  We exhibit a connection between geometric stability theory and the
classification of unstable structures at the level of simplicity and the
$\mathrm{NSOP}_{1}$-$\mathrm{SOP}_{3}$ gap. Particularly, we introduce generic
expansions $T^{R}$ of a theory $T$ associated with a definable relation $R$ of
$T$, which can consist of adding a new unary predicate or a new equivalence
relation. When $T$ is weakly minimal and $R$ is a ternary fiber algebraic
relation, 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 exact
correspondence between the geometry of $R$ and the classification-theoretic
complexity of $T^{R}$. Namely, $T^{R}$ is $\mathrm{SOP}_{3}$, and
$\mathrm{TP}_{2}$ exactly when $R$ is geometrically equivalent to the graph of
a type-definable group operation; otherwise, $T^{R}$ is either simple (in the
predicate version of $T^{R}$) or $\mathrm{NSOP}_{1}$ (in the equivalence
relation version.) This gives us new examples of strictly $\mathrm{NSOP}_{1}$
theories.
