User blog comment:Koteitan/Googol Map -Phylogenetics of Googology-/@comment-1605058-20170204155733

Few comments:

There is no indication that the numbers/functions described by Friedman have evolved in any particular manner. His field of research is unique in that all of the discoveries could have pretty much been made independently of each other.

Block subsequence theorem was known to Friedman by July 1998.

According to this site, the notation \(^yx\) for tetration was used already in 1901. Wikipedia also lists as a reference a paper "Über die Funktion \(y=x^{[x^{[x(\cdots )]}]}}\) für ganzzahliges Argument (Abundanzen)." dated to 1901.

It's really weird to write "D5(99) < CoC", especially because this function is not "weaker" than CoC, it's "equivalent" to it.

We may say that xi function is inspired by the busy beaver function, since it is an analogue of it for the \(SKI\Omega\) calculus.

To write \(x\uparrow^n y<f_\omega(n)\) is, to say the least, incorrect. It's not true that \(100\uparrow^2 100<f_\omega(2)\). The RHS doesn't depend on \(x,y\) in any way. I think writing \(n\uparrow^nn\) will make this fine though. Same for tetration - one should replace x with n in the base.

Also, in some boxes, LHS and RHS have different function arguments, like circle theorem, block subsequence theorem, brace notation, expanded array notation. Moreover, two boxes miss a function's argument on RHS completely. Overall, I'd recommend changing all function arguments to the same one, not use three different ones (\(n,k,a\)).

Hope all of this helps :)