1) The heavily populated mean-motion resonances in the Kuiper belt strongly suggest that the orbits of the planets have migrated. In particular, it has been inferred that Neptune moved outwards by 10 AU or so. Migration is driven by torques resulting from the scattering of bodies out of the Solar system.
2) The mass now in the Kuiper belt (about 0.1 Earth mass or less) is orders of magnitude two small for the KBOs to have grown by binary accretion on timescales short compared to the age of the Solar system. The inference is that much more mass was once present, perhaps 100 to 1000 times more than now (10 to 100 Earth masses).
In addition, it aims to account for the Late-Heavy Bombardment, a period near 3.8 Gyr when some people believe the Moon was bombarded by an unexpectedly high flux of projectiles. This belief is based on crater counts and rock sample ages from the Lunar surface.
The initial conditions of the model place J and S outside but near the 2:1 resonance. Torques from a massive Kuiper Belt (the initial model assumed 30 Earth masses) cause the planets to migrate. By adjusting parameters carefully, the model can reach 2:1 resonance between J and S at the time of the Late Heavy Bombardment, about 800 Myr after the formation of the Solar system.
The model provides a way to lose most of the initial mass from the Kuiper belt. It can populate the Trojan swarms of the giant planets. Through dynamical friction, it can account for the present (nearly circular) orbits of the giant planets.
The model makes few observationally testable predictions (because, with many parameters, a wide range of outcomes can be reached). So, although it is attractive in terms of its ability to fit the data, we do not know how to determine its correctness.