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Let $L_r$ denote the ring that is universal with an invertible $1 \\times r$ matrix. Let $M_m(L_r^{\\otimes t})$ denote the ring of $m \\times m$ matrices over the tensor product of $t$ copies of $L_r$. In a natural way, $M_m(L_r^{\\otimes t})$ is a partially ordered ring with involution. Let $PU_m(L_r^{\\otimes t})$ denote the group of positive unitary elements. 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