Pathology of the random ideal

Determine whether the random ideal R generated by cliques and anticliques of the random graph is pathological.

Background

The paper establishes pathology for ideals generated by cliques and anticliques in random d-uniform hypergraphs when d is at least 3. The corresponding question for the ordinary random graph ideal R is not resolved by the techniques developed in the paper.

References

the pathology of the random ideal R remains an open question.

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in Section 1, page 3; Question 5.19, page 28