Generation conjecture for the algebra $W_{0,3}(SL_m(\mathbb{C}))$

Let $W_{0,3}(SL_m(\mathbb{C}))$ be the algebra associated with the three-pointed genus-zero construction, and let extended conformal blocks of level $1$ be the generators under consideration. Generation conjecture. The algebra $W_{0,3}(SL_m(\mathbb{C}))$ is generated by the extended conformal blocks of level $1$. This is a concrete type $A$ instance of the paper's conformal-block approach to compactifying character varieties; the source provides no resolution or further qualifications of the conjecture.