We obtain a characterization of left perfect rings via superstability the class flat modules with pure embeddings. $\mathbf{Theorem.}$ For ring $R$ following are equivalent. - is perfect. The $R$-modules embeddings superstable. There exists $\lambda \geq (|R| + \aleph_0)^+$ such that has uniqueness limit models cardinality $\lambda$. Every model in $\Sigma$-cotorsion. A key step our argum...