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Harnessing tailored disorder for broadband light scattering enables high-resolution signal analysis in nanophotonic spectrometers with a small device footprint. Multiple scattering events in the disordered medium enhance the effective path length which leads to increased resolution. Here we demonstrate an on-chip random spectrometer cointegrated with superconducting single-photon detectors suitable for photon-scarce environments. We combine an efficient broadband fiber-to-chip coupling approach with a random scattering area and broadband