User blog comment:P進大好きbot/Relation between an OCF and an Ordinal Notation/@comment-30754445-20180810102658/@comment-30754445-20180810133214

The 2nd system is the one I'm talking about.

The 1st system is actually pretty easy to analyze. It reaches the BHO, if I remember correctly.

The 2nd system is the one where all the wild speculation is going on. As you said, this the one that Taranovsky himself claims to reach PTO(Z2). And I've never met a math pro (other than Taranovsky himself, who is obviously biased) who believe this claim.