  Basso, Komatsu and Vieira recently proposed an all-loop framework for the
computation of three-point functions of single-trace operators of ${\cal N}=4$
super-Yang-Mills, the "hexagon program". This proposal results in several
remarkable predictions, including the three-point function of two protected
operators with an unprotected one in the $SU(2)$ and $SL(2)$ sectors. Such
predictions consist of an "asymptotic" part---similar in spirit to the
asymptotic Bethe Ansatz of Beisert and Staudacher for two-point functions---as
well as additional finite-size "wrapping" L\"uscher-like corrections. The focus
of this paper is on such wrapping corrections, which we compute at three-loops
in the $SL(2)$ sector. The resulting structure constants perfectly match the
ones obtained in the literature from four-point correlators of protected
operators.
