Kapovich–Potyagailo–Vinberg's noncoherence conjecture for arithmetic lattices

Let $\Gamma\subset \operatorname{Mob}(\mathbb S^n)$ be an arithmetic lattice with $n\ge 3$. Kapovich–Potyagailo–Vinberg's conjecture. The group $\Gamma$ is noncoherent: it contains a finitely generated subgroup $\Delta$ that is not finitely presentable. The statement is presented as an expectation about the prevalence of algebraic pathologies in higher-dimensional Kleinian groups, and no resolution is given.