Star embedding conjecture for Euclidean Steiner trees

Let $G$ be a graph with $m$ edges, and embed each edge by its characteristic vector, as in the Vertex Cover reduction discussed in the source. Consider the Euclidean Steiner tree of the resulting point configuration. Star embedding conjecture. Over all graphs with $m$ edges, the embedding of the star graph on $m$ edges has the minimum cost Steiner tree. The source presents this as a weaker version of the fixed-terminal simplex conjecture and as relevant to proving APX-hardness of Euclidean Steiner Tree. Its resolution is not stated.