Why does this weird quantum system hide a hidden symmetry despite looking broken?

Researchers studied a degenerate quantum oscillator that classically produces solutions with secular terms (growing oscillations). They discovered the quantum version conceals a hidden u(2,1) algebra that generates finite-dimensional invariant subspaces with Jordan structure—a form of degeneracy that mirrors the classical breakdown. The model reveals how higher-derivative systems can simultaneously exhibit mathematical brokenness and hidden symmetry.