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We report on spectroscopy of the white-dwarf companion of the millisecondradio pulsar PSR J1012+5307. We find strong Balmer absorption lines, as wouldbe expected for a cool DA white dwarf. The profiles are much narrower thanusual, however, and lines are seen up to H12, indicating that the companion hasa low gravity and hence a low mass. This is consistent with theexpectation---based on evolutionary considerations and on the massfunction---that it is a low-mass white dwarf with a helium core. By comparingthe spectra to model atmospheres, we derive an effective temperature$T_{\rm{}eff}=8550\pm25\,$K and a surface gravity $\log{}g=6.75\pm0.07$ (cgsunits). Using the Hamada-Salpeter mass-radius relation for helium white dwarfs,with an approximate correction for finite-temperature effects, we infer a mass$\mwd=0.16\pm0.02\,\msun$. This is the lowest mass among all spectroscopicallyidentified white dwarfs. We determine radial velocities from our spectra, andfind a radial-velocity amplitude of $280\pm15\,\kms$. With the pulsar'sradial-velocity amplitude, the mass ratio $\mpsr/\mwd=13.3\pm0.7$. From allconstraints, we find that with 95\% confidence $1.5<\mpsr/\msun<3.2$.Comment: 6 pages of text and figures. Refereed version, resubmitted to ApJL.  Needs aas2pp4.sty, epsf.st

The Masses of the Millisecond Pulsar J1012+5307 and Its White Dwarf Companion