Hadwiger's conjecture for oriented matroids

Let $M$ be a loopless oriented matroid with no $M(K_4)$ minor. A Hadwiger conjecture for oriented matroids. $M$ has a nowhere-zero $3$-coflow. This is the first non-trivial open case of the oriented-matroid generalization of Hadwiger's graph-colouring conjecture; its dual formulation asserts the analogous statement for coloop-free oriented matroids and nowhere-zero $3$-flows. For regular oriented matroids, the conjecture includes the open cases $k=4$ and $k=5$ of Tutte's $k$-flow conjecture.