Relational Closure Algebras and the Emergence of Color Gauge Symmetry

Quantum chromodynamics (QCD) describes the strong interaction through a non-Abelian gauge theory with color symmetry . Although experimentally well verified, the structural origin of this internal symmetry remains conceptually unclear. In this work we propose a relational operator framework in which gauge symmetries arise from closure relations among primitive observables. Minimal non-Abelian relational closure generates an algebra isomorphic to , interpreted as an elementary interaction cell. When several equivalent closure cells exist, invariance under linear mixing implies an internal symmetry group . Promoting this multiplicity symmetry to a local covariance principle introduces a gauge connection and Yang–Mills curvature. The first non-trivial tripled closure sector () reproduces the internal gauge algebra underlying QCD. In this interpretation quarks correspond to excitations of closure channels, while gluons correspond to generators of traceless channel mixing. The framework connects algebraic quantum mechanics, gauge theory, and relational approaches to fundamental physics. Possible links to exceptional symmetry and octonionic structures are discussed. These results suggest that non-Abelian gauge interactions may emerge naturally from minimal relational closure principles.