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We exhibit a connection between geometric stability theory and theclassification of unstable structures at the level of simplicity and the$\mathrm{NSOP}_{1}$-$\mathrm{SOP}_{3}$ gap. Particularly, we introduce genericexpansions $T^{R}$ of a theory $T$ associated with a definable relation $R$ of$T$, which can consist of adding a new unary predicate or a new equivalencerelation. When $T$ is weakly minimal and $R$ is a ternary fiber algebraicrelation, we show that $T^{R}$ is a well-defined $\mathrm{NSOP}_{4}$ theory,and use one of the main results of geometric stability theory, the\textit{group configuration theorem} of Hrushovski, to give an exactcorrespondence between the geometry of $R$ and the classification-theoreticcomplexity of $T^{R}$. Namely, $T^{R}$ is $\mathrm{SOP}_{3}$, and$\mathrm{TP}_{2}$ exactly when $R$ is geometrically equivalent to the graph ofa type-definable group operation; otherwise, $T^{R}$ is either simple (in thepredicate version of $T^{R}$) or $\mathrm{NSOP}_{1}$ (in the equivalencerelation version.) This gives us new examples of strictly $\mathrm{NSOP}_{1}$theories.

Generic expansions and the group configuration theorem