Standard Model Gauge Groups as Emergent Topological Symmetries of the Higher-Dimensional Embedding Interface in Absolute Frame Theory

Abstract

Version of August 23rd, 2026, following technical development within the Absolute Frame Theory programme. We show that the gauge structure SU(3)_c x SU(2)_L x U(1)_Y of the Standard Model emerges as a topological property of the embedding interface between a four-dimensional observable manifold M and a higher-dimensional substratum A, as posited by the Absolute Frame Theory (AFT) [P. E. Valenzuela, Zenodo (2026), DOI 10.5281/zenodo.20248039]. Analyzing the fiber-bundle structure of the immersion X:M -> A, we identify the structure group of the normal bundle as SO(N-4). We then demonstrate that three requirements (gauge containment, chirality of the Standard Model, and anomaly-freedom of one fermion generation) force N=14 as the minimal admissible dimension. The four tangent directions reproduce spacetime and the induced metric g_(mu nu)=d_mu X.d_nu X, while the ten normal directions carry an internal SO(10) grand-unified structure. We further show the following. First, the natural connection on the normal bundle is an so(N-4)-valued one-form, whose components are the internal gauge fields. Second, the Nyquist mode of the channel between M and A induces a compatible complex structure on the ten-dimensional normal fiber whose stabilizer in SO(10) is U(5) = (SU(5) x U(1))/Z_5, the Georgi–Glashow group. That stabilizer realizes the full SU(5) grand-unified group contains SU(3)_c x SU(2)_L x U(1)_Y as a derived geometric consequence, with color SU(3) x U(1) recovered on the SO(6) subset of SO(10) sub-block. Third, the chiral electroweak factor SU(2)_L is an internal factor of the normal SO(10), commuting with the reconstructed Lorentz group by tangent/normal orthogonality exactly as color does. The observed weak chirality arises as a correlation between the internal 16 and the spacetime chirality of the Spin(14) frame-spinor 64=(2,1;16) + (1,2;16-bar). Fourth, the hypercharges of the Standard Model fermions are derived as Y = 2T^3_R + (B-L), with explicit numerical verification for the eight fermions of a generation and sin^2(theta_W) = 3/8 at the unification scale. A Goedelian analysis of lower dimensions shows that chirality and anomaly-freedom, not dimensional counting alone, place the structural lower bound at N=14. The framework inherits SO(10) grand-unified phenomenology. Its sharpest experimental test is proton decay p-> e^+pi^0: within Hyper-Kamiokande reach conditional on the unification-threshold displacement, a scale the framework classifies with its identified onset data rather than derives. The two-loop crossing computed here with the declared content, the displacement bands that condition the lifetime, and that classification are given in the text. The dimension N=14 and the Spin(4) x Spin(10) skeleton coincide with the graviweak unification programme, although AFT realizes them by a distinct embedding mechanism in which gravity is not gauged and the Coleman–Mandula theorem is respected. These results, combined with the entropic-gravity derivation of the embedding tension in the foundational paper of the AFT framework, close Conjecture VI of that work: no fundamental forces exist within M. All four interactions are manifestations of the same underlying M–A embedding structure.