The twisted XXZ-chain 1-sum conjecture

Let $L=2n$ and consider the twisted XXZ chain at $\Delta=-\frac{1}{2}$, with the groundstate wavefunction normalised as in the source. Let $S_{2n}^{(1)}$ denote the sum of its wavefunction components, and let $A_n$ be the number of $n\times n$ alternating sign matrices. The twisted-chain 1-sum conjecture.

$$S_{2n}^{(1)}=3^{n/2}A_n.$$

The groundstate is complex because of the twist, but its component sum is conjectured to retain a direct alternating-sign-matrix enumeration. The claim is based only on finite-size exploration in the source.