How to measure the reactor neutrino flux below the inverse beta decay threshold with CE$\nu$NS

Most antineutrinos produced in a nuclear reactor have energies below the inverse beta decay threshold, and have not yet been detected. We show that a coherent elastic neutrino-nucleus scattering experiment with an ultra-low energy threshold like NUCLEUS can measure the flux of reactor neutrinos below 1.8 MeV. Using a regularized unfolding procedure, we find that a meaningful upper bound can be placed on the low energy flux, but the existence of the neutron capture component cannot be established.