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We are writing this letter to express our interest in pursuing an experiment at Fermilab to search for neutrinoless conversion of muons into electrons in the field of a nucleus, which is a lepton flavor-violating (LFV) reaction. The sensitivity goal of this experiment represents an improvement of more than a factor of 10,000 over existing limits. It would provide the most sensitive test of LFV, a unique and essential window on new physics unavailable at the high energy frontier. We present adoi:10.2172/924918 fatcat:ynlvurn4aractnmp5aua66t7ti