Why do Auger and Telescope Array spectra differ above $3e19\,\mathrm{eV}$?
In plain words
The two largest cosmic-ray observatories, one in each hemisphere, disagree on how many particles arrive at the very highest energies.
Precise statement
After cross-calibration of energy scales, the Telescope Array flux above $\sim 3e19\ \mathrm{eV}$ and its suppression energy remain higher than those of the Pierre Auger Observatory. Determine whether the residual difference is instrumental (energy-scale nonlinearity, aperture, atmospheric corrections) or a real dependence on sky direction that would imply a nearby source in the northern sky. Answer: yes or no for a direction-dependent flux, with significance after systematics, evaluated in the declination band seen by both.
What would settle it
Measurements in the common declination band with identical detector types at both sites, such as Auger-type surface stations operated at the Telescope Array site.