  Let $G$ be a ribbon graph. Matthew Baker and Yao Wang proved that the
rotor-routing torsor and the Bernardi torsor for $G$, which are two torsor
structures on the set of spanning trees for the Picard group of $G$, coincide
when $G$ is planar. We prove the conjecture raised by them that the two torsors
disagree when $G$ is non-planar.
