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tokens: Acknowledgements This work has benefited greatly from discussions with the following individuals: Andy Burkert, Benedikt Diemer, Oliver Hahn, Andrew Hearin, Fangzhou Jiang, Johannes Lange, and Fred Rasio. We also acknowledge the referee, Chris Power, for an insightful, constructive referee report. FvdB is grateful to the Munich Excellence Cluster for its hospitality, and is supported by the Klaus Tschira Foundation and by the US National Science Foundation through grant AST 1516962. Part of this work was performed at the Aspen Center for Physics, which is supported by the National Science Foundation under grant PHY-1066293, and at the Kavli Institute for Theoretical Physics, which is supported by the National Science Foundation under grant PHY-1125915. GO is supported by funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 679145, project ‘COSMO-SIMS’). Some of the numerical computations were carried out on HA-PACS at the Center for Computational Sciences at University of Tsukuba.