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Moments of the leptonic angular distribution in the Drell-Yan process have recently been shown to be sensitive probes of a specific class of dimension-8, four-fermion operators in the Standard Model Effective Field Theory, involving a pair of quarks and leptons. The same operators are also subject to positivity bounds, when requiring the associated (unknown) UV completion to obey basic principles of quantum field theory. I will briefly review positivity bounds for dimension-8 operators from elastic scattering to the positivity cone. I then discuss our phenomenological study to quantify the sensitivity of the high-luminosity LHC to this set of operators and, by extension, the positivity bounds. It makes use of an extended angular basis of moments and double differential information to improve the ability to disentangle the different operators, leading to a sensitivity to new physics scales up to 3 TeV. I use this information to explore the violation of positivity at the LHC as a way to test the underlying principles of quantum field theory. Finally, I will present a case study which combines collider sensitivity with the positivity cone to infer model independent bounds on possible tree-level UV completions.