  The beta decay of tritium in the form of molecular TT is the basis of
sensitive experiments to measure neutrino mass. The final-state electronic,
vibrational, and rotational excitations modify the beta spectrum significantly,
and are obtained from theory. We report measurements of the branching ratios to
specific ionization states for the isotopolog HT. Two earlier, concordant
measurements gave branching ratios of HT to the bound HHe$^+$ ion of 89.5% and
93.2%, in sharp disagreement with the theoretical prediction of 55-57%, raising
concerns about the theory's reliability in neutrino mass experiments. Our
result, 56.5(6)%, is compatible with the theoretical expectation and disagrees
strongly with the previous measurements.
