However, one must question the reliability of the account.. Because after seeing this sword first hand - it was said that the priest was banished and the other priests who saw it with him all died suddenly under mysterious circumstances..
So what and where could this sword really be?
Most believe that the Edo account is correct and that the sword is STILL at Atsuya shrine in Nagoya, though there have been many official replicas such as the one used at the 2019 coronation event.
However, a replica or the real thing was believed to have been lost at sea in the 12th century, and other accounts that suggest that the sword at the coronation event is not a replica at all..
Whatever the case may be, because it is such a sacred symbol of Japanese identity, no-one is going to go around and start checking what is inside the various 'sword boxes' that may or may not contain it and it will remain a mystery..
However, stripping away the mythological origins - chances are that if there is an ancient sword in one of the boxes, it will be one of the earliest types of swords - Jōkotō swords - and logically would have most likely have been forged before the 4th century Yamato culture, and so would probably not be a Chinese style Chokuto (and waaay too early to be a Katana) but would most probably be a Yayoi period blade - based on a Chinese Jian and, as the Edo account suggests, shaped like a Calamus leaf and relatively short bladed..
Chances are that if it is a real sword, it is a cousin of the Inariyama burial-mound sword and other early period swords that were made using the Chinese method (and often using Chinese steel).