I think I may have found the "original", or non-compatible with other models, sprocket for the Honda PS50K1.
It is this Ebay auction that shows the right one, including part number 412010-081-000. The picture comes from CMSNL, but the part number cannot be found there for some odd reason.
This needs to be verified still, but I think this would be the right one. (but not for me as I needed 37/38 teeth)