Batchelor–de Gier–Nienhuis squared-component-sum conjecture

Let $|\Psi^{(2n)}\rangle$ be the ground-state vector for the twisted XXZ chain with $2n$ sites, let $W^{(2n)}$ index its components, and let $A_n$ be the number of alternating-sign $n\times n$ matrices. Batchelor–de Gier–Nienhuis squared-component-sum conjecture. The sum of the squared components is

$$\sum_{A\in W^{(2n)}}[\Psi_A^{(2n)}]^2=A_n^2.$$

This was proposed as an analogue of a periodic-chain conjecture; the source gives no resolution.