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

Classification of Non-Supersymmetric Pati-Salam Heterotic String Models