity bound for intersecting uniform hypergraphs

Let $\mathcal{F}\subset \binom{[n]}{k}$ be an intersecting family, and let $\gamma(\mathcal{F})$ denote its ordinary diversity. Suppose that $n>4k$. Ordinary diversity conjecture.

$$\gamma(\mathcal{F})\leq \binom{n-3}{k-2}.$$

This is posed as an open problem concerning the ordinary diversity of intersecting families. It asks for a sharp upper bound under the linear condition $n>4k$; the supplied text does not report a resolution.