  We use Super-K data to place new strong limits on interactions of sub-GeV
Dark Matter (DM) with nuclei, that rely on the DM flux inevitably induced by
cosmic-ray upscatterings. We derive analogous sensitivities at Hyper-K and DUNE
and compare them with others, e.g. at JUNO. Using simplified models, we find
that our proposal tests genuinely new parameter space, allowed both by
theoretical consistency and by other direct detection experiments, cosmology,
meson decays and our recast of monojet. Our results thus motivate and shape a
new physics case for any large volume detector sensitive to nuclear recoils.
