Hi Grey,
Dr. Sato was much more of a nihonto expert then a tosogu expert so the attribution may not be so accurate.
The first column from the far right side says top to bottom: tate maru-gata (竪丸形), tetsu-ji (鉄地).
The second column from the far right side says from top to bottom: ko-sukashi (小透), shinchu zogan (真鍮象嵌).
The third column from the far right side says: mumei (無銘), Onin (応仁).
The fourth column from the far right side says: Kanzan plus hanko.
The front of the box says: kiku sukashi (菊透), zogan tsuba (象嵌鐔).
I only had to ask my wife twice. :lol: From looking at the front and back of lid they look like they were written by the same hand.