The completely reversible edge-coloring form of the linear arboricity conjecture

Let $\Sigma$ be a simple signed graph, let $\Delta(\Sigma)$ be its maximum degree, and let $\chi'_R(\Sigma)$ be the minimum number of colors in a completely reversible zero-free proper edge coloring of $\Sigma$. Linear arboricity edge-coloring conjecture.

$$\Delta(\Sigma)\leq\chi'_R(\Sigma)\leq\Delta(\Sigma)+2.$$

This is the paper's signed-edge-coloring formulation of the linear arboricity conjecture, obtained by representing color classes as linear forests. The parser provides no resolution evidence, so the claim is recorded as open.