  We consider the billiard flow of elastically colliding hard balls on the flat
$\nu$-torus ($\nu\ge 2$), and prove that no singularity manifold can even
locally coincide with a manifold describing future non-hyperbolicity of the
trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli
mixing property) of all such systems, i.e. the verification of the
Boltzmann-Sinai Ergodic Hypothesis.
