Mubayi–Zhao conjecture for forbidden traces of complete uniform hypergraphs

Let $K_s^{(t)}$ be the complete $s$-vertex $t$-uniform hypergraph. Let $\operatorname{Tr}_r(K_s^{(t)})$ be the family of all $r$-uniform induced Berge copies of $K_s^{(t)}$, and let $H_{t,s}^r$ be the member with the maximum number of vertices, obtained by adding $r-t$ new vertices to each edge of $K_s^{(t)}$, with each new vertex used by only one edge.

Mubayi–Zhao conjecture. Given positive integers $n,r,s,t$ with $2\leqslant t<\min\{r,s\}$, there exists $n_0>0$ such that for $n>n_0$,

$$\operatorname{ex}(n,\operatorname{Tr}_r(K_s^{(t)}))= \begin{cases} \operatorname{ex}(n,H_{t,s}^r) & \text{if }r<s,\\ \operatorname{ex}(n-r+s-1,\operatorname{Tr}_{s-1}(K_s^{(t)}))=\operatorname{ex}(n-r+s-1,H_{t,s}^{s-1}) & \text{if }r\geqslant s. \end{cases}$$

The stated formula would determine the asymptotic extremal number for forbidden induced Berge copies of complete uniform hypergraphs; the general case is presented as an open problem.