The generalized torsion characterization of bi-orderable 3-manifold groups

Let $G$ be the fundamental group of a $3$-manifold. A non-trivial element $g\in G$ is a generalized torsion element if some non-empty finite product of conjugates of $g$ equals the identity; the group $G$ is bi-orderable if it admits a strict total ordering invariant under multiplication from the left and right. Generalized torsion conjecture for 3-manifold groups. The group $G$ is bi-orderable if and only if $G$ has no generalized torsion element.

This conjecture proposes that, among fundamental groups of $3$-manifolds, generalized torsion is exactly the obstruction to bi-orderability. The source presents it as an expectation and attributes it to the authors' earlier work; no resolution is given here.