Bobby's spherical flow conjecture for bridgeless cubic graphs

Let $G$ be a bridgeless cubic graph. An $\mathbb{S}^2$-flow is a unit vector flow with values on the unit sphere $\mathbb{S}^2$. Bobby's spherical flow conjecture. Every bridgeless cubic graph has an $\mathbb{S}^2$-flow. This conjecture is proposed as one of two conjectures intended to imply Tutte's $5$-flow conjecture; its status is not resolved in the supplied text.