B-representability of the convexity ideal

Determine whether hom(conv), the ideal of finite unions generated by homogeneous sets of the convexity coloring conv on [N]^3, 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 is B-representable.