Extremality of direct sums

Prove that the direct sum of extremal matroids is extremal; specifically, establish that if matroids M_1,\ldots,M_s are extremal, then M_1\oplus\cdots\oplus M_s is extremal.

Background

The paper defines a matroid as extremal when its associated point is a vertex of the unlabelled polytope \Omega_{r,n}. It proves that extremality passes from an extremal direct sum to each of its direct summands, but the converse is left unresolved. Computational verification confirms the converse for disconnected matroids on at most seven elements, motivating the conjecture in general.