  In the context of planar conformal gauge theory, we study five-point
correlation functions between the interaction Lagrangian and four of the
lightest single-trace, gauge-invariant scalar primaries. After performing two
light-cone OPEs, we express this correlator in terms of the three-point
functions between two leading-twist spinning operators and the Lagrangian. For
finite values of spin, we compute these structure constants in perturbation
theory up to two loops in $\mathcal{N}=4$ Super Yang-Mills theory. Large values
of spin are captured by null polygon kinematics, where we use dualities with
null polygon Wilson loops as well as factorization properties to bootstrap the
universal behavior of the structure constants at all loops. We find explicit
maps that relate the Lagrangian structure constants with the leading-twist
anomalous dimension. From the large-spin map, we recover the cusp anomalous
dimension at strong and weak coupling, including genus-one terms.
