We propose that the observed deviation in the muon anomalous magnetic moment arises from critical collective modes of an underlying discrete spacetime network, rather than from new elementary particles. Within the Granular Entropic Physics (GEP) framework, spacetime is modeled as a bipartite tetrahedral network with SU (2) -valued links. Near a non-trivial renormalization group fixed point, long-range correlations of Wilson loop holonomies generate an effective magnetic dipole operator at an emergent TeV scale. Two-body loop correlations induce the non-Abelian field strength through the commutator structure of gauge fields, leading to the standard Pauli operator with a coefficient controlled by the renormalized network stiffness. Using an epsilon-expansion estimate of the anomalous dimension of the F² operator, we obtain a critical exponent p ~ 0. 1-0. 25, yielding delta aₘu ~ 10^-9, consistent with the Fermilab measurement. The mechanism predicts universal lepton mass scaling delta aₗ proportional to mₗ², requires no new light degrees of freedom below the TeV scale, and implies characteristic deviations in high-energy dilepton observables. Several elements remain open, including the precise Wilson coefficient, the fixed-point structure, and the dynamical origin of criticality. The results suggest that the muon g-2 anomaly may provide a probe of emergent spacetime geometry rather than new particle content.
Štěpán Sekanina (Fri,) studied this question.