[19/20]Connectivity Geometric Unified Field Theory III: Topological Classification of Three-Generation Fermions and Geometric Emergence of the Grand Unified Energy Scale

The Standard Model faces two major structural defects: the number of fermion generations lacks a first-principles origin, and gauge couplings cannot be precisely unified in a non-supersymmetric framework. Traditional Grand Unified Theories (GUTs) must introduce supersymmetry or extra dimensions to fix the running divergence. In the framework of connectivity geometry, this paper proves that both defects originate from the presupposition of continuous spacetime in traditional field theories. By introducing the topological charge of the Z_3 homology group and the global anomaly cancellation mechanism of the underlying discrete network, we rigorously prove that in a 3+1 dimensional manifold, three-generation fermions are the unique allowed solution constrained jointly by topological rigidity, chiral zero-mode completeness, and prime topological symmetry. Furthermore, combined with the Tensor Network Renormalization Group (TRG), this paper reveals the non-perturbative geometric corrections generated by topological coarse-graining in the high-energy limit. This mechanism provides a novel scheme that achieves precise gauge coupling unification without supersymmetry, without introducing extra fundamental fields, and without tunable free parameters, and the unification energy scale E_GUT ~ 10^16 GeV is uniquely determined by the network topological order. Finally, the unitarity of the CKM matrix and the CP-violating phase are proven to originate from the natural complete orthogonality of the topological defect basis and the Berry phase accumulation under non-trivial topology, respectively. This result completes the core closure of the Standard Model of particle physics under pure geometric topology.