Asymptotic signature formula for irreducible modules of arbitrary support

Let $W$ be a finite real reflection group, let $c\in\mathfrak{p}_{\mathbb{R}}$, and let $\lambda\in\operatorname{Irr}(W)$. Let $L_c(\lambda)$ be the corresponding irreducible rational Cherednik algebra module, and choose a generic point $b\in\operatorname{Supp}(L_c(\lambda))\cap\mathfrak{h}_{\mathbb{R}}=\operatorname{Supp}K_{c,\lambda}$. Set $W'=\operatorname{Stab}_W(b)$ and use the local decomposition and Hermitian forms $h_\mu$ from the local structure conjecture. Asymptotic signature conjecture. The asymptotic signature $a_{c,\lambda}$ is

$$a_{c,\lambda}=\frac{\displaystyle\sum_{\substack{\mu\in\operatorname{Irr}(W')\\ \dim L_c(\mu)<\infty}}\dim L_c(\mu)\,a_{c,\mu}\,\operatorname{sign}(h_\mu)}{\dim\operatorname{Res}_b L_c(\lambda)}.$$

For full-support modules this specializes to the established signature theorem, while the arbitrary-support formula depends on the preceding local description and is presented as a conjectural extension.