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Swords carrying this signature on their tang (nakago) had particular place in Japanese history. Reason si that  meaning of  name of swordsmith was believed to bring the luck thus it was usually given as a special gift for important person.  Also when the new Shogun was entrhoned he has obtained as a gift sword with Rai Kunimitsu on its mei- signature as a present from all important Daimio.  Trully there were lack of swords made by this particular swordsmith so it was made as falsum, sometimes. Still the sword with false signature needed to be pretty good to look like the one Kunimitsu made himself!