The homotopy Gerstenhaber structure conjecture for topological vertex operator algebras

Let $V^\bullet[\cdot]$ be a topological vertex operator algebra (TVOA), with dot product and bracket product defined by the vertex-operator operations above. The homotopy Gerstenhaber structure conjecture. The dot product and the skew-symmetrization of the bracket can be extended to a $G_\infty$-algebra structure on $V^\bullet[\cdot]$. This would lift the Gerstenhaber algebra structure known on the BRST cohomology of a TVOA to a homotopy-coherent structure on the cochain-level TVOA itself. The supplied text does not establish the extension, so its resolution is unknown.