Genericity conjecture for sphere packings

Let $G=(V,E)$ be the contact graph of a sphere packing $P$ with generic radii, where generic means that the radii form an algebraically independent set. Regard $P$ as a bar-and-joint framework in three-dimensional Euclidean space, and call it stress-free if it has no nonzero self-stress. Genericity conjecture for sphere packings. The framework $P$ is stress-free, and hence

$$|E| \leq 3|V|-6$$

whenever $|V|\geq 3$. This predicts that randomly chosen radii force a low contact number; Maxwell's result gives the displayed bound for stress-free frameworks.