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Anomalous Collision of Exceptional Points on Nonorientable Manifolds

Band degeneracies, ranging from Hermitian Dirac points to non-Hermitian exceptional points (EPs), play a central role in topological phase transitions. Beyond the topology of individual degeneracies, their mutual interactions yield richer phenomena. A representative example is the anomalous non-annihilating collision of pairwise-created degeneracies, previously believed to occur only in non-Abelian multiband systems. Here, we theoretically reveal and experimentally demonstrate that such an anomalous collision can emerge even in a simple two-band system without non-Abelian nature. In a two-dimensional non-Hermitian lattice whose Brillouin zone forms a nonorientable Klein bottle, two EPs with opposite topological charges, pairwise created from a hybrid point, merge into a new vortex point upon re-encounter, instead of annihilating. Remarkably, the hybrid point is a defective degeneracy featuring no eigenenergy braiding, whereas the vortex point is a non-defective degeneracy yet exhibits nontrivial eigenenergy braiding. This process manifests a non-Hermitian phase transition from a gapped phase to a gapless phase, a scenario that we directly observe in a hybrid-dimensional acoustic lattice via momentum-resolved band braid and Berry phase measurements. Our findings identify nonorientability as a new arena for engineering band degeneracies and topological phases, and pave the way for experimentally exploring the interplay between exceptional and nonorientable topology.