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The same region of the sky contains 86,685 Gaia DR2 sources, of which 77448 have a valid five-parameter astrometric solution, and 68638 have also a valid G magnitude.  For the first matching stage, we do not require valid magnitude or five-parameter astrometry; the direct positional match with a generous 10" radius finds 82,398 matches, with the vast majority well within 1":

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In this comparison, it is useful to distinguish point sources from extended sources.  The latter wuill likely be treated differently in Gaia vs. Pan_STARRS, and their astrometric and photometric accuracy is likely poorer.  One way to distinguish point from extended sources is to use the difference between Kron and PSF magnitudes; another is encoded in the QF_OBJ_EXT bit (bit 1) from the qualityFlag parameter in ObjectThin (extracted from the query in Step 1):

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