The 5-flow reconfiguration conjecture

Let $G$ be a graph, and let $\mathcal{F}(G,k)$ denote its reconfiguration graph whose vertices are nowhere-zero $k$-flows, with adjacency given by changing flow values only on a cycle of $G$. A graph is 2-edge-connected if it has no bridge. The 5-flow reconfiguration conjecture. For every 2-edge-connected graph $G$, the reconfiguration graph

$$\mathcal{F}(G,5)$$

is connected. This is a reconfiguration analogue of the existence question in Tutte's 5-flow conjecture; unlike existence, connectedness does not imply that the reconfiguration graph is nonempty, and the conjecture remains open.