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tokens: Acknowledgements We thank Julien Devriendt, Bhuvnesh Jain, Vinu Vikram and Risa Wechsler for helpful discussions during the course of this work, and Tessa Baker, Gary Mamon, Stacy McGaugh and an anonymous referee for comments on the manuscript. HD received support from the Balzan foundation via New College, Oxford, the U.S. Department of Energy under contract number DE-AC02-76SF00515, and St John's College, Oxford. PGF is supported by ERC H2020 693024 GravityLS project, the Beecroft Trust and STFC. GL acknowledges financial support from ‘Programme National de Cosmologie and Galaxies’ (PNCG) of CNRS/INSU, France. GL is supported by ANR grant ANR-16-CE23-0002. This work made use of the Dark Sky simulations, which were produced using an INCITE 2014 allocation on the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory. We thank the Dark Sky collaboration for creating and providing access to this simulation, and Sam Skillman and Yao-Yuan Mao for running rockstar and consistent trees on it, respectively. Additional computation was performed at SLAC National Accelerator Laboratory. This research was supported by the DFG cluster of excellence ‘Origin and Structure of the Universe’ ( www.universe-cluster.de ). This work was partly made in the ILP LABEX (under reference ANR-10-LABX-63) supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02.