In the ergodic theory of semi-dispersing billiards the Local Ergodic Theorem,
proved by Chernov and Sinai in 1987, plays a central role. So far, all existing
proofs of this theorem had to use an annoying global hypothesis, namely the
almost sure hyperbolicity of singular orbits. (This is the so called
Chernov--Sinai Ansatz.) Here we introduce some new geometric ideas to overcome
this difficulty and liberate the proof from the tyranny of the Ansatz. The
presented proof is a substantial generalization of my previous joint result
with N. Chernov (which is a $2D$ result) to arbitrary dimensions.
An important corollary of the presented ansatz-free proof of the Local
Ergodic Theorem is finally completing the proof of the Boltzmann--Sinai Ergodic
Hypothesis for hard ball systems in full generality.