Petukhov–Shestakov conjecture on the just infinite GK-dimension of the positive Witt enveloping algebra

Let $\mathbb K$ be a field of characteristic zero, and let $W_+$ be the positive Witt algebra with basis $\{e_n:n\geqslant 1\}$ and Lie bracket $[e_i,e_j]=(j-i)e_{i+j}$. Its universal enveloping algebra is $U(W_+)$. Petukhov–Shestakov's conjecture. The algebra $U(W_+)$ has just infinite Gelfand–Kirillov dimension: for every non-zero ideal $I$ of $U(W_+)$, the quotient $U(W_+)/I$ has polynomial growth. This conjecture concerns the sparse two-sided ideal structure of the enveloping algebra of the positive Witt algebra; the supplied text does not state whether it has been resolved.