The pseudo-fibered triple promotion conjecture

Let $(G,\operatorname{\mathcal{L}}_1,\operatorname{\mathcal{L}}_2)$ be a pseudo-fibered triple. Suppose that $G$ is finitely generated, torsion-free, and freely indecomposable. Pseudo-fibered triple promotion conjecture. One of the following three possibilities holds: $G$ is virtually abelian; $G$ is topologically conjugated into $\operatorname{PSL}_2(\mathbb{R})$; or $G$ is isomorphic to a closed hyperbolic $3$-manifold group. The source attributes this conjecture to earlier work and records partial results, but does not state that it has been resolved.