http://en.wikipedia.org/wiki/Alien_registration_in_Japan
Alien registration may also be evidenced by a certificate of matters in the alien registration records (外国人登録原票記載事項証明書 gaikokujin tōroku genpyō kisai jikō shōmeisho?), which is an A4-sized printed copy of the information currently on file, similar in form to the residency registration certificates used by Japanese nationals. Because this form of certificate does not contain the subject's photograph, it is not as widely accepted as the ARC for identity verification purposes, and is mainly used as a temporary certificate when an ARC is unavailable.

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Note added at 14 mins (2011-02-24 13:40:42 GMT)
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People seem to translate this phrase in many different ways, but I would actually use the following: http://www.mofa.go.jp/j_info/visit/visa/short/pdfs/procedure...
""Certificate of Registered Matters on Alien Registration"

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Note added at 18 mins (2011-02-24 13:45:19 GMT)
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Just a note: I prefer my original response, but I think the closest you will come to an official translation is the MOFA translation. I don't like the repetition of "registered" and "registration," but the MOFA is the ministry that handles alien registration, after all.