Updated bounds on the (1,2) neutrino oscillation parameters after first JUNO results

Within the standard $3\nu$ framework, we discuss updated bounds on the leading oscillation parameters related to the $(\nu_1,\,\nu_2)$ states, namely, the squared mass difference $\delta m^2=m^2_2-m^2_1$ and the mixing parameter $\sin^2\theta_{12}$. A previous global analysis of 2024 oscillation data estimated $\delta m^2$ and $\sin^2\theta_{12}$ with fractional $1\sigma$ errors of about $2.3\%$ and $4.5\%$, respectively. First we update the analysis by applying the latest SNO+ constraints, that slightly shift the $(\delta m^2,\,\sin^2\theta_{12})$ best fits. Then we apply the constraints placed by the first JUNO results, that significantly reduce the uncertainties of both parameters. Our updated global bounds (as of 2025) can be summarized as: $\delta m^2/10^{-5}{\rm eV}^2 = 7.48\pm 0.10$ and $\sin^2\theta_{12}=0.3085\pm0.0073$ (with correlation $\rho=-0.20$), corresponding to $1\sigma$ uncertainties as small as $1.3\%$ and $2.4\%$, respectively. We also comment on minor physical and statistical effects that, in the future, may contribute to lift the current mass-ordering degeneracy of $(\delta m^2,\,\theta_{12})$ estimates.