Soliton resolution conjecture for the Benjamin-Ono equation in the sharp well-posedness space

We prove the soliton resolution conjecture for the Benjamin-Ono equation in the sharp well-posedness space $H^s\left(\mathbb{R}\right)$ for $s>-\frac12$. This extends soliton resolution to the sharp regularity, whereas previous results required weighted $H^{1,1}\left(\mathbb{R}\right)$ initial data.