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

Consider the dense O(1) loop model with periodic boundary conditions and even system size $L=2n$, and normalise its groundstate wavefunction so that its smallest element is $1$. Let $A_{n-1}$ denote the number of $(n-1)\times(n-1)$ alternating sign matrices. The periodic even-size largest-component conjecture. The largest element of the wavefunction is $A_{n-1}$.

For even periodic size, the conjecture identifies the extremal component with an alternating-sign-matrix number, equivalently a descending-plane-partition enumeration. It is inferred from the tabulated wavefunctions and remains open in the source.