Half-density limit for the maximum number of clusters

Let $S(n)$ denote the maximum number of connected components (clusters) obtainable in a bounded confidence (BC) process with $n$ agents. Half-density limit conjecture.

$$\lim\limits_{n\to\infty}\frac{S(n)}{n}=\frac{1}{2}$$

Determining this limit would give the asymptotic maximum fraction of agents-sized clusters that can occur. The source presents the value as a conjectural possibility after discussing finite-case restrictions, and gives no proof or resolution.