The cyclotron frequency ratio of $^{187}mathrm{Os}^{29+}$ to $^{187}mathrm{Re}^{29+}$ ions was measured with the Penning-trap mass spectrometer PENTATRAP. The achieved result of $R=1.000:000:013:882(5)$ is to date the most precise such measurement performed on ions. Furthermore, the total binding-energy difference of the 29 missing electrons in Re and Os was calculated by relativistic multiconfiguration methods, yielding the value of $Delta E = 53.5(10)$ eV. Finally, using the achieved results, the mass difference between neutral $^{187}$Re and $^{187}$Os, i.e., the $Q$ value of the $beta^-$ decay of $^{187}$Re, is determined to be 2470.9(13) eV.
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