Emergent Yang–Mills Dynamics and Confinement from a Granular Entropic Network

We derive non-Abelian gauge dynamics and confinement from a discrete spacetime model based on a bipartite tetrahedral network within the Granular Entropic Physics (GEP) framework. Link orientations define SU(2) gauge variables and fermions emerge as Möbius topological defects. Starting from Wilson's lattice action with coupling g² = 1/κ, where κ is the network stiffness, we derive the Yang–Mills action in the continuum limit. The effective potential between static fermionic defects is computed via rectangular Wilson loops: in the weak-coupling regime a Coulomb potential V(r) = −3/(16πκr) is recovered; in the strong-coupling regime the area law gives linear confinement V(r) = σr with string tension σ_phys = (1/a²)ln(1/κ). Confinement is interpreted geometrically as the energetic cost of topological frustration in link orientations — a flux tube of non-trivial holonomy. The isotropy of the tetrahedral network, confirmed by T^ab = 4δ^ab, ensures recovery of the standard propagator in the infrared limit. This establishes a direct geometric origin of Yang–Mills dynamics and suggests that gauge interactions may not be fundamental but emerge from microscopic network structure.