Assess whether double-role operators constitute a worthwhile research subject

Determine whether the complexity of double-role operators reflects a mathematically rich subject for further study or instead indicates that the concept is misguided and not worth pursuing.

Background

Double-role operators are operators that simultaneously serve as hopping operators for topological excitations and symmetry patch operators. The paper finds that their statistics and anomalies can exhibit varied and intricate relationships, with filling patterns depending on the dimension, form degree, and fusion group.

The authors leave unresolved whether this complexity reveals a productive area of investigation or signals that double-role operators are conceptually inappropriate for relating statistics and anomaly. The question is explicitly presented as an open question, although the paper notes that its answer will influence the direction of future work.