Relative hyperbolicity conjecture for fully irreducible automorphisms of infinitely ended groups

Let $G$ be the fundamental group of a non-sporadic graph of groups with finite edge stabilisers, and let $\Phi\in\operatorname{Aut}(G)$ be fully irreducible relative to this splitting. A suspension of a subgroup associated to $\Phi$ is its semidirect product with the cyclic factor induced by $\Phi$. Relative hyperbolicity conjecture. Then, for some positive integer $N$, the group

$$G\rtimes_{\Phi^N}\mathbb{Z}$$

is hyperbolic relative to the suspensions of the polynomially growing subgroups of $\Phi$. A proof would extend the relative hyperbolicity argument to general infinitely ended groups and complete the main theorem without an assumption on torsion; the statement remains open in the source.