User blog comment:Ubersketch/Lexicographic ordinal notation up to the Bachmann-Howard ordinal/@comment-30869823-20190913225449/@comment-35470197-20190917090927

@Syst3ms

My proof is given by an order-preserving surjective map from Buchholz's ordinal notation to the notation associated to PSS. It is perhaps an isomorphism (I did not check it because the surjectivity was sufficient for the termination proof), but was not so easy for me. If I correctly understand, he was trying to construct a variant of Buchholz's OCF so that it admits an easy isomorphism.

On the other hand, I have not read precise definitions of the OCF or the associated ordinal notation, and have not read a precise proof of the termination based on the notation. Therefore I will be happy if we can read them. If its proof length is actually smaller than 20 pages, then it will help other googologists to understand how to verify the termination of such a strong notation. Also, I am personally interested in how to formalise an OCF so that it admits an easy isomorphism to PSS, because it is generally difficult to construct an OCF from its desired expansion rules.