The unification in an $\widehat{\mathfrak{s}\mathfrak{u}}(8{)}_{k_U=1}$ affine Lie algebra

A flavor-unified theory based on the simple Lie algebra of $\mathfrak{s}\mathfrak{u}(8)$ was previously proposed to generate the observed Standard Model quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern due to their non-universal symmetry properties. A level-$1$ affine Lie algebra of $\widehat{\mathfrak{s}\mathfrak{u}}(8{)}_{k_U=1}$ with the $\mathcal{N}=1$ supersymmetric extension is found to unify three gauge couplings through the maximally symmetry breaking pattern.