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We note that neither Teo and Kane's arguments (Ref. 20) nor ours determine the phase θ. In a 2D system of anyons, it is not an arbitrary phase. For instance, in a system of Ising anyons, θ must be equal to π/8. Any value of θ which is not a 16th root of unity necessarily implies that the theory has additional structure and, therefore, additional particle types.
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