Bennett–Bohman folklore conjecture for complete-hypergraph removal

Let $K^{(k)}_\ell$ be the $k$-uniform complete hypergraph on $\ell$ vertices, and let $R_n(K^{(k)}_\ell)$ denote the final number of edges in its removal process. Bennett–Bohman folklore conjecture. If $2\leq k<\ell$, then for every $\varepsilon>0$ there is $n_0\geq0$ such that, for every $n\geq n_0$, with high probability,

$$n^{k-\frac{\ell-k}{\binom{\ell}{k}-1}-\varepsilon}\leq R_n(K^{(k)}_\ell)\leq n^{k-\frac{\ell-k}{\binom{\ell}{k}-1}+\varepsilon}.$$

Beyond the triangle case, the paper reports no comparably close results for other forbidden hypergraphs and identifies asymptotic estimates for $R_n(K_4)$ as a central open problem.