The general-position quartic lower-bound conjecture for radial orderings

Let $S$ be a set of $n$ points in general position in the plane, meaning that no three points are collinear. General-position quartic lower-bound conjecture. $S$ has at least $\Omega(n^4)$ distinct radial orderings.

The proved lower bound assumes strong general position; this conjecture asserts that ordinary general position is sufficient as well.