  We present an integrability-based conjecture for the three-point functions of
single-trace operators in planar $\mathcal{N}=4$ super-Yang-Mills theory at
finite coupling, in the case where two operators are protected. Our proposal is
based on the hexagon representation for structure constants of long operators,
which we complete to incorporate operators of any length using data from the
TBA/QSC formalism. We perform various tests of our conjecture, at weak and
strong coupling, finding agreement with the gauge theory through 5 loops for
the shortest three-point function and with string theory in the classical
limit.
