The pivot-layer colouring conjecture for diagonal poset Ramsey numbers

Let $Q_n$ denote the diagonal poset on $n$ elements, and let $R(Q_n,Q_n)$ be its two-colour Ramsey number. For a positive integer $L$, consider the colouring construction in which $2L$ pairs of layers are modified by $2$ families of pivots. Pivot-layer colouring conjecture. For every $\epsilon>0$, there exist $L$ and a constant $a$ such that this type of colouring gives

$$R(Q_n,Q_n)\geq(3-\epsilon)n+a.$$

The conjecture asserts that optimizing this family of colourings can asymptotically approach a coefficient of $3$, improving on the bounds established in the paper; whether the required choices of layer parameters exist remains open.