A diffusive origin for the cosmic-ray spectral hardening reveals signatures of a nearbysource in the leptons and protons data

In this work we aim at reproducing, simultaneously, the spectral feature at $\sim 10 \, \mathrm{TeV}$ in the cosmic-ray proton spectrum, recently reported by the DAMPE Collaboration, together with the spectral break at $\sim 1 \, \mathrm{TeV}$ measured by H.E.S.S. in the lepton spectrum. Those features are interpreted as signatures of one nearby hidden cosmic-ray accelerator. We show that this interpretation is consistent with the dipole-anisotropy data as long as the rigidity scaling of the diffusion coefficient features a hardening at $\sim 200 \, \mathrm{GV}$, as suggested by the light-nuclei data measured with high accuracy by the AMS-02 Collaboration. Such rigidity-dependent diffusion coefficient is applied consistently to the large-scale diffuse cosmic-ray sea as well as to the particles injected by the nearby source.