Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems (opens in new tab)

Accurate numerical eigenvalues are often difficult to certify, especially in singular or non-normal settings. This article reports a human--AI collaboration on two such computations. For a singular self-adjoint Schr\"odinger operator, a verified zero count and Dirichlet--Neumann bracketing certify the complete negative spectrum to ten decimal places. For a delicate non-normal atom--molecule benchmark, a previously unresolved resonance pair is ...