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We present high resolution (R=55,000) optical spectra obtained with MIKE on the 6.5 m Magellan Clay Telescope as well as Spitzer MIPS photometry and IRS low resolution (R~60) spectroscopy of the close (14 AU separation) binary, HD 101088, a member of the ~12 Myr old southern region of the Lower Centaurus Crux (LCC) subgroup of the Scorpius-Centaurus OB association. We find that the primary and/or secondary is accreting from a tenuous circumprimary and/or circumsecondary disk despite the apparent lack of a massive circumbinary disk. We estimate a lower limit to the accretion rate of > 1x10^-9 solar masses per year, which our multiple observation epochs show varies over a timescale of months. The upper limit on the 70 micron flux allows us to place an upper limit on the mass of dust grains smaller than several microns present in a circumbinary disk of 0.16 moon masses. We conclude that the classification of disks into either protoplanetary or debris disks based on fractional infrared luminosity alone may be misleading.
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