The relative hyperbolicity classification conjecture for hierarchical twist-free graphs of multicurves

A hierarchical, twist-free graph of multicurves is a graph $d4a2$ equipped with the hierarchical structure described in the paper, with no twists. The associated HHS structure is the one constructed for $d4a2$ in Theorem described in the source.

Relative hyperbolicity classification conjecture. $d4a2$ is relatively hyperbolic if and only if this HHS structure has isolated orthogonality.

This conjecture would characterize relative hyperbolicity directly from the natural HHS structure of a hierarchical, twist-free graph of multicurves. The preceding discussion establishes only that isolated orthogonality is a sufficient condition, so the converse remains open.