Approximation conjecture for analytic torsion along shrinking congruence subgroups

Let $G$ be the reductive group defining the symmetric space $\widetilde{X}$, let $\tau\in\operatorname{Rep}(G(\mathbb{R}))$ satisfy $\tau\not\cong\tau_\theta$, and let $\{K_j\}_{j\in\mathbb{N}}$ be open compact subgroups of $G(\mathbb{A}_f)$ such that $K_j\to 1$. Write $X(K_j)$ for the associated adelic quotient, and let $t^{(2)}_{\widetilde{X}}(\tau)$ denote the $L^2$-torsion density of $\widetilde{X}$. Approximation conjecture. One has

$$\lim_{j\to\infty}\frac{\log T_{X(K_j)}(\tau)}{\operatorname{vol}(X(K_j))}=t^{(2)}_{\widetilde{X}}(\tau).$$

This conjecture predicts that normalized analytic torsion on increasingly deep congruence quotients is governed by the $L^2$-torsion of the universal symmetric space. It generalizes known approximation results in the compact case to broader reductive groups; its status is not resolved in the supplied text.