Every reference I have seen, including e.g. question (a) on page 5 of these notes or the comments in the answer of this post, use a hand-wavy perturbation theory argument for non-degeneracy of the ground state to explain why the ground state of helium is a singlet.
However, is there any mathematically rigorous way to prove that this is actually the case? (Ideally without perturbation theory, but using precise perturbation bounds would also be accepted begrudgingly).
Any help is much appreciated! :)
