Lu–Thompson conjecture on subquadratic diagonal poset Ramsey numbers

Let $Q_n$ denote the Boolean lattice of subsets of an $n$-element set, and let $R(Q_m,Q_n)$ be the induced poset Ramsey number for the pair $(Q_m,Q_n)$. Lu–Thompson's conjecture. For $nge m$ and sufficiently large $m$,

$$R(Q_m,Q_n)=o(n^2).$$

This conjecture asks for a subquadratic upper bound in the diagonal regime and is presented as a target beyond the paper's superlinear improvement of the basic upper bound. Its resolution is not specified in the source.