The divergence conjecture for CR $Q$-curvature

Let $M$ be a strictly pseudoconvex CR manifold of dimension $2n+1$, with integrable holomorphic tangent bundle $T^{1,0}M$. Choose a contact form $\theta$, and let $Q_\theta$ denote its CR $Q$-curvature. Write $\nabla_a$ and $\nabla_{\overline{a}}$ for covariant derivatives associated with the Tanaka–Webster connection.

Divergence conjecture. On CR manifolds, the $Q$-curvature is a divergence: there exist form-valued local invariants $T_a$ and $T_{\overline{a}}$ of $\theta$ such that

$$Q_\theta=\nabla_{\overline{a}}T_a+\nabla_aT_{\overline{a}}.$$

If true, this would provide a local-invariant divergence expression for the CR $Q$-curvature, extending the explicit divergence formula known in dimension $3$. The supplied text does not indicate whether the conjecture has been resolved.