  We consider the system of $N$ ($\ge2$) elastically colliding hard balls of
masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$,
$\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the
full hyperbolicity and ergodicity of such systems for every selection
$(m_1,...,m_N;r)$ of the external geometric parameters, provided that almost
every singular orbit is geometrically hyperbolic (sufficient), i. e. the so
called Chernov-Sinai Ansatz is true. The present proof does not use the
formerly developed, rather involved algebraic techniques, instead it employs
exclusively dynamical methods and tools from geometric analysis.
