The half-turn symmetric alternating-sign-matrix enumeration conjecture for the D_r qKZ ground state

At the Razumov–Stroganov point $q=e^{2i\pi/3}$, take the homogeneous limit $w_i=1$ for all $i$ in the level-one $D_r$ $q$KZ solution, viewed as the Perron–Frobenius eigenvector $\Psi$ of the transfer-matrix Hamiltonian $H_D$. Normalize $\Psi$ so that its smallest entry is $\Psi_{\pi_0}=1$. Half-turn symmetric alternating-sign-matrix conjecture. The sum of the entries is the number of half-turn symmetric alternating sign matrices of size $r$:

$$\sum_\pi\Psi_\pi=A_{HT}(r).$$

This conjecture connects the homogeneous ground-state vector of the $D_r$ model with half-turn symmetric alternating sign matrices. The source presents the equality as a finding at the Razumov–Stroganov point and provides no proof or resolution.