Electroweak Gauge Structure from Boundary-Mode Bundles in a Triadic Spiral-Time Effective Geometry

We present a conservative geometric derivation of an electroweak-like gauge redundancy from a universal two-dimensional boundary-mode bundle associated with quasicrystalline cells in the Helix-Light-Vortex (HLV) framework. The construction assumes only (i) a canonical twofold degeneracy of relevant edge modes, (ii) locality of orthonormal frame choices on the boundary-mode space, and (iii) a physical separation between an overall phase rotation and special-unitary mixing. We prove three lemmas: a Degeneracy Lemma yielding a canonical rank-2 complex vector bundle, a Bundle-Connection Lemma identifying the natural non-Abelian redundancy as U(2) with an SU(2) connection on the determinant-free subbundle, and a Hypercharge Separation Lemma showing why an additional U(1) phase is not absorbed into SU(2). We then embed this gauge structure into the triadic spiral-time operator \psi(t)=t+i\phi(t)+j\chi(t) and the kinetic weight A(t)=1+\epsilon(t) used in HLV effective dynamics, emphasizing that octonionic bookkeeping can represent internal phase/memory algebra without modifying standard quantum field dynamics.