Angle convergence conjecture for cyclic pursuit on compact manifolds

Let $M$ be a compact manifold, let $\{b_i(t)\}_{i\in \mathbb{Z}/n}$ be pursuit curves, and let $l_i(t)$ and $\theta_i(t)$ denote the associated edge lengths and angles. Angle convergence conjecture. If $l_i(t)>0$ for every $i\in\mathbb{Z}/n$ and every $t\geq 0$, then

$$\theta_i(t)\rightarrow 0$$

for every $i\in\mathbb{Z}/n$. This conjecture would imply convergence to a closed geodesic, or a point, on compact manifolds whose space of closed geodesics is discrete; the supplied source does not state that it has been resolved.