User blog comment:Dchew89/Possible (Uncomputable) Function with Growth Rate of w 1^CK/@comment-35470197-20190213072103/@comment-38080588-20190213211144

The functions must be defined based on a very specific set of rules, for example, each new function must grow faster than all previous defined functions, but also have a domain and range that input and output a limited set of values when being defined. I'll admit, it is pretty compact writing, and I may rewrite it if I ever have time to, but I was thorough in clarifying details such as those, mostly in the first paragraph.

Additionally, it is much simpler to use the overall function based on a single notation system, like the FGH as shown, which could make it much easier to analyze the function as a whole from a more limited, but still mostly representative perspective. I may post some bounds of function output values I have found written with the FGH. I am confident it reaches beyond the equivalent of \(f_{varphi(\omega,0)}(2)\) given an input of less than 2^^10, which is far less than the output of, for example, d(6). I am starting to notice patterns in the function behavior, but not yet anything to solidly predict its growth rate limit, though I am beginning to doubt it reaches  \(\omega_1^{\textrm{CK}}\), or even near it.