The periodic even-size O(1) loop-model 1-sum conjecture

Consider the dense O(1) loop model with periodic boundary conditions and even system size $L=2n$, and let $S_{2n}^{(1)}$ be the sum of the components of its groundstate wavefunction. Let $A_n$ denote the number of $n\times n$ alternating sign matrices. The periodic even-size 1-sum conjecture.

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

This conjecture gives the periodic O(1) loop-model sum the same alternating-sign-matrix sequence that appears in the periodic XXZ problem. The source supports it by finite-size data and leaves it unproved.