It seems that Lan Nguyen proved [in a preprint on arxiv](https://arxiv.org/abs/1309.7675) of 2013 that the Tate-Shafarevich group of a rational elliptic curve is finite. However, I couldn't find any published version thereof. So is it now known that the Tate-Shafarevich group of a rational elliptic curve is finite? Many thanks in advance.