The bounded negativity conjecture for blow-ups of the plane at generic points

Let $X$ be obtained by blowing up $r>9$ generic points of $\mathbb{P}^{2}$. A prime divisor is an irreducible divisor $C\subset X$.

Bounded negativity conjecture for generic blow-ups. Then $C^2\ge -1$ for every prime divisor $C$, with equality if and only if $C$ is a smooth rational curve with $K_X\cdot C=-1$.

This is presented as a case of bounded negativity not yet known for blow-ups at more than nine generic points, where the effective cone is not finitely generated.