Bergeron–Venkatesh–Lück torsion growth conjecture for 3-manifolds

Let $M$ be a compact connected orientable and irreducible $3$-manifold with infinite fundamental group and empty or toroidal boundary. A cofinal tower of regular finite-sheeted covers is a sequence

$$M=M_0\twoheadleftarrow M_1\twoheadleftarrow M_2\twoheadleftarrow\cdots$$

of regular finite-sheeted covers whose corresponding subgroups are cofinal. Let $P_i$ be the hyperbolic pieces in the JSJ decomposition of $M$. Bergeron–Venkatesh–Lück conjecture. Then $M$ admits such a tower for which

$$\lim_{n\rightarrow\infty}\frac{\log\left(\left|\operatorname{Tor}(H_1(M_n;\mathbb{Z}))\right|\right)}{[\pi_1(M):\pi_1(M_n)]}=\frac{\sum_i\operatorname{vol}(P_i)}{6\pi}.$$

This conjecture predicts that torsion in first homology grows at a rate determined by the total volume of the hyperbolic JSJ pieces. The supplied text attributes it to influential work of Bergeron–Venkatesh and Lück but gives no resolution, so its status is left open.