  The hierarchical triple system PSR J0337+1715 offers an unprecedented
laboratory to study secular evolution of interacting systems and to explore the
complicated mass-transfer history that forms millisecond pulsars and
helium-core white dwarfs. The latter in particular, however, requires knowledge
of the properties of the individual components of the system. Here we present
precise optical spectroscopy of the inner companion in the PSR J0337+1715
system. We confirm it as a hot, low-gravity DA white dwarf with
Teff=15,800+/-100 K and log(g)=5.82+/-0.05. We also measure an inner mass ratio
of 0.1364+/-0.0015, entirely consistent with that inferred from pulsar timing,
and a systemic radial velocity of 29.7+/-0.3 km/s. Combined with the mass
(0.19751 Msun) determined from pulsar timing, our measurement of the surface
gravity implies a radius of 0.091+/-0.005 Rsun; combined further with the
effective temperature and extinction, the photometry implies a distance of
1300+/-80 pc. The high temperature of the companion is somewhat puzzling: with
current models, it likely requires a recent period of unstable hydrogen
burning, and suggests a surprisingly short lifetime for objects at this phase
in their evolution. We discuss the implications of these measurements in the
context of understanding the PSR J0337+1715 system, as well as of low-mass
white dwarfs in general.
