Lower dimensionality at higher energies has manifold theoretical advantages as recently pointed out by Anchordoqui et al. [arXiv:1003.5914]. Moreover, it appears that experimental evidence may already exist for it: A statistically significant planar alignment of events with energies higher than TeV has been observed in some earlier cosmic ray experiments. We propose a robust and independent test for this new paradigm. Since ( 2 + 1 )-dimensional spacetimes have no gravitational degrees of freedom, gravity waves cannot be produced in that epoch. This places a universal maximum frequency at which primordial waves can propagate, marked by the transition between dimensions. We show that this cutoff frequency may be accessible to future gravitational wave detectors such as the Laser Interferometer Space Antenna