Dimensional reduction conjecture for $-2$-shifted symplectic derived schemes

Let $\boldsymbol{Y}$ be a $-2$-shifted symplectic derived scheme over $\operatorname{Spec}{\mathbb C}$, equipped with an orientation, and set $Y=t_0(\boldsymbol{Y})$. Let $\widetilde{Y}=t_0(\mathbf{T}^*[-1]\boldsymbol{Y})$, let $q\colon\widetilde{Y}\to{\mathbb A}^1$ be the quadratic function induced by the $-2$-shifted symplectic form, let $\varphi_{\mathbf{T}^*[-1]\boldsymbol{Y}}$ be the associated perverse sheaf, and let $0_Y\colon Y\to\widetilde{Y}$ be the zero section. Dimensional reduction conjecture. There exist natural isomorphisms

\gamma\colon 0_Y^!\varphi_{\mathbf{T}^*[-1]\boldsymbol{Y}]\cong{\mathbb Q}_Y[\operatorname{vdim}\boldsymbol{Y}],\qquad \bar{\gamma}\colon 0_Y^*\varphi_{\mathbf{T}^*[-1]\boldsymbol{Y}]\cong\omega_Y[-\operatorname{vdim}\boldsymbol{Y}],

and there exists a natural isomorphism

$$\delta\colon 0_Y^!\varphi_q(\varphi_{\mathbf{T}^*[-1]\boldsymbol{Y}})\cong\omega_Y$$

which depends on the chosen orientation. The conjecture is proposed as a sheaf-theoretic basis for constructing the DT4 virtual class; the supplied text gives no resolution status.