  Among the 28,000 targeted stars in K2 Field 10 is the white dwarf WD 1202-024
(EPIC 201283111), first noted in the SDSS survey (SDSS 120515.80-024222.7). We
have found that this hot white dwarf (Teff = 22,640 K) is in a very close orbit
(P = 71 min) with a star of near brown-dwarf mass ~ 0.061 Msun. This period is
very close to, or somewhat below, the minimum orbital period of cataclysmic
variables with H-rich donor stars. However, we find no evidence that this
binary is currently, or ever was, transferring mass from the low-mass companion
to the white dwarf. We therefore tentatively conclude that this system is still
in the pre-cataclysmic variable phase, having emerged from a common envelope
some 50 +/- 20 Myr ago. Because of the 29-minute integration time of K2, we use
follow-up ground-based photometry to better evaluate the eclipsing light curve.
We also utilize the original SDSS spectra, in approximately 15-min segments, to
estimate the radial velocity of the white dwarf in its orbit. An analysis of
the light curve, with supplementary constraints, leads to the following system
parameters: Mwd = 0.415 +/- 0.028 Msun, Rwd = 0.021 +/- 0.001 Rsun, Mcom =
0.061 +\- 0.010 Msun, and Rcom = 0.088 +\- 0.005 Rsun where the subscripts 'wd'
and 'com' refer to the white dwarf and low-mass companion respectively. If our
interpretation of this system as a pre-CV is correct, it has the shortest
period of any such system yet found and should become a compact CV in less than
250 Myr.
