User blog comment:B1mb0w/Unique Ordinal Representation/@comment-5529393-20160125081041/@comment-10262436-20160125085619

This blog only gives one example of how to construct an ordinal and large number. Many more rules apply that will force only one unique representation for a given sequence.

The uniqueness of the sequences is best explained in the Sandpit J_8 function. I have added more examples and logic on that blog.