Before revision:  As such, we believe that it is an important first step towards discovering the structural properties behind the tractability of arbitrary k-CSPs for constraint densities up to the algorithmic barrier \ge  .
After revision:  As such, we believe that it is an important first step towards discovering the structural properties behind the tractability of arbitrary k-CSPs for constraint densities up to the algorithmic barrier . Our main technical contribution is to prove that, for every k\ge .