Temporal-interference (TI) stimulation promises what other non-invasive methods cannot: focal, steerable stimulation deep in the brain, produced where two high-frequency currents overlap and their amplitudes beat at a low difference frequency. Yet a puzzle sits at its core. An amplitude-modulated field carries no power at that beat frequency, so no passive, linear part of a neuron can follow it; recovering the beat requires a nonlinearity, usually sought in single-cell ion channels. Here we show that the recovery, and its tuning, are properties of the neural population rather than the single cell. In a neural mass—the $ $$10⁴$-neuron unit that generates the EEG—the firing-rate nonlinearity acts as a square-law detector that demodulates the beat, while the recurrent synaptic network, poised near a Hopf bifurcation, resonantly amplifies the recovered rhythm at its own natural frequency. Detection is inherited from the single neuron; the sharp, frequency-selective amplification is emergent—set by how near the network sits to criticality, and tunable by its own connectivity. Demonstrated in a heuristic cortical column and in an exact next-generation mean field, the mechanism reproduces TI’s known behavior: it is independent of the carrier once the membrane polarization is matched, largest when the beat matches a region’s intrinsic rhythm, and—because the resonance amplifies oscillatory timing far more than mean rate—locks spike timing without changing firing rate, as observed in vivo. Because the gain depends on brain state, TI efficacy should be as much a property of the brain as of the device: the cortical column behaves as a tuned AM radio receiver.: temporal interference; transcranial stimulation; neural mass model; amplitude demodulation; Hopf bifurcation; cross-frequency coupling; Jansen–Rit; LaNMM.