Vertically symmetric ground-state conjecture for even open dense O(1) loops

Let $N=2n$ be even and impose open boundary conditions. Let $\Pi^{\mathrm{V}}_{2n+1}$ be the set of vertically symmetric pairing patterns, identified with the basis of the dense $O(1)$ loop model, and let $A^{\mathrm{V}}_{2n+1}(\pi)$ denote the number of vertically symmetric alternating-sign-matrix configurations with pairing pattern $\pi$.

Vertically symmetric ground-state conjecture. The vector

$$\boldsymbol{\Psi}=\sum_{\pi\in\Pi^{\mathrm{V}}_{2n+1}} A^{\mathrm{V}}_{2n+1}(\pi)\,\pi$$

is the ground state vector of the open dense $O(1)$ loop model.

This is the paper's second new conjecture and relates the even open model to vertically symmetric alternating-sign-matrix enumerations. The source also says that it has not succeeded in formulating a similar conjecture for odd open $N$, but gives no resolution status for this claim.