User blog comment:B1mb0w/Growth Rate of the S Function/@comment-5529393-20160712123611/@comment-5529393-20160712125131

To see the "very similar" structure of S and FGH functions, you have to know how the S function works under the original definition. You say that S(n,T(0),2) == f_w^2(n), but I can't just take your word for it; I need to apply the original definition and see for myself.

Right now, applying the original definition appears to lead to a problem, and that needs to be addressed.