Perverse-sheaf and BV-quantization conjecture for shifted symplectic stacks

Let $(\mathsf{X}, \omega)$ be a $(-1)$-shifted symplectic Artin stack equipped with orientation data, namely a square root $\det(\mathbb{L}_\mathsf{X})^{\frac12}$ of its determinant line. Let $P_\mathsf{X}$ be the canonical perverse sheaf of $k$-vector spaces on the underlying classical stack $t_0(\mathsf{X})$, and let $\hbar$ be a formal parameter.

Perverse-sheaf and BV-quantization conjecture. There is a canonical BV quantization $\Delta_\hbar$ of $\det(\mathbb{L}_\mathsf{X})^{\frac12}$ and a quasi-isomorphism

$$\mathbf{R}\Gamma(t_0(\mathsf{X}), P_\mathsf{X})(\!(\hbar)\!)\cong (\mathbf{R}\Gamma(\mathsf{X}, \det(\mathbb{L}_\mathsf{X})^{\frac12})(\!(\hbar)\!), \Delta_\hbar)$$

of chain complexes of $k(\!(\hbar)\!)$-vector spaces.

This conjecture proposes that the canonical perverse sheaf associated with an oriented $(-1)$-shifted symplectic Artin stack is captured by its BV quantization after passing to Laurent series in $\hbar$. The preceding results establish the existence of the perverse sheaf and provide examples, but the claimed canonical quantization and quasi-isomorphism are not resolved in the supplied source.