The embedding of $\mathrm{SU}{\mathrm{}\left(k\right)\mathrm{}}_{\mathrm{HC}}$ composite schemes within flavor-chiral color-asymptotically-free $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ grand unifying theories is examined. It is shown that unless $k=3\mathrm{}$, the associated spectator-composite structure conspires to be real under the residual gauge interactions. The exceptional $n$-preon SU${\mathrm{}\left(3\right)\mathrm{}}_{\mathrm{HC}}$ scheme is capable of supporting a nonexotic quark/lepton spectrum only if $n=4, 5$. The SU(8)-embeddable $n=5\mathrm{}$ case leads to a multigenerational Georgi-Glashow SU(5) picture.

• Received 15 September 1982

DOI:https://doi.org/10.1103/PhysRevLett.50.1339