The negative-curve conjecture for blow-ups of the plane

Let $C$ be a prime divisor on ${\rm Bl}_{s}(\mathbb{P}^{2})$. Negative-curve conjecture. If

$$C^{2}<0,$$

then $C$ is a $(-1)$-curve. This conjecture describes the expected negative curves on blow-ups of the projective plane and is related to the structure of their effective and nef cones. The supplied text gives no resolution status.