This is a cool statistical paper, one of many depressing papers that makes me wish I knew more math. The "gravitational wave" angle is apparently that it uses some statistical methods that originated in gravity wave research. There are no ultra-sensitive new measurements or anything like that. They use the same X-ray measurements as the Clickspring article from a few years ago (https://bhi.co.uk/antikytheramechanism/) and basically support Clickspring's conclusion (that the Antikythera was a lunar calendar) with increased statistical confidence.