Origin of cosmic-ray spectral hardening and softening below the knee
In plain words
The energy spectra of cosmic-ray protons and helium flatten near a few hundred GeV and steepen again near 10 TeV. Simple models of acceleration and travel through the Galaxy predict a single smooth slope.
Precise statement
Proton and helium spectra harden at rigidity $R \sim 200\ \text{to}\ 300\,\mathrm{GV}$ (PAMELA, AMS-02) and soften near $10\ \text{to}\ 15\,\mathrm{TeV}$ (DAMPE, CALET), and secondary-to-primary ratios such as $B/C$ also harden above about $200\,\mathrm{GV}$. Determine whether these features come from propagation (a break in the diffusion coefficient, self-generated turbulence), from source spectra, or from a nearby source, consistent with all species and with anisotropy data.
What would settle it
A single propagation model that fits primary and secondary spectra of all measured nuclei and the anisotropy across the two breaks.