Caprace–Kalantar–Monod conjecture on type I locally compact groups

Let $G$ be a second countable locally compact group of type I, meaning that any two irreducible unitary representations of $G$ that are weakly equivalent are unitarily equivalent. Caprace–Kalantar–Monod's conjecture. The group $G$ admits a cocompact amenable subgroup. The paper proves this assertion for second countable, unimodular locally compact hyperbolic groups, while the conjecture for general second countable locally compact groups of type I remains open.