Breuil--Mézard weight conjecture without a tameness hypothesis

Let $\overline r$ be as in the paper, and let $W_{\mathrm{gen}}(\overline r)$ be the subset of generic modular Serre weights. Let $W^{\mathrm{BM}}_{\mathrm{gen}}(\overline r_p)$ be the set of generic weights detected by the supports of the Breuil--Mézard cycles. Breuil--Mézard weight conjecture.

$$W_{\mathrm{gen}}(\overline r)=W^{\mathrm{BM}}_{\mathrm{gen}}(\overline r_p).$$

This is presented as a generalization of the tame Gee--Herzig--Savitt weight conjecture to representations that are not necessarily tame at places above $p$; the source does not state a resolution here.