It's based on knowledge of the related estimates, applying similar techniques to geometric problems, knowledge of all the prior works that lead to the current work, and speaking with members of the team themselves. They are much further along than it appears at first glance. All of the major bottlenecks have fallen; the only concern was whether double precision accuracy is good enough. The team seems to have estimates that are strong enough for this, but obviously keep them close to their chest.

PINNs are different in concept, yes, but clearly no less important, so the additional attention will be appreciated. Asking LLMs for proofs is a different vein of research, often involving Lean. It is much further behind, but still making ground.