Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems

The article presents a human-AI collaboration that successfully verified numerical eigenvalues in challenging settings, specifically achieving ten decimal places of accuracy for a singular self-adjoint Schrödinger operator and resolving a non-normal atom-molecule resonance pair. The latter was accomplished by reformulating the problem into a global matching system for projective solution lines, utilizing a Krawczyk-Brouwer inclusion for certification. This work highlights the potential of AI in enhancing mathematical verification processes while emphasizing the necessity for rigorous standards in validation and the critical role of human oversight in mathematical proofs.