  Higher-dimensional multi-gluon interactions affect essentially all effective
Lagrangian analyses at the LHC. We show that, contrary to common lore, such
operators are best constrained in multi-jet production. Our limit on the
corresponding new physics scale in the multi-TeV range exceeds the typical
reach of global dimension-6 Higgs and top analyses. This implies that the pure
Yang-Mills operator can safely be neglected in almost all specific
higher-dimensional analyses at Run II.
