Spectral degeneracies (dubbed nodal points in momentum space) play fundamental roles in understanding exotic properties of light and matter. In lattice systems, unpaired band-structure degeneracies are subject to well-established no-go (doubling) theorems that universally apply to both closed Hermitian systems and open non-Hermitian systems. However, the non-Abelian braid topology of non-Hermitian multiband systems provides a loophole to these constraints. Here we successfully leverage this loophole in a non-Hermitian three-band system, implementing an unpaired third-order exceptional point (EP3), which manifests as a non-Abelian monopole. We explicitly demonstrate the intricate braiding topology and non-Abelian, path-dependent, fusion rules underlying the unpaired EP3. The experiment uses a new design of single-photon interferometry, enabling eigenstate and spectral resolutions for multiband systems with widely tunable parameters. Thus, the union of state-of-the-art experiments, fundamental theory, and everyday concepts such as braids pave the way toward the highly exotic non-Abelian topology unique to non-Hermitian settings.

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• Quantum simulation
• Topological phase transition
• Topological phases of matter
• Exceptional points
• Non-Hermitian systems
• Topology