Uniform convergence conjecture for mapping torus subgroups

Let $G_\phi$ be the mapping torus subgroup from the preceding conjecture, acting on $S^2$ by the action constructed in the paper's false proof.

Uniform convergence conjecture. This action is a uniform convergence group.

The conjecture is proposed as a stronger version of the convergence-group conjecture because the proof fails only when a limiting point may be fixed by the monodromy. The paper does not resolve this issue, so the stronger conjecture remains open.