The SHGH conjecture for blow-ups of the projective plane

Let $X$ be a composite of blow-ups of $\mathbb P^2$ at points $p_1,\ldots,p_n$ in very general position. A $(-1)$-rational curve is a rational curve with self-intersection $-1$. The SHGH conjecture. Every negative curve on $X$ is a $(-1)$-rational curve. The source notes that this conjecture implies Nagata's conjecture and is motivated by Hilbert's fourteenth problem. Its status is not specified in the source.