Mubayi–Suk tower-growth conjecture for off-diagonal hypergraph Ramsey numbers

Let $K^{<(k)}_n$ denote the ordered complete $k$-uniform hypergraph, let $MP^{<(k)}_{k+1}$ denote the monotone $(k+1)$-vertex path in the $k$-uniform setting, and let $t_{k-1}$ be the height-$(k-1)$ tower function. Mubayi–Suk conjecture. For any fixed integer $k\geq4$,

$$R_<(K^{<(k)},MP^{<(k)}_{k+1})\geq t_{k-1}(\Omega(n)).$$

This is presented as a strengthening of a conjecture of Erd6s and Hajnal. The surrounding results relate this ordered Ramsey number to classical off-diagonal hypergraph Ramsey numbers, but the stated tower lower bound remains unresolved.