Robertson's representativity conjecture for toroidal graphs

Let $G$ be a $2$-edge-connected graph embedded in the torus. Robertson's conjecture. If the representativity of the embedding is at least $3$, then $G$ has a nowhere-zero $4$-flow. The paper states that its theorem on cyclically $4$-edge-connected toroidal graphs implies this conjecture, so it is solved by the result presented.