Uniqueness of the nucleon state

The spin and isospin structure of the nucleon is shown to be uniquely determined from its S${\mathrm{U}\left(3\right)\mathrm{}}_{\mathrm{flavor}}$×S${\mathrm{U}\left(2\right)\mathrm{}}_{\mathrm{spin}}$×S${\mathrm{U}\left(3\right)\mathrm{}}_{\mathrm{color}}$ assignments and the anticommutation properties of the quark operators (assuming a symmetric space part). No invocation of SU(6) is necessary.