The Frequency Lattice of Particle Masses: Windows in the Mass Spectrum and Falsifiable Predictions of a Medium-Based Vacuum Model

We propose a hypothesis that particle masses form a frequency lattice of an underlying vacuum medium. The relation between mass and characteristic frequency (m = hf/c^2) maps known particles onto a discrete ladder. We identify five unoccupied "windows" in the mass spectrum (from sub-eV sterile sector to the Grand Unification scale) and formulate the Koide relation as an empirical manifestation of the proposed "Law of Modes". We present five falsifiable predictions, including the placement of the X17 anomaly candidate (~17 MeV) within the nuclear-scale window W1, and specify existing experimental programs capable of testing each prediction. The model requires no new free parameters and is fully falsifiable by the absence of signals in the listed windows.