🌀 0. A Geometric Resonance Condition for Gauge Group Selection

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🌀 0. A Geometric Resonance Condition for Gauge Group Selection

Core Result: Shows that a 'Geometric Filter' selects the Standard Model's non-Abelian gauge groups by distinguishing between 'viable' and 'unstable' resonance, passing SU(2) and SU(3) while failing SU(4).

This paper proposes a mathematical mechanism for the selection of the Standard Model's non-Abelian gauge groups. It first derives a unique mapping, f(N) = N+2, from SU(N) groups to harmonic modes based on a set of axioms. A 'Geometric Filter' is then constructed to test pairs of these modes for both static resonance and dynamic stability. The results show that the pairs corresponding to SU(2) and SU(3) exhibit a 'viable resonance,' passing both tests. In contrast, the SU(4) pair finds a deeper static resonance but is dynamically unstable. This suggests that nature selects gauge groups not for the deepest possible coherence, but for the most dynamically accessible one.

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