The disjoint-edge lower bound for dense geometric graphs

Let $G$ be a geometric graph with $2|E(G)|\geq |V(G)|$. The disjoint-edge lower-bound conjecture. Then

$$|DJ(G)|\geq \frac{n}{2}\cdot \binom{d(G)}{3}.$$

This conjecture gives a lower bound for the number of disjoint edge pairs in a sufficiently edge-dense geometric graph. The source gives no resolution, so the claim remains open.