Muon $g$$-$2: correlation-induced uncertainties in precision data combinations

We present a general and systematic framework to quantify uncertainties arising from imperfectly known systematic correlations in data combinations. Formulated at the level of the combined data, the method enables controlled variation of the correlation structure, leading to the construction of covariance matrices directly on the resulting combination and thus providing a robust and systematic estimate of correlation-induced uncertainties. We apply the method to $e^+e^- \to \mathrm{hadrons}$ cross section data, with the resulting covariance matrices propagated to derived observables, including dispersive determinations of the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_\mu^\mathrm{HVP}$. We find that uncertainties from systematic correlation assumptions are generally subdominant but non-negligible, and do not fully account for differences between existing $e^+e^- \to \mathrm{hadrons}$ data combinations. The framework is broadly applicable to correlated data combinations in precision measurements and constitutes a new component of the upcoming KNTW data combination for $a_\mu^\mathrm{HVP}$.