  The gravity water waves equations describe the evolution of the surface of an
incompressible, irrotational fluid in the presence of gravity. The classical
regularity threshold for the well-posedness of this system requires initial
velocity field in $H^s$, with $s > \frac{1}{2} + 1$, and can be obtained by
proving standard energy estimates. This threshold was improved by additionally
proving Strichartz estimates with loss. In this article, we establish the
well-posedness result for $s > \frac{1}{2} + 1 - \frac{1}{8}$, corresponding to
proving lossless Strichartz estimates. This provides the sharp regularity
threshold with respect to the approach of combining Strichartz estimates with
energy estimates.
