  Lower-dimensionality at higher energies has manifold theoretical advantages
as recently pointed out. Moreover, it appears that experimental evidence may
already exists 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 cut-off frequency may be accessible to
future gravitational wave detectors such as LISA.
