Computable versus Baire complexity on integer grids

Determine whether BAIRE(Z^n) is contained in COMPUTABLE(Z^n) for every integer n at least 2, noting that any such inclusion would necessarily be strict.

Background

The paper proves that COMPUTABLE(Zn) is not contained in BAIRE(Zn), thereby separating the two classes in one direction. The reverse inclusion remains unresolved and is explicitly posed as a question.

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”; Section 7, subsection “Open problems”