Building on the experience of the high-resolution community with the suite of VLT high-resolution spectrographs, which has been tremendously successful, we outline here the (science) case for a high-fidelity, high-resolution spectrograph with wide wavelength coverage at the E-ELT. Flagship science drivers include: the study of exo-planetary atmospheres with the prospect of the detection of signatures of life on rocky planets; the chemical composition of planetary debris on the surface of white dwarfs; the spectroscopic study of protoplanetary and proto-stellar disks; the extension of Galactic archaeology to the Local Group and beyond; spectroscopic studies of the evolution of galaxies with samples that, unlike now, are no longer restricted to strongly star forming and/or very massive galaxies; the unraveling of the complex roles of stellar and AGN feedback; the study of the chemical signatures imprinted by population III stars on the IGM during the epoch of reionization; the exciting possibility of paradigm-changing contributions to fundamental physics. The requirements of these science cases can be met by a stable instrument with a spectral resolution of R~100,000 and broad, simultaneous spectral coverage extending from 370nm to 2500nm. Most science cases do not require spatially resolved information, and can be pursued in seeing-limited mode, although some of them would benefit by the E-ELT diffraction limited resolution. Some multiplexing would also be beneficial for some of the science cases. (Abridged)
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