Koszulness conjecture for Chow rings of matroids

A matroid Chow ring is the Chow ring associated with a matroid. These rings form a conjectural class of quadratic algebras arising in the same general setting as the cohomology rings of wonderful models.

Matroid Chow-ring conjecture. The Chow ring of any matroid is Koszul.

Matroid Chow rings are known to be quadratic, and the conjecture asks whether they are therefore Koszul. This remains open in the source.