Just-infinite GK-dimension conjecture for the positive Witt enveloping algebra

Let ${\rm U}(W_+)$ be the universal enveloping algebra of the positive Witt algebra $W_+$ over a field of characteristic zero. The algebra ${\rm U}(W_+)$ has just infinite Gelfand–Kirillov dimension: if $I$ is a nonzero two-sided ideal of ${\rm U}(W_+)$, then

$$\operatorname{GKdim}({\rm U}(W_+)/I)<\infty.$$

This conjecture proposes that every nonzero quotient has finite Gelfand–Kirillov dimension, extending the finite-dimensionality result known for several classes of ideals, including ideals generated by quadratic expressions. The general case remains open.