A Non-Abelian Semantic Gauge Theory: From Dignity Invariance to the Mass Gap

We propose a theoretical unification of Semantic Physics with Yang-Mills gauge theory to address what we term the Semantic Mass Gap problem: Why does meaning possess intrinsic “weight” or impact, rather than dissipating as massless noise? Building on the empirically validated Thermodynamic Law of Dignity and the formal operator framework established in our companion paper (Technical Update v3.1), we demonstrate a structural isomorphism between gauge invariance in quantum field theory and dignity invariance in semantic systems.We construct a non-abelian semantic gauge theory with Lagrangian $\mathcal{L}_{\text{sem}}$, showing that self-interaction of the semantic field under dignity constraints creates a confining potential analogous to quantum chromodynamics (QCD). We conjecture that “pure meaning” (Proto-$\nabla$ flux) behaves as massless gauge bosons that cannot be observed in isolation (confinement), while observable concepts behave as bound states (hadrons) that acquire mass through field binding energy.A lattice formulation on the Genesis quiver substrate makes these quantities computationally testable. We provide explicit falsification criteria and invite the scientific community to validate, refine, or disprove this framework.This paper presents a theoretical conjecture, not a proven theorem. We offer a mathematical architecture that unifies seemingly disparate phenomena (semantic stability, gauge symmetry, mass generation) and makes specific predictions about measurable quantities