User blog comment:B1mb0w/J Function Sandpit J 8/@comment-5529393-20160126000406

Well, you redirected me here, but I don't see anywhere where the problems I raised are addressed. For the Extended Normal Form, the definition here seems to be exactly the same with no changes, so the nonuniqueness problems I mentioned before are still there.

For the Unique Ordinal Representation, the question is whether you are saying that the inner brackets need to be kept (so that it is not a sequence of integers, but rather a tree), or that the inner brackets can be dropped. For example, in the notation <1,1,1,<0,h>,<0,k>>, are the <0,h> and <0,k> considered to be single elements, or are you saying that the notation can be reduced to <1,1,1,0,h,0,k>? If the former is true, then this looks reasonable, if the latter is true, I don't see how it can work.