  We show that a randomly chosen 3-CNF formula over n variables with
clauses-to-variables ratio at least 4.4898 is, as n grows large, asymptotically
almost surely unsatisfiable. The previous best such bound, due to Dubois in
1999, was 4.506. The first such bound, independently discovered by many groups
of researchers since 1983, was 5.19. Several decreasing values between 5.19 and
4.506 were published in the years between. The probabilistic techniques we use
for the proof are, we believe, of independent interest.
