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Galactic cosmic rays reach energies of at least a few petaelectronvolts (of the order of 10¹⁵ electronvolts). This implies that our Galaxy contains petaelectronvolt accelerators (‘PeVatrons’), but all proposed models of Galactic cosmic-ray accelerators encounter difficulties at exactly these energies. Dozens of Galactic accelerators capable of accelerating particles to energies of tens of teraelectronvolts (of the order of 10¹³ electronvolts) were inferred from recent γ-ray observations. However, none of the currently known accelerators—not even the handful of shell-type supernova remnants commonly believed to supply most Galactic cosmic rays—has shown the characteristic tracers of petaelectronvolt particles, namely, power-law spectra of γ-rays extending without a cut-off or a spectral break to tens of teraelectronvolts. Here we report deep γ-ray observations with arcminute angular resolution of the region surrounding …