O-31 - Fly's Eye detected a 3 x 10^20 eV air shower on 1991 October 15
The highest-energy cosmic ray ever recorded at the time (the “Oh-My-God” event; the detailed analysis is Bird et al. 1995). For the main question this is the direct existence proof of collisions in nature at nucleon-nucleon CM energies far above the LHC’s 14 TeV: a 3 x 10^20 eV proton on a nucleon at rest gives sqrt(s) ~ 750 TeV. In these data no definite conclusion is drawn about the existence of the GZK cutoff (above 10^19.95 eV ~3 events expected from extrapolation, statistics insufficient).
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Why this is evidence
The X_max of the event matches a proton shower, which is expected under the protonic accounts (H-9, H-21) and disfavored under H-12’s helium/CNO composition at the highest energies. Separately, one event a factor of several above the suppression energy is more surprising under a sharp source-rigidity cutoff (H-12) than under GZK propagation from a possibly nearby source (H-9).