Mironov–Morozov expansion formula for the BGW tau-function

Let $\operatorname{DP}$ denote the set of strict partitions, let $Q_\lambda({\bf t})$ be the normalized Schur Q-function, and let $\delta_{k,j}$ denote the specialization with value $1$ when $k=j$ and $0$ otherwise. The BGW partition function is denoted by $\tau_{BGW}$. Mironov–Morozov's BGW expansion conjecture.

$$\tau_{BGW}= \sum_{\lambda \in \operatorname{DP}} \left(\frac{\hbar}{16}\right)^{|\lambda|} \frac{Q_\lambda({\bf t}) Q_\lambda(\delta_{k,1})^3}{Q_{2\lambda}(\delta_{k,1})^2}.$$

This is proposed as the BGW analogue of the Mironov–Morozov expansion for the Kontsevich–Witten tau-function; the source does not establish the formula in the stated conjectural passage.