Stretching cusps conjecture for arithmetic locally symmetric manifolds

Let $N$ be a cusped arithmetic hyperbolic $n$-manifold, or more generally a negatively curved, arithmetic locally symmetric manifold that is noncompact but has finite volume. Let $M$ be the double of $N$, and let $(g_i)$ be a sequence of Riemannian metrics on $M$ such that $(M,g_i)$ has at least $i$ hidden symmetries.

Stretching cusps conjecture. The sequence $\{(M,g_i)\}$ Gromov–Hausdorff converges, in the appropriate sense, to a disjoint union of two isometric copies of $N$.

This conjecture proposes that arbitrarily many hidden symmetries force the doubled manifold to degenerate toward its two copies of the finite-volume piece. The supplied text gives no evidence that the conjecture has been resolved.