This proposal establishes the electroweak and strong sectors through Z/nZ structures, indicating foundational properties in physics.
I propose that the electroweak and strong sectors of the Standard Model are instantiations of a Z/nZ principal bundle structure at n=2 and n=3 respectively. The central mathematical object is a graded real vector space V = V_G ⊕ V_Q equipped with an involutive operator X: V→V satisfying X² = −Id_V. I prove three theorems: (T1) any involutive operator on a graded bundle has a unique invariant direction with zero curvature, identified with the massless photon; (T2) the minimal cyclic group Z/nZ admitting a closed triangular representation with non-trivial holonomy is Z/3Z, giving the structural origin of three color charges; (T3) color confinement follows as a topological theorem from the closure condition of the Z/3Z bundle. Five corollaries are derived without free parameters: photon masslessness, three-generation structure, color confinement, W/Z mass ratio, and absence of magnetic monopoles. The relation to centre symmetry in SU(N) gauge theories, the Atiyah-Singer index theorem, and Connes' noncommutative geometry programme is established.
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Andrea Succi (2026) studied this question.
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