The rigged-configuration characterization of solitons

Fix a node $r\in I_0$. Let $p$ be a state, and let $(\nu,J)=\Phi^{-1}(p)$ be its inverse image under the rigged-configuration bijection. Write $\nu^{(r)}$ for the partition associated with node $r$.

Soliton characterization conjecture. The state $p$ corresponds to a soliton of length $\ell$ if and only if

$$\nu^{(r)}=(\ell).$$

Moreover, the theorem identifying the parts of $\nu^{(r)}$ with the sizes of sufficiently separated solitons should hold for every $r\in I_0$.

The source presents this as an equivalent proposed definition of solitons, extending a proved result for special nodes and nodes related to $0$ to all nodes. The full extension is left conjectural.