User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-5529393-20160724103034/@comment-28633611-20160725112315

Why can't I reply to Simplicityaboveall's reply?

I still don't see a definition of R anywhere, which is the crux of the problem. It's exactly the same problem we have with the climbing method and BEAF: Actually defining the process is much trickier than it seems at first glance.

And at any rate, any such process - once defined - will be limited by some countable recursive ordinal. If you use the SGH->FGH transformation as your basis (and you'll still need to rigorously define the process - which you haven't) then the limited would be something like ψ(Ω_ω)). The actual ordinal would depend on the exact process, but it will never get you to Rayo's number since Rayo's function is uncomputable.