BdGN's largest-entry conjecture for the open B model

At $q=e^{2i\pi/3}$ and in the homogeneous limit, let

be the ground-state eigenvector of the open-boundary Hamiltonian for the $B_r$ model, normalized so that its smallest entry is $1$. Let $A_V(r)$ denote the corresponding Vertically Symmetric Alternating Sign Matrix enumeration (with the even case identified with the relevant Cyclically Symmetric Transpose Complement Plane Partition enumeration). **BdGN's largest-entry conjecture.** The largest entry of

, with arches connecting consecutive points, is $A_V(r)$. The sum-of-entries formula is established in the supplied discussion, whereas this largest-entry formula is presented as an unproved assertion.