This work presents the COS–GUT module, a discrete grand unification framework formulated on a quantized shell–filament background. Within this model, the Standard Model fields and interactions are implemented on Wilson-type principal bundles defined over shell graphs, while the chiral structure is maintained through a Ginsparg–Wilson Dirac operator under Osterwalder–Schrader conditions. The paper constructs the per-shell realizations of the SU(5), SO(10), and E6 grand unification groups, defines the embeddings of the Standard Model fields, and formulates the closure conditions of the complete operator algebra. The analysis shows that closure-violating corrections are of order O(aᵢ) and vanish in the continuum limit. The Higgs sector and spontaneous symmetry breaking are expressed through shell-dependent vacuum expectation values, naturally incorporating doublet–triplet splitting and E6-induced U(1) mixing. Furthermore, the discrete renormalization group (RG) flow of gauge, Yukawa, and scalar couplings is derived using a step-scaling scheme with multi-stage threshold matching and matrix-valued Abelian mixing. A controlled geometric O(aᵢ²) shift appears in the RG equations. The framework explains the origin of Yukawa textures through shell-geodesic suppression, providing consistent neutrino masses via a seesaw mechanism and realistic flavor structure. The study also discusses leading proton decay channels, potential Z′ signals, and the robustness of unification in the presence of discrete thresholds and mixings. Interfaces with the COS–SM, COS–SUSY, and COS–QD modules form a unified numerical pipeline (COS–NUM). In the continuum limit, standard GUT results are recovered. Overall, the COS–GUT module provides a coherent, predictive grand unification framework on a discrete background, linking theoretical consistency with experimental phenomenology.
Attila Görhöny (Sat,) studied this question.