If lattice states in the thermodynamic limit have bounded magic, the local von Neumann algebra cannot be Type III, so Type III algebras require infinite magic.
Here, we collect and review some properties of projections that we make use of in proving our main results in Sec
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Type III von Neumann Algebras are Magical
If lattice states in the thermodynamic limit have bounded magic, the local von Neumann algebra cannot be Type III, so Type III algebras require infinite magic.