Positive-energy linear diameter growth (${\mathrm{liminf}}_{t\to \infty }R(t)/t\ge \sqrt{E/(2A_1)}$)

For an isolated Newtonian point-mass system, $\ddot{I}=T+E\ge E>0$. Twice integrating gives a quadratic lower bound on $I$. The maximum-separation inertia bounds then give at-least-linear asymptotic growth of the diameter $R$ for a trajectory existing for arbitrarily large times. The bound does not assert instantaneous monotonicity or escape of every particle.