Baire versus computable complexity on grids

Determine whether the inclusion BAIRE(Z^n) is contained in COMPUTABLE(Z^n) for every integer n at least 2.

Background

The paper proves that COMPUTABLE(Zn) is not contained in BAIRE(Zn) for n at least 2. The reverse inclusion is not settled, so the two complexity notions may still be strictly ordered in the opposite direction or may be incomparable.

References

We do not know whether the opposite inclusion $BAIRE(Zn) \subseteq COMPUTABLE(Zn)$ holds; indeed, it could even be that $BAIRE() \subseteq COMPUTABLE()$ for every finitely generated group $\Gamma$.

— Separating complexity classes of LCL problems on grids  (2501.17445 - Berlow et al., 29 Jan 2025) in Section 1, subsection “Computable combinatorics”

Does the ({necessarily strict} inclusion $BAIRE(Zn) \subset COMPUTABLE(Zn)$ hold?

— Separating complexity classes of LCL problems on grids  (2501.17445 - Berlow et al., 29 Jan 2025) in Section 6, subsection “Open problems”