Which sources accelerate cosmic rays above $10^{19}\,\mathrm{eV}$?
In plain words
The most energetic cosmic rays come from outside our galaxy, but magnetic fields bend their paths, so their sources have not been identified.
Precise statement
For $E > 8 \times 10^{18}\ \mathrm{eV}$ (Auger large-scale dipole, amplitude $\sim 6.5\%$, pointing away from the Galactic center) and $E > 4 \times 10^{19}\ \mathrm{eV}$ (intermediate-scale excesses near Centaurus A and starburst galaxies for Auger, the hotspot for Telescope Array), identify the source population (AGN jets, starburst galaxies, gamma-ray bursts, tidal disruption events, magnetars). Answer: a source class whose emissivity, maximum rigidity and composition reproduce the spectrum, the shower-depth ($X_{\max}$) distributions and the arrival-direction anisotropies after propagation through Galactic and extragalactic magnetic fields.
What would settle it
Per-event mass estimates above $4 \times 10^{19}\,\mathrm{eV}$ (AugerPrime) allowing light nuclei to be traced back, together with a $5\sigma$ intermediate-scale anisotropy associated with a source catalog.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
2023: Telescope Array reported a $2.4 \times 10^{20}\ \mathrm{eV}$ event (Amaterasu) whose arrival direction points toward the Local Void with no plausible nearby source.
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