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Although the first results of the KATRIN neutrino mass experiment areconsistent with a new improved upper limit of 1.1 eV for the effective mass ofthe electron neutrino, surprisingly they are also consistent with an exoticmodel of the neutrino masses put forward in 2013 that includes one tachyonicmass state doublet having $m^2\sim - 0.2$ keV$^2$. A definitive conclusion onthe validity of the model should be possible after less than one year of KATRINdata-taking.

First results of the KATRIN neutrino mass experiment and their consistency with an exotic $3+3$ model