The two-dimensional Chebyshev flow-number conjecture

Let $G$ be a bridgeless graph, and let $\Phi^\infty_2(G)$ denote its two-dimensional flow number for the Chebyshev norm.

Two-dimensional Chebyshev flow-number conjecture. For every bridgeless graph $G$,

$$\Phi^\infty_2(G)\leq\frac52.$$

The conjecture is presented as one of the paper's two principal open problems and is described as a stronger consequence of the $1/2$-flow-pair conjecture.