  We compute the non-planar contribution to the universal anomalous dimension
of twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops
through Lorentz spin eighteen. Exploiting the results of this and our previous
calculations along with recent analytic results for the cusp anomalous
dimension and some expected analytic properties, we reconstruct a general
expression valid for arbitrary Lorentz spin. We study various properties of
this general result, such as its large-spin limit, its small-x limit, and
others. In particular, we present a prediction for the non-planar contribution
to the anomalous dimension of the single-magnon operator in the beta-deformed
version of the theory.
