5 COS-SM - Collapsing-Structure Standard Model: Gauge Symmetry, Fermions, Higgs, and Yukawa Couplings on a Discrete Shell-Filament Background

This article develops the COS–SM module, a discrete Standard Model interface on the shell–filament background of the Collapsing Structures (COS) program. It formulates U (1) Y×SU (2) L×SU (3) CU (1) Y SU (2) L SU (3) CU (1) Y×SU (2) L×SU (3) C gauge-bundle data, edge holonomies, plaquette curvatures, vertex-supported spinors, and gauge-covariant Dirac/Yang–Mills structures on discrete shells. The paper introduces compatible Higgs and Yukawa sectors, spontaneous symmetry breaking, CKM/PMNS-type mixing structures, a discrete topological QCD θθ-sector, and gauge-preserving GKSL dynamics. Chiral structure and anomaly cancellation are treated through controlled Ginsparg–Wilson/overlap and admissibility/gap-protected settings; the full chiral-fermion problem on dynamically topology-changing backgrounds remains an open SM/STAB/QD interface task. Continuum matching and renormalization are discussed through conditional Γ-convergence and discrete block-RG statements under regularity, refinement, and numerical assumptions. Observable protocols with confidence intervals and minimal reproducibility guidance are included, together with appendices on group theory, discrete Dirac/overlap constructions, Higgs–Yukawa formulae, glossary material, and the FMS interpretation.