Classify irreducible superquiver representations up to autoequivalence

Prove or disprove that the irreducible representations of any superquiver in a hereditary category are unique up to autoequivalences of that category.

Background

In the superquiver framework, irreducible representations are proposed as the representations that may correspond to Hom-Ext quivers. The paper then raises a stronger classification problem concerning the possible multiplicity of such realizations.

The conjecture asks whether the ambient category's autoequivalences account for all possible irreducible representations of a fixed superquiver, which would provide a categorical uniqueness principle for Hom-Ext-quiver realizations.

References

Conjecture: The irreducible $\mathcal C$ representations of any superquiver are unique up to autoequivalences of $\mathcal C$.

The Hom-Ext quiver and applications to exceptional collections  (2509.16388 - Igusa et al., 19 Sep 2025) in Section 5, immediately after the question characterizing Hom-Ext quivers