  We calculate the $\mathcal{O}(\langle H^{\dagger} H \rangle^{2} / \Lambda^{4}
)$ corrections to LEP electroweak precision data using the geometric
formulation of the Standard Model Effective Field Theory (SMEFT). We report our
results in simple-to-use interpolation tables that allow the interpretation of
this data set to dimension eight for the first time. We demonstrate the impact
of these previously unknown terms in the case of a general analysis in the
SMEFT, and also in the cases of two distinct models matched to dimension eight.
Neglecting such dimension-eight corrections to LEP observables introduces a
theoretical error in SMEFT studies. We report some preliminary studies defining
such a theory error, explicitly demonstrating the effect of previously unknown
dimension-eight SMEFT corrections on LEP observables.
