Refined scaffold exchange symmetry conjecture

Fix $n\ge1$, a diagonal multiset $m$ realizable by an area word of size $n$, $k\ge0$, $r\ge1$, a scaffold $\Xi$, and a matrix $g=(g_{t,\delta})$ recording per-gap, per-diagonal numbers of undecorated active rows. Let $\Phi^{(r)}_{m,k,\Xi,g}(u,v;q)$ be the corresponding refined class generating function. Refined scaffold exchange conjecture. For every such $n,m,k,r,\Xi,g$, with incompatible data and inadmissible $g$ assigned value $0$, the generating function $\Phi^{(r)}_{m,k,\Xi,g}(u,v;q)$ is symmetric in $u$ and $v$. This strengthens the scaffold exchange conjecture by retaining per-gap and per-diagonal data. Computations support it, including area-two cases, but it remains open.