Dewar's degree-threshold conjecture for globally rigid vertex-transitive graphs

A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A graph is globally rigid in $\mathbb{R}^d$ if almost all embeddings of its vertices in $\mathbb{R}^d$ are unique up to isometries. The degree of a graph is the common number of neighbours of each vertex when the graph is regular.

Dewar's conjecture. There exists a function $f \colon \mathbb{N}\rightarrow \mathbb{N}$ with the following property. For $d\in \mathbb{N}$, if $G$ is a vertex-transitive graph of degree at least $f(d)$, then $G$ is globally rigid in $\mathbb{R}^d$.

This conjecture asks for a dimension-dependent degree threshold guaranteeing global rigidity for vertex-transitive graphs. The source states that the conjecture is positively answered by the paper, so it is solved; the abstract also says that the constant obtained for regularity is best possible.