The dynamical structure of the Kuiper belt beyond 50 au is not well understood .
Here we report results of a numerical model with long-range , slow and grainy migration of Neptune .
The model implies that bodies scattered outward by Neptune to semimajor axes a > 50 au often evolve into resonances which subsequently act to raise the perihelion distances of orbits to q > 40 au .
The implication of the model is that the orbits with 50 < a < 100 au and q > 40 au should cluster near ( but not in ) the resonances with Neptune ( 3:1 at a = 62.6 au , 4:1 at a = 75.9 au , 5:1 at a = 88.0 au , etc . ) .
The recent detection of several distant Kuiper Belt Objects ( KBOs ) near resonances is consistent with this prediction , but it is not yet clear whether the orbits are really non-resonant as our model predicts .
We estimate from the model that there should presently be \sim 1600-2400 bodies at the 3:1 resonance and \sim 1000-1400 bodies at the 4:1 resonance ( for q > 40 au and diameters D > 100 km ) .
These results favorably compare with the population census of distant KBOs inferred from existing observations .