da Silva's conjecture on realizability of positively oriented matroids

An oriented matroid is a combinatorial abstraction of the dependence relations among a set of real vectors together with their signs; a positively oriented matroid is an oriented matroid for which all bases have a positive orientation. A matroid is realizable if it can be represented by a set of vectors in a real vector space.

da Silva's conjecture. Every positively oriented matroid is realizable.

The paper proves this conjecture more strongly by showing that every positively oriented matroid is a positroid, and hence is realizable over $\mathbb{Q}$.