The veering sphere conjecture for veering triangulations

Let $M$ be the manifold under consideration, let $\alpha$ denote the relevant veering structure, and let $S^2(\alpha)$ be the veering sphere constructed from it. Let $\partial_\infty \mathbb{H}^3$ be the sphere at infinity of hyperbolic three-space, with $\pi_1(M)$ acting through its discrete and faithful representation. Veering sphere conjecture. The veering sphere $S^2(\alpha)$ is equivariantly homeomorphic to $\partial_\infty \mathbb{H}^3$. This identifies the sphere obtained from the veering construction with the natural boundary at infinity associated to the hyperbolic action of $\pi_1(M)$.