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