The limiting canonical basis conjecture for the level-one representation

Let $B_n$ be the compatible bases of the level-one representation obtained by applying the canonical basis of the completed quantum loop-algebra positive part to the vectors $v_n$, and let $B_{-\infty}$ be the resulting well-defined limiting basis of $L_{\Lambda_0}$. Let $B^+$ denote the Leclerc–Thibon basis. Limiting canonical basis conjecture. The limiting basis coincides with the Leclerc–Thibon basis:

$$B_{-\infty}=B^+.$$

The conjecture compares the geometrically constructed limiting basis with the established Fock-space canonical basis. The supplied text gives no proof or resolution.