Mass difference of $^{115}$In and $^{115}$Sn*

At the Canadian Penning Trap mass spectrometer we have measured the atomic mass difference $\Delta M$ between the ground states of $^{115}$In and $^{115}$Sn with uncertainty below 0.5 keV. Our measurement was occasioned by a reported observation of a $\beta^{-}$ decay from the ground state of $^{115}$In ($9/2+$) to the first excited state of $^{115}$Sn ($3/2+$). Based on the known value of $\Delta M$, this hypothetical decay was known to have a ``$Q$ value'' of 2$\pm$4 keV. If positive, this value would be among the smallest for any known $\beta$ decay and could have implications for direct neutrino mass measurements that rely on high-resolution mapping of a $\beta$ spectrum near its endpoint. Our measurement is a test of whether this decay is physically possible, and if so, provides its $Q$ value.