It does appear to be American Standard Cadet, with 16 Splines, and about .375 diameter broach. (I had to look this up to see what that meant). The metal part without the washer is about an inch and a quarter long, with the washer it's about an inch and 3/4. I put it back in after taking the handle off, and realized it wasn't tight, tightened it and it quit leaking. So it works for now. However, I also note that the cold handle sits up above the ring, and the hot sits right on the ring, so there appears to be a cylindrical part missing between the ring and the handle. Assuming the entire assembly is American Standard, I will now search for that. I will also purchase a replacement set of stems, the old one does look worn.
Thanks very much for the help, none of the local area stores had a clue. If I can buy what I need from the sponsor of this thread, I will certainly try to do so, even though it's no great purchase. Thanks again.