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

Version of July 26th, 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), and 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 = ∂_μX · ∂_νX, while the ten normal directions carry an internal SO(10) grand-unified structure. We further show that (i) the natural connection on the normal bundle is an so(N−4)-valued one-form, whose components are the internal gauge fields; (ii) 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))/ℤ₅, the Georgi–Glashow group, realizing 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; (iii) 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, with the observed weak chirality arising as a correlation between the internal 16 and the spacetime chirality of the Spin(14) frame-spinor 64 = (2,1;16) ⊕ (1,2;16̄); and (iv) 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 headline falsifiable prediction is proton decay p → e⁺π⁰ at a rate just above the current Super-Kamiokande bound and within Hyper-Kamiokande reach. 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.