The constrained crossing–uncrossing closure conjecture for Go-diagrams

Let $D'$ be a Go-diagram in a partition $\lambda$, and let $c\prec c'$ be a crossing and uncrossing pair in $D'$ with $D'(c)=\circ$. Let $D$ be obtained by replacing the stones at $c$ and $c'$ with $+$. Let $i<j$ be the labels of the pipes crossing at $c$ in $D'$. The constrained crossing–uncrossing closure conjecture. Suppose that, after recolouring stones appropriately, $D$ is a Go-diagram with no cells in the forbidden configuration, and that $i$ and $j$ do not form a crossing and uncrossing pair with any $k$ satisfying $i<k<j$ between $c$ and $c'$ in $D'$. Then

$$\mathcal{D}_{D'}\subset \overline{\mathcal{D}_D}.$$

This conjecture gives a special setting in which corrective flips are unnecessary. It strengthens the known adjacent-pipe closure result and is intended as a constrained version of Marcott's conjecture; the source does not establish its resolution.