  We give a new upper bound on the maximum degree of the Jones polynomial of a
fibered positive link. In particular, we prove that the maximum degree of the
Jones polynomial of a fibered positive knot is at most four times the minimum
degree. Using this result, we can complete the classification of all knots of
crossing number $\leq 12$ as positive or not positive, by showing that the
seven remaining knots for which positivity was unknown are not positive. That
classification was also done independently at around the same time by
Stoimenow.
