A wavelike solution for the non-relativistic universal dark matter (wave-DM) is rapidly gaining interest, following distinctive predictions of pioneering simulations of cosmic structure as an interference pattern of coherently oscillating bosons. A prominent solitonic standing wave is predicted at the center of every galaxy, representing the ground state, that has been identified with the wide, kpc scale dark cores of common dwarf-spheroidal galaxies, providing a boson mass of, $simeq 10^{-22}$ eV. A denser soliton is predicted for Milky Way sized galaxies where momentum is higher, so the de Broglie scale of the soliton is smaller, $simeq 100$ pc, of mass $simeq 10^9 M_odot$. Here we show the central motion of bulge stars in the Milky Way implies the presence of such a dark core, where the velocity dispersion rises inversely with radius to a maximum of $simeq 130$ km/s, corresponding to an excess central mass of $simeq 1.5times 10^9 M_odot$ within $simeq 100$ pc, favouring a boson mass of $simeq 10^{-22}$ eV. This quantitative agreement with such a unique and distinctive prediction is therefore strong evidence for a light bosonic solution to the long standing Dark Matter puzzle, such as the axions generic in String Theory.
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