Standard Model Emergence and Hierarchy Resolution in T^6/Z_3: Grand Unification and Higgs Mass Generation via Geometric Compactification

We present a geometric derivation of the Standard Model gauge group SU(3)xSU(2)xU(1) and a natural resolution to the Gauge Hierarchy Problem within the compact 6D Calabi-Yau orbifold T^6/Z_3. The symmetry breaking from an underlying E_8 Grand Unified Theory (GUT) to the low-energy gauge group is driven by the discrete action of the Z_3 isometry over the 36 homological 3-cycles H_3(T^6/Z_3, Z). Furthermore, we prove that the electroweak scale and the Higgs boson vacuum expectation value (v = 246 GeV) are dynamically suppressed relative to the Planck scale M_P via the geometric volume factor V_6 = T_b^3 - 27 T_s^3, thereby eliminating the fine-tuning requirement without supersymmetry breaking parameters. Charge quantization is fully fixed by the topological intersection numbers of the local A_2 singular cycles.