Maximal tensor products of uniform matroids and birigidity duality

Prove that the family of tensor products of two uniform matroids has a unique maximal element under the weak order and that this unique maximal element is the dual of the generic birigidity matroid R_{d1,d2}(K_{n1,n2}).

Background

Brakensiek et al. identified the dual of the generic (d1,d2)-birigidity matroid as a tensor product of uniform matroids. The conjecture asks for uniqueness of a maximal such tensor product, paralleling Mason’s symmetric-power question.

This would yield a dual maximality principle for birigidity akin to that conjectured for rigidity.