Quantum extension conjecture for the beta-gamma and bc vertex algebras

Let $cmathfrak{gl}(1|1)$ be the smallest type-A Lie superalgebra, let $cmathcal V_{chbar,k}(cmathfrak{gl}(1|1))$ be its quantum vertex algebra, and set

$$\mathcal V=\bigoplus_n\sigma^{n,0}\mathcal V_1(\mathfrak{gl}(1|1)).$$

Here $csigma^{n,0}$ denotes the spectral-flow action. Quantum extension conjecture. The $cwidehat{DY}_{chbar,cell}(cmathfrak{gl}(1|1))$-module $cmathcal V$ has the structure of a quantum vertex algebra extending $cmathcal V_1(cmathfrak{gl}(1|1))$, and it quantizes $V_{cbetacgamma}cotimes V_{bc}$. This is the quantum counterpart of the known classical extension $V_{cbetacgamma}cotimes V_{bc}\cong\bigoplus_n V_{n,0}$; no resolution is given.