Characterize Hom-Ext-quiver classification up to derived autoequivalence

Determine whether exceptional collections over general representation-infinite algebras have isomorphic Hom-Ext quivers exactly when they are related by an autoequivalence of their bounded derived categories.

Background

The paper proves for quivers of type $\widetilde{\mathbb A}$ that two exceptional collections have isomorphic Hom-Ext quivers if and only if they are related, after suitable embeddings into the derived category, by a derived autoequivalence. This establishes a classification result in the affine hereditary case.

The authors ask whether the same equivalence holds in general. A positive answer would make the Hom-Ext quiver a tool for classifying exceptional collections over broader classes of representation-infinite algebras.