  We explore a simplified model of the outcome of an early outer Solar System
gravitational upheaval during which objects were captured into Neptune's 3:2
mean motion resonance via scattering rather than smooth planetary migration. We
use N-body simulations containing the Sun, the four giant planets, and test
particles in the 3:2 resonance to determine whether long-term stability
sculpting over 4.5 Gyr can reproduce the observed 3:2 resonant population from
an initially randomly scattered 3:2 population. After passing our simulated 3:2
resonant objects through a survey simulator, we find that the semimajor axis
(a) and eccentricity (e) distributions are consistent with the observational
data (assuming an absolute magnitude distribution constrained by prior
studies), suggesting that these could be a result of stability sculpting.
However, the inclination (i) distribution cannot be produced be stability
sculpting and thus must result from a distinct process that excited the
inclinations. Our simulations modestly under-predict the number of objects with
high libration amplitudes (A{\phi}), possibly because we do not model transient
sticking. Finally, our model under-populates the Kozai subresonance compared to
both observations and to smooth migration models. Future work is needed to
determine whether smooth migration occurring as Neptune's eccentricity damped
to its current value can resolve this discrepancy.
