  We consider correlation functions of single trace operators approaching the
cusps of null polygons in a double-scaling limit where so-called $\textit{cusp
times}$ $t_i^2 = g^2 \log x_{i-1,i}^2\log x_{i,i+1}^2$ are held fixed and the
t'Hooft coupling is small. With the help of stampedes, symbols and educated
guesses, we find that any such correlator can be uniquely fixed through a set
of coupled lattice PDEs of Toda type with several intriguing novel features.
These results hold for most conformal gauge theories with a large number of
colours, including planar $\mathcal{N}=4$ SYM.
