Identical-quark pair spin in a ground-state baryon ($S_{qq}=1$)

For an identical-flavour pair in the symmetric spatial ground state of a baryon, the flavour factor is symmetric and the three-quark colour singlet is antisymmetric under their exchange. The Pauli exclusion principle therefore requires a symmetric pair spin factor. Two spin-one-half quarks then form a triplet state, $S_{qq}=1$, rather than a spin singlet. The conclusion applies to the identical pair in both spin-one-half and spin-three-half ground-state baryons.