Xie's bilipschitz conjecture for quasiconformal mappings of Carnot groups

Let $G$ be a Carnot group, and let $U,U'\subset G$ be open sets. Xie's conjecture. If $G$ is neither $\mathbb{R}^n$ nor a Heisenberg group $\mathbb{H}_n$, then every quasiconformal homeomorphism

$$f:G\supset U\to U'\subset G$$

is locally bilipschitz. If $U=G$, then $f$ is bilipschitz. This conjecture concerns the higher-integrability versus local-bilipschitz regularity of quasiconformal maps; the supplied source notes that, outside Euclidean and Heisenberg cases, known examples are locally bilipschitz, but does not state a resolution.