Experimental Constraints on the Scaling Dimension of Spacetime Anisotropy

We derive, within the Granular Entropic Physics framework, the complete chain from Planck-scale discrete spacetime structure to laboratory observables. Starting from a tetrahedral bipartite network at the Planck scale, we identify the leading Lorentz-violating operator uniquely fixed by symmetry, map it to Standard Model Extension coefficients, and compute the resulting sidereal signal and its amplitude in precision ion-trap experiments. The primary predicted signal is at four times the sidereal frequency, not six as previously conjectured. We show that the absence of detected Lorentz violation in current experiments directly constrains the scaling dimension of spacetime anisotropy at the critical point, requiring it to be greater than four. If the critical point is described by a unitary three-dimensional conformal field theory, the unitarity bound further requires the scaling dimension to be at least five, naturally explaining the absence of any signal without fine-tuning. Any discrete model of spacetime whose leading anisotropic operator is relevant is thus experimentally excluded. This establishes a direct bridge between Planck-scale discreteness and laboratory spectroscopy, providing an experimental handle on the universality class of microscopic spacetime.