Not yet reviewed by Pith; the record is open.

We examine the minimal U(1)$_{L_\mu-L_\tau}$ gauge model in light of the latest neutrino data, including neutrino oscillations, cosmological observations, direct mass measurements, and neutrinoless double-beta decay. Using the most conservative oscillation data, we find that normal ordering is excluded at approximately the 90% confidence level (CL). Incorporating cosmological constraints from Cosmic Microwave Background (CMB) observations strengthens this exclusion to about 95% CL, while further including Baryon Acoustic Oscillation (BAO) data increases it to nearly 99% CL. The inverted ordering is even more strongly disfavored. Our analysis is performed within a frequentist framework, minimizing sensitivity to prior assumptions inherent in Bayesian approaches. These results impose strong constraints on the viability of the minimal U(1)$_{L_\mu-L_\tau}$ gauge model.