Classification conjecture for irreducible modules of $W_{1+\infty,-N}$

Let $W_{1+\infty,-N}$ be the vertex algebra at central charge $-N$, let $\mathfrak h$ be the parameter space used to construct the modules $V(\lambda,-N)$, and let $V(\lambda,-N)$ denote the irreducible $W_{1+\infty,-N}$-subquotient generated by the vector $v_\lambda$ in the corresponding module $M(1,\lambda)$. Classification conjecture. The set $V(\lambda,-N)$, with $\lambda\in\mathfrak h$, lists all the irreducible modules for the vertex algebra $W_{1+\infty,-N}$. The preceding theorem establishes that each $V(\lambda,-N)$ is irreducible, but the text provides no resolution of whether every irreducible module arises in this way.