The induction formula for fundamental classes in equivariant Lagrangian homology

Let $X$ and $X'$ be the varieties in the induction diagram, with a map $g\relationships W\to X'$ and the induced map

$$\xi\colon U\to \operatorname{T}^*X',\qquad (w,l')\mapsto (g(w),l'),$$

where

$$U=\{(w,l')\in W\times_{X'}\operatorname{T}^*X'\mid l'\circ \mathrm{d}g(w)=0\}.$$

Let $[X]\in \operatorname{Lagr}^{\mathbb{G}_{\mathrm{m}}}(\operatorname{T}^*X)$ be the fundamental class of $X$. For every $\Lambda\in\operatorname{Lagr}^{\mathbb{G}_{\mathrm{m}}}(\operatorname{T}^*X')$, choose a general point $x_{\Lambda}=(x',l')\in\Lambda$ such that $\xi^{-1}(x',l')$ is smooth. Induction formula.

$$\operatorname{Ind}([X])=\sum_{\Lambda'\in\operatorname{Lagr}^{\mathbb{G}_{\mathrm{m}}}(\operatorname{T}^*X')}(-1)^{\dim(\Lambda'\cap X')}\chi\bigl(\xi^{-1}(x_{\Lambda'})\bigr)[\Lambda'].$$

This formula would describe the induction map on the fundamental class in terms of Euler characteristics of the fibers of $\xi$, and is intended to clarify the connection between constructible functions on the seminilpotent stack and the top cohomological Hall algebra. The source does not state whether the conjecture is resolved.