  A recently discovered generalized Gribov-Lipatov reciprocity holds for the
anomalous dimensions of various twist operators in N=4 SYM. Here, we consider a
class of scaling psu(2,2|4) operators that reduce at one-loop to twist-3
maximal helicity gluonic operators. We extract from the asymptotic long-range
Bethe Ansatz a closed expression for the spin dependent anomalous dimension at
four loop order and provide a complete proof of reciprocity. We comment about
the interplay with possible, yet unknown, wrapping corrections.
