Number of fermion generations from a novel grand unified model

Electroweak interactions based on the gauge group SU(3)L×U(1)X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SU}(3)_\mathrm{L}\times \mathrm{U}(1)_\mathrm{X}$$\end{document}, coupled to the QCD gauge group SU(3)c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{SU}}(3)_\mathrm{c}$$\end{document}, can predict the number of generations to be multiples of three. We first try to unify these models within SU(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{SU}}(N)$$\end{document} groups, using antisymmetric tensor representations only. After examining why these attempts fail, we continue to search for an SU(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{SU}}(N)$$\end{document} GUT that can explain the number of fermion generations. We show that such a model can be found for N=9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=9$$\end{document}, with fermions in antisymmetric rank-1 and rank-3 representations only, and we examine the constraints on various masses in the model coming from the requirement of unification.