Third-harmonic signature of linear-GUP kinematics in mesoscopic Aharonov-Bohm rings

We implement a linear Generalized Uncertainty Principle (GUP) in a phase-coherent Aharonov-Bohm ring and show that it imprints a distinctive mesoscopic signature. The deformation produces a cubic correction to the kinetic energy that skews the equilibrium current-flux sawtooth and turns on a robust third Fourier harmonic whose amplitude grows linearly with the deformation strength. Closed form many-body results at zero temperature yield a symmetry-protected third-to-first harmonic ratio that cleanly isolates the linear-GUP signal while canceling nonuniversal prefactors, making the observable resilient to material specifics, weak disorder, spin, and moderate thermal smearing. Using the harmonic-resolution capabilities of current ring experiments, we translate realistic sensitivities into direct bounds on the deformation parameter and on its standard dimensionless coupling in quantum gravity phenomenology. The framework provides a crisp discriminator between linear and purely quadratic GUP deformations, only the linear case activates an even-under-flux-inversion harmonic sector with a leading third harmonic. Beyond phenomenology, the minimal resolvable length implied by the GUP naturally bounds the information content of the flux-current map and the number of harmonics that can be stably resolved, suggesting a pragmatic analogy without claiming formal equivalence to classical limits on computation and decidability. Taken together, these results establish persistent-current harmonics as a tabletop, symmetry protected probe of minimal-length physics and outline clear routes, i.e., smaller rings, ring arrays, and low-noise harmonic readout to substantially tighten the resulting constraints.