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 \ge 2, every k-uniform hypergaph of degree \Delta and girth at least 5 is efficiently (1+o(1) )(k-1) (\Delta / \ln \Delta )^{1/(k-1) .