Minkowski-plane bead-gap tightness conjecture for Steiner minimum paths

Let $N$ be a set of $n$ terminals in a Minkowski plane $M$ with unit ball $B$, and let $T_S$ and $T_{\mathrm{opt}}$ be a $d_M$-SMT and a $d_M$-MSPT on $N$, respectively. Minkowski-plane bead-gap conjecture. The upper bound

$$\mathrm{beads}(T_S)-\mathrm{beads}(T_{\mathrm{opt}})\leq 2n-4$$

is tight if and only if $B$ is not a parallelogram. This conjecture concerns the sharp performance gap between Steiner minimum trees and minimum Steiner point trees in Minkowski planes; the supplied text gives no resolution.