Non-pathology of Q-coloring ideals

Determine whether Q-coloring ideals are non-pathological.

Background

Q-coloring ideals are square unions of two non-pathological Fσ ideals and are locally non-pathological by Proposition 5.31. Their global non-pathology is not resolved.

References

We do not know if Q-coloring ideals are non-pathological.

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in p. 30; Question 5.37, p. 32