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The purpose of this document is to describe the upgrade of the CRESST dark matter search at LNGS. The proposed strategy will allow to explore a region of the parameter space for spin-independent WIMP-nucleon elastic scattering corresponding to WIMP m asses below 10GeV/c$^text{2}$, that has not been covered by other experiments. These results can be achieved only with outstanding detector performances in terms of threshold and background. This proposal shows how CRESST can match these performance requirements, adding a unique piece of information to the dark matter puzzle. The results of this program will fix a new state-of-the-art in the low mass WIMP exploration, opening new perspectives of understanding the dark matter scenario.
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