The Z/nZ Bundle and the Standard Model: Electroweak Symmetry Breaking as Z/2Z Instantiation and a Structured Formal Proposal for Strong Interaction as Z/3Z Extension

The Standard Model of particle physics is a gauge theory based on SU(3)×SU(2)×U(1). Its two principal sectors — electroweak and strong — share a common mathematical language but have not been given a common structural explanation within a single geometric framework. This paper proposes that both sectors are instantiations of a Z/nZ principal bundle structure governing the G→X→Q→N generative cycle at two distinct levels: the electroweak sector as a Z/2Z bundle instantiation (formal derivation), and the strong sector as a Z/3Z bundle extension (structured formal proposal). The electroweak identification is developed as a formal derivation: the pre-breaking SU(2)×U(1) symmetry is the G state, the Higgs field is operator X, and spontaneous breaking produces three massive bosons W⁺W⁻Z (Q pole) and one massless photon (residual G component). The universal relation |φ_Q|² = m²/g is verified across three independent systems spanning twenty orders of magnitude in energy scale with zero free parameters. For the Z/3Z proposal: G is identified as the geometric center of the equilateral triangle in Z/3Z — not a vertex — invariant under the Z/3Z action (1+ω+ω²=0 implies F∇|G=0, zero curvature at the center, confinement as geometric necessity). The connection 1-form is derived from the triangular holonomy structure, and the eight gluons emerge as 3 arcs × 3 colour directions − 1 (U(1) trace) = 8 independent components. Colour confinement is the bundle closure condition r·g·b = ω³ = 1. The paper explicitly engages with the center symmetry literature ('t Hooft 1978, Svetitsky & Yaffe 1982) and identifies the specific contribution: not the Z₃ center symmetry in isolation, but its unification with Z₂ through the Z/nZ bundle as common structural origin.