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

Version of September 10th, 2026, following technical development within the Absolute Frame Theory programme. We show that the gauge structure SU(3)_c × SU(2)_L × 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_μν=∂_μ X·∂_ν 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) × U(1))/ℤ_5, the Georgi–Glashow group. That stabilizer realizes the full SU(5) grand-unified group ⊃ SU(3)_c×SU(2)_L×U(1)_Y as a derived geometric consequence, with color SU(3)×U(1) recovered on the SO(6)⊂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;16̄). Fourth, the hypercharges of the Standard Model fermions are derived as Y = 2T³_R + (B-L), with explicit numerical verification for the eight fermions of a generation and sin²θ_W = 3/8 at the unification scale. A Gödelian 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⁺π⁰: 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)×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.