Generic-motion conjecture for noncollision and super-hyperbolic $N$-body orbits

Consider initial conditions for the $N$-body problem, and call an initial condition generic in the sense intended by the source: outside the exceptional sets associated with noncollision singularities and super-hyperbolic orbits.

Generic-motion conjecture. For generic initial condition, the solution of the $N$-body problem is globally defined on $\mathbb R$. As $t\to\pm\infty$, each body approaches either a linear motion with constant velocity or a Kepler elliptic motion around a center moving linearly with constant velocity.

The source motivates this conjecture by recalling the expectation that noncollision singularities have zero Lebesgue measure and are of first category, and says it is natural to expect the same for super-hyperbolic orbits. It recapitulates the conjecture from the cited work as a simpler generic picture of final motions; no resolution is supplied.