[math] \newcommand{\mathds}{\mathbb}[/math]

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Extract from the general theory developed above a concise proof for the fact that the Pauli matrix model

[[math]] \pi:C(S_4^+)\subset M_4(C(SU_2)) [[/math]]

[[math]] \pi(u_{ij})=[x\to Proj(c_ixc_j)] [[/math]]

where [math]x\in SU_2[/math], and [math]c_1,c_2,c_3,c_4[/math] are the Pauli matrices, is faithful.