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

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, preprint, under review in Foundations of Physics (2026). By analyzing the natural fiber bundle structure of the embedding X: M A, we identify the structure group of the normal bundle as SO (N-4), and demonstrate that a parsimony argument based on dimensional counting under the constraint of reproducing the Standard Model gauge structure forces N=10 as the minimal admissible dimension. We further show that (i) the natural connection on the normal bundle is an so (N-4) -valued one-form, whose components are the gauge field candidates; (ii) the Nyquist mode of the channel between M and A induces a compatible complex structure on the normal fiber whose stabilizer in SO (6) is U (3) (SU (3) U (1) ) /Z₃, realizing the Pati-Salam strong-hypercharge structure as a derived geometric consequence; (iii) the chiral electroweak factor SU (2) L emerges from the spin double cover of the tangent bundle of A through the decomposition Spin (10) Spin (4) Spin (6) (SU (2) L SU (2) R) SU (4), surviving the signature transition from Euclidean A to Lorentzian M as an internal symmetry; and (iv) the hypercharges of the Standard Model fermions are derived as Y = 2T^3ₑ + (B-L), with explicit numerical verification for the eight fermions of a generation. A G\"odelian analysis evaluating dimensions N<10 shows that the observable complexity of the Standard Model places a structural lower bound on N. 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.