  We consider a gas of $N$ identical hard spheres in the whole space, and we
enforce the Boltzmann-Grad scaling. We may suppose that the particles are
essentially independent of each other at some initial time; even so,
correlations will be created by the dynamics. We will prove a structure theorem
for the correlations which develop at positive time. Our result generalizes a
previous result which states that there are phase points where the
three-particle marginal density factorizes into two-particle and one-particle
parts, while further factorization is impossible. The result depends on uniform
bounds which are known to hold on a small time interval, or globally in time
when the mean free path is large.
