Razumov–Stroganov conjecture for fully packed loop connectivities

Let $pi$ be a link pattern of size $2n$. Let $\psi'_pi$ be the corresponding entry of the properly normalized Perron–Frobenius eigenvector of the Hamiltonian of the Temperley–Lieb$(1)$ loop model, and let $\psi_pi$ be the number of fully packed loop configurations with connectivity $pi$.

Razumov–Stroganov conjecture. For every link pattern $pi$ of size $2n$,

$$\psi'_pi=\psi_pi.$$

The conjecture identifies entries of the Perron–Frobenius eigenvector with enumerations of fully packed loop configurations, linking the Temperley–Lieb loop model to FPL combinatorics. The supplied text gives no evidence resolving the conjecture.