Torsion conjecture for three-dimensional closed CR Yamabe solitons

Let $(M^3,J,\theta,f,\mu)$ be a three-dimensional closed CR Yamabe soliton, where $P_0$ is the CR Paneitz operator. Assume that $P_0f=0$ and that $f$ is nowhere vanishing. Torsion conjecture. The soliton has zero pseudohermitian torsion. This follows in the paper from its stated vanishing CR $Q$-curvature conjecture together with the torsion-vanishing theorem, so its independent status depends on that preceding conjecture.