B-representability of the convexity homogeneous ideal

Determine whether the ideal hom(conv), generated by homogeneous sets of the convexity coloring, is a B-ideal.

Background

The paper constructs the convexity coloring and proves that both hom(conv) and B(phom0(conv)) are tall Borel ideals with notable Katětov properties. It does not determine whether hom(conv) itself has a B-representation.