[7] COS-GUT - Collapsing-Structure Grand Unification: SU(5)–SO(10)–E6 Embeddings Realized on Discrete Shell Graphs and Candidate Phenomenological Links

This work develops the COS–GUT module, a discrete GUT-compatible interface within the Collapsing-Structure (COS) program. It investigates how SU(5)SU(5)SU(5), SO(10)SO(10)SO(10), E6E_6E6, and related grand-unification structures can be represented on a quantized shell–filament background and connected to the COS–SM, COS–SUSY, and COS–QD modules. The manuscript organizes Standard Model multiplets, gauge connections, Higgs sectors, and Yukawa structures through Wilson-type discrete principal-bundle data on shell graphs. Chiral structure and anomaly conditions are treated using Ginsparg–Wilson/overlap-type constructions on admissible, gap-protected, reconstruction-compatible backgrounds. Shellwise embeddings, gauge-invariance conditions, anomaly checks, and operator-closure conditions are formulated with correction terms controlled under stated locality, admissibility, and refinement assumptions. The paper discusses SU(5)SU(5)SU(5), SO(10)SO(10)SO(10), and E6E_6E6 representation embeddings, hypercharge normalization, seesaw-related neutrino structures, E6-motivated Abelian mixing, shell-dependent symmetry breaking, doublet–triplet separation mechanisms, threshold matching, and proton-decay-sensitive operators. A discrete step-scaling RG scheme is outlined for gauge, Yukawa, and scalar couplings, including threshold effects and geometric O(ai2)O(a_i^2)O(ai2)-type corrections. Candidate phenomenological outputs include coupling-unification diagnostics, proton-decay channels, neutrino-sector fits, Z'-related signatures, flavor/CP observables, and electroweak precision constraints. These are presented as model-dependent targets for further numerical fitting and COS–NUM implementation, not as closed predictions. The module provides a structured GUT-compatible formalism and numerical-interface roadmap rather than a fully closed predictive grand-unification model.