Boundedness of internal energy for non-collision singularities

Determine whether the internal energy of an isolated cluster undergoing a non-collision singularity in the n-body problem with pair potentials homogeneous of degree $-alpha$ and bounded external forces must remain bounded.

Background

The paper proves that an isolated cluster whose internal moment of inertia remains bounded has bounded internal energy. By the generalized von Zeipel theorem, bounded internal moment of inertia corresponds to collision behavior or absence of a singularity. The authors explicitly note that their estimates do not establish the analogous boundedness conclusion for clusters with non-collision singularities. They mention that existing four-body estimates only show that the total internal energy grows more slowly than the kinetic energy, which does not rule out unbounded internal energy.