The Steiner subratio conjecture for the Euclidean plane

Let $\operatorname{ssr}(\mathbb R^2)$ denote the Steiner subratio of the Euclidean plane, defined as the infimum of the ratios of minimal-filling weight to Steiner minimal-tree length over all nontrivial finite subsets. Steiner subratio conjecture. The infimum is attained at the vertex set of a regular triangle and

$$\operatorname{ssr}(\mathbb R^2)=\sqrt{3}/2.$$

The source records the exact values for three- and four-point subsets and proposes that the global Steiner subratio has the same value, but gives no resolution of the conjecture.