Robertson's surface representativity conjecture for nowhere-zero 4-flows

Let $S$ be a surface. Robertson's surface conjecture. There is a constant $r$ such that every $2$-edge-connected graph embedded in $S$ with representativity at least $r$ has a nowhere-zero $4$-flow. The toroidal case with threshold $3$ is implied by the paper's theorem, but the source does not state that the conjecture for every surface has been resolved.