topological analytics shows that under like-like exchanges multiple distinct pathways exist in 2D (in 3D topology does not have distinct pathways for these exchanges). this permits real anyon particles to exist when the physics is confined to 2D within quantum limits such as in a layer of graphene. certain configurations of layers (“moire materials”) can be made periodic to provide a suitable scale lattice for anyons to localize and adopt particular quantum states
anyons lie somewhere between fermions and bosons in their state occupancy and statistics - no 2 fermions may occupy the same state, bosons can all occupy the same state, anyons follow rational number patterns eg up to 2 anyons can occupy 3 states
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