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tokens: We acknowledge many useful conversations on the algorithms presented in this paper with Marijn Franx. We greatly appreciate Pratika Dayal, Kristian Finlator, Nicholas Gnedin, Chuanwu Liu, Brian O’Shea, Pierre Ocvirk, and Bin Yue for sending us the predictions they derive for the LF results at high redshift. We thank Kristian Finlator for discussing with us at length different turn-over mechanisms that would impact the UV LF at low luminosities. Austin Hoag kindly sent us the v2 Bradac models for HFF cluster MACS 0416. R.S.E. acknowledges financial support from the European Research Council under Advanced Grant FP7/669253. In addition, we acknowledge the support of NASA grant HST-AR-13252, NASA grant HST-GO-13872, NASA grant HST-GO-13792, NWO vrij competitie grant 600.065.140.11N211, and NWO TOP grant TOP1.16.057.