The rational span conjecture for the Verma module

Let $M(\boldsymbol a)$ be the Verma module, let ${}^{\mathbf R}M(\boldsymbol a)$ be its relevant $\mathbf R_T$-form, and let $\widehat W[\boldsymbol\lambda]$ be the operators indexed by $\ell$-partitions $\boldsymbol\lambda$. Rational span conjecture. One has

$${}^{\mathbf R}M(\boldsymbol a)=\operatorname{Span}_{\mathbf R_T}\{\widehat W[\boldsymbol\lambda]|\boldsymbol a\rangle\}.$$

This is introduced explicitly as a speculation concerning the rational form of the Verma module. The source supplies no proof or resolution evidence.