Observational constraints on the physical nature of submillimetre source multiplicity: chance projections are common

The Flatiron Institute is supported by the Simons Foundation. Some of this work was supported by a National Aeronautics and Space Administration (NASA) Keck PI Data Award, administered by the NASA Exoplanet Science Institute. EI acknowledges partial support from Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) through grant no.  1171710. MJM acknowledges the support of the National Science Centre, Poland through POLONEZ grant 2015/19/P/ST9/04010. This project has received funding from the European Union's Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no.  665778. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and NASA. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Partially based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the National Science Foundation (NSF) on behalf of the Gemini partnership: the NSF (United States), the National Research Council (Canada), Comisión Nacional de Investigación Científica y Tecnológica (CONICYT) (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil). This research has made use of the NASA/Infrared Processing and Analysis Center (IPAC) Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the Nati