  We analyse the CFT-data of planar 4D $\mathcal{N} = 4$ Super-Yang-Mills
theory at strong coupling. By combining spectral data extracted from
integrability, with recent advances in computing the AdS Virasoro-Shapiro
amplitude, we extract predictions for leading order OPE coefficients on entire
Kaluza-Klein (KK-)towers of states. We observe that the appropriately
normalised leading order OPE coefficients for all states in a given KK-tower
are the same. Furthermore, we also notice that, in many cases, the leading
order OPE coefficients of all states in the KK-tower vanish, suggesting a
simplification of the physics in this limit.
