Existence of interpolation categories that are not MZ-solvable

Determine whether there exist interpolation categories that are not MZ-solvable; that is, identify whether some interpolation category C satisfies (MZ)^n(C) ≠ Vec_k for all finite n.

Background

The authors define a pre-Tannakian category C to be MZ-solvable if iterating the MZ operation finitely many times gives Vec_k. They show many examples are MZ-solvable and analyze inert categories where MZ(C)=C.

Despite extensive examples, they explicitly state that they do not know any interpolation categories failing MZ-solvability, highlighting the existence question.

References

In fact, we don't know any interpolation categories that are not MZ-solvable.

— The Drinfeld center of an oligomorphic tensor category  (2604.00290 - Etingof et al., 31 Mar 2026) in Section 9.2 (The MZ operation)