Highlight the propensity of cuprate antiferromagnetic Mott insulator states to condense a superconductor in the presence of small hole doping by showing that even the AF Mott insulator limit of SU(4) symmetry implies non-zero pairing correlations in the ground state unless the hole doping $x$ is identically zero. $\mathrm{SU}(4)$ symmetry requires that $Q^{2}+\Delta^{2}+\Pi^{2}=\frac{1}{4}\left(1-x^{2}\right)$, where $\Delta$ is the singlet pair correlation, $\Pi$ is the triplet pair correlation, and $Q$ is the $\mathrm{AF}$ correlation, but for the $\mathrm{SU}(4) \supset \mathrm{SO}(4)$ AF symmetry limit $Q^{2}=\frac{1}{4}(1-x)^{2}$.