Classification of nonsupersymmetric Pati-Salam heterotic string models

We extend the classification of fermionic $\mathbb{Z}_2\times\mathbb{Z}_2$ heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in two classes vacua, that we dub $\tilde S$--models and $S$--models. The first correspond compactifications a tachyonic ten--dimensional vacuum, whereas second tachyon--free $SO(16)\times SO(16)$ string. In both cases develop systematic method extract four--dimensional models. show configurations arise with probability $\sim0.002$ $\sim0.01$ case, respectively. adapt `fertility methodology' facilitates extraction phenomenological do not contain heavy Higgs scalar representations are required break PS symmetry Standard Model therefore phenomenologically viable. Hence, argue $SO(10)$ GUT must be broken at scale Standard--like subgroup. three generation an equal number massless bosonic degrees freedom, ${\it i.e.}$ $a_{00}=N_b^0-N_f^0=0$, analyse their one--loop partition function.