Lowest-weight rigged-configuration formula conjecture

Let $\mathfrak{g}$ be of affine type other than $A_n^{(1)}$, with parameters $N_0$, $\kappa$, $c_a$, and $t_a$ as defined in the source. For a classically lowest weight element $(\nu,J)\in B(\kappa k\overline{\Lambda}_{N_0})\subseteq B^{N_0,\kappa s}$, write $(c_a/t_a)^m$ for a rectangular partition with $c_a/t_a$ rows of length $m$. Lowest-weight formula conjecture. The element is given by

$$\nu^{(a)}=(c_a/t_a)^{2t_as-\kappa k},$$

with all riggings equal to $0$ except those in $(\nu,J)^{(N_0)}$, which are $-s-\kappa k$. This gives an explicit description of the classically lowest weight element predicted by the proposed uniform affine rigged-configuration structure.