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\section*{Acknowledgements}  We are indebted to Andreas Hoecker for his help with the GFitter fitting program (http://cern.ch/gfitter), and for his patient explanations of the underlying physics. We would like to acknowledge the contributions of all participants in the design study and in the first five TLEP workshops. The writing process of Writing  this article was greatly eased by the use of the online collaborative editor, Authorea (https://www.authorea.com/), ceaselessly improved by the founders, Nathan Jenkins and Alberto Pepe. The support of the CERN PH department, of the European Commission under the FP7 Research Infrastructures project EuCARD, grant agreement no. 227579 ( http://cern.ch/eucard) and under the FP7 Capacities project EuCARD-2, grant agreement no. 312453 (http://cern.ch/eucard2), and of the Swiss National Foundation under the grant 200021-144133, are gratefully acknowledged. The work of J.E. was supported in part by the London Centre for Terauniverse Studies (LCTS), using funding from the European Research Council via the Advanced Investigator Grant 267352.