Tangent-character conjecture for duals of zero-dimensional quiver varieties

Let $\mathcal{M}^{!}=\overline{\mathcal{W}}^{\lambda}_{\mu}$ be the 3d mirror dual of a zero-dimensional quiver variety, with unique torus fixed point $p^{!}$, and set $\hbar^{!}=q/\hbar$. Tangent-character conjecture. The character of the tangent space of $\mathcal{M}^{!}$ at $p^{!}$ is

$$\sum_{\alpha\in\Phi^{-,\mathrm{re}}_\mu}\sum_{i=1}^{\langle\alpha,\mu\rangle}(\hbar^{!})^{1-i}e^{\alpha}+(\hbar^{!})^ie^{-\alpha}.$$

The conjecture agrees dimensionally with the expected Coulomb-branch dimension and is proved in ADE type; its validity beyond ADE type remains open.