For all I know, 1/128 isn’t the cutoff. But I worked with a guy that was, and had his little card to prove it. I’m 1/16 and claim nothing, and was a little disgusted that someone 7 generations removed, who had no idea who Wilma Mankiller was, was getting free dental. Of course, it dovetails nicely with his Scottish heritage, which seems to entail getting teeth knocked out in bar fights.