Lian–Zuckerman's lifting conjecture for topological vertex algebras

Let $V$ be a topological vertex algebra with parity $p(x)$, vacuum and vertex operations $x_{(n)}y$, and distinguished odd element $G$. Define the symmetrized product and bracket by

$$x\cdot y=\frac{1}{2}\left(x_{(-1)}y+(-1)^{p(x)p(y)}y_{(-1)}x\right),$$ $$(-1)^{p(x)}[x,y]=\frac{1}{2}\left((G_{(0)}x)_{(0)}y+(-1)^{p(x)p(y)}(G_{(0)}y)_{(0)}x\right).$$

Lian–Zuckerman's lifting conjecture. The product and bracket extend to a $G_\infty$ structure on $V$. The conjecture is presented as an open problem in the source, with no resolution supplied here.