Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.
And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!
Bibliography:
Video 1.
The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)
. Source.
The name actually comes from "any". Amazing.
Can only exist in 2D surfaces, not 3D, where fermions and bosons are the only options.
All known anyons are quasiparticles.
On particle exchange:
so it is a generalization of bosons and fermions which have and respectively.
Key physical experiment: fractional quantum Hall effect.
Exotic and hard to find experimentally.
Video "The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)" at youtu.be/dQWn9NzvX4s?t=3707 says that no one has ever been able to come up with an intuitive reason for the proof.

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