The three-dimensional Manhattan flow conjecture

Let $G$ be a bridgeless graph, and let $\Phi^1_3(G)$ be its three-dimensional flow number for the Manhattan norm.

Three-dimensional Manhattan flow conjecture. For every bridgeless graph $G$,

$$\Phi^1_3(G)=2.$$

The analogous assertion for the Chebyshev norm is proved in the paper, whereas the Manhattan-norm assertion is stated because the authors are unable to establish it.