A quantum black hole modeled as a fuzzy sphere has a half-filled Fermi sea. As the black hole evaporates, the sphere shrinks — which means the Fermi sea must lose states. But fermion number is conserved. The tunneling amplitude from a large fuzzy sphere to a small one should be zero: you cannot remove fermions from the sea without violating the conservation law.
Chu (arXiv:2603.12199) shows that a monopole on the fuzzy sphere supplies zero modes — states at exactly zero energy that can absorb or release fermions without violating any conservation law. The monopole is not an optional addition. It is demanded by the topology of the fuzzy sphere itself: the gauge field on a compact surface must have non-trivial topology, and non-trivial topology means monopoles, and monopoles mean zero modes. The conservation law that forbids the tunneling simultaneously dictates what must be present (a topological defect) that permits it.
The released fermions follow a Boltzmann distribution at the Hawking temperature. They are Hawking radiation — not derived from quantum field theory on curved spacetime (Hawking's original route) but from the quantum mechanics of a finite-dimensional Hilbert space tunneling between sizes. The semiclassical result emerges from a completely different starting point.
What makes this structurally sharp is not that a loophole exists — physics is full of processes that evade prohibitions through subtle mechanisms. It is that the constraint uniquely specifies the loophole. Fermion conservation says: you cannot do this unless you have zero modes. The topology of the sphere says: you must have a monopole. The monopole says: here are your zero modes. Each link in the chain is not one option among many. It is the only option. The conservation law does not merely permit the tunneling mechanism — it dictates what the tunneling mechanism must be.
This inverts the usual relationship between conservation laws and dynamics. Normally, conservation laws are constraints: they reduce the space of allowed processes. Here, the constraint is so specific that it leaves only one path open, and that path turns out to reproduce the physics that was known from entirely different methods. The constraint is not a wall. It is a corridor — and the corridor leads exactly where it should.
Unitarity, in this model, is manifest: the full quantum state is tracked through the tunneling. No information is lost because the microscopic description (a finite-dimensional Hilbert space with conserved quantum numbers) never had room for information to hide. The paradox dissolves not by finding where the information went, but by using a description where it was never missing.