Abstract
In previous papers with similar titles we proved uniqueness of the SO(10) grand unified theory under some general assumptions. However, we made there extra Ans\"atze such that quarks cannot have any integral electric charges of 0, 1, or -1. Here, we omit these assumptions and show that the SO(10) group is still unique. The color group ${G}_{C}$ must be the SU(2) group for the integrally charged quarks. Together with a similar case for fractionally charged SU(3) quarks, these two cases are essentially the only two possible solutions, where the irreducible representation space is always a 16-dimensional spinor representation of SO(10). The connection between the present work and some preon models is also pointed out.
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