The classification conjecture for essentially 4-edge-connected pseudo 2-factor isomorphic cubic bipartite graphs

A pseudo $2$-factor isomorphic graph is a graph admitting a $2$-factor such that the parity of the number of cycles is the same for all its $2$-factors. A graph is cubic if every vertex has degree $3$, and it is essentially $4$-edge-connected if it has no non-trivial $3$-edge-cut. Let $G$ be an essentially $4$-edge-connected pseudo $2$-factor isomorphic cubic bipartite graph. The classification conjecture. $G$ must be $K_{3,3}$, the Heawood graph, or the Pappus graph. This conjecture was refuted when Jan Goedgebeur computationally found a pseudo $2$-factor isomorphic cubic bipartite graph on $30$ vertices that is essentially $4$-edge-connected and cyclically $6$-edge-connected.