Hikami--GPPV--Manolescu radial limit conjecture for WRT invariants

Let $M$ be a rational homology sphere. For each $\operatorname{Spin}^c$ structure $b\in\operatorname{Spin}^c(M)$, suppose there are invariants $\Delta_b\in\mathbb{Q}$, $c\in\mathbb{Z}_{\ge 0}$, and $\widehat{Z}_b(q;M)\in 2^{-c}q^{\Delta_b}\mathbb{Z}[[q]]$ that are conjugation-invariant and converge for $|q|<1$. Let $\zeta_k=\bm{e}(1/k)$ for positive integers $k$. The radial limit conjecture. For infinitely many $k\in\mathbb{Z}_{>0}$, the radial limits $\lim_{q\to\zeta_k}\widehat{Z}_b(q;M)$ converge and

$$Z_k(M)=\lim_{q\to\zeta_k}\frac{1}{(\zeta_{2k}-\zeta_{2k}^{-1})\sqrt{|H_1(M,\mathbb{Z})|}}\sum_{a,b\in\operatorname{Spin}^c(M)}\bm{e}(k\operatorname{lk}(a,a)-\operatorname{lk}(a,b))\widehat{Z}_b(q;M),$$

where $\operatorname{lk}$ is the linking form $H_1(M,\mathbb{Z})\times H_1(M,\mathbb{Z})\to\mathbb{Z}$. This conjecture connects WRT invariants with radial limits of $q$-series and has been proved by Murakami except for convergence of the individual radial limits.