The gauge principle is a cornerstone of particle-physics model building. Nevertheless, many constructions leave certain global $U(1)$ redundancies ungauged. In this work, we take the gauge principle to its logical extreme by promoting all $SU(N)$ symmetries to $U(N)$. We focus on a model based on local $U(3)\times U(2)$ invariance. This framework accounts for several otherwise ad hoc features of the Standard Model, including charge quantization and the observed hypercharge assignments, which emerge here as unique predictions. Furthermore, the internal consistency of the model requires the introduction of right-handed neutrinos and implies the presence of an additional $U(1)$ factor that can be identified with $B-L$, thereby naturally yielding nonzero neutrino masses. In light of these findings, we hypothesize that $U(3)\times U(2)$ constitutes the underlying symmetry of the strong and electroweak interactions. More importantly, our approach opens up novel avenues for model building, driven by this extended interpretation of the gauge principle.

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• Electroweak interaction
• Gauge theories
• Grand unified models
• Hypothetical particle physics models
• Particle interactions
• Symmetries
• Group theory