User blog comment:Vel!/Ordinal BEAF/@comment-5150073-20130315133136/@comment-5150073-20130315203734

FB100Z, You meant phi(w,0)? If yes, then it is just ordinal that diagonalizes over tetration, pentation, hexation, ... In otherwords, it is {n,n,n} array. Notice that f_w(n) is about {n,n,n}, and f_phi(w,0)(n) is about {n,n,n} & n. It really makes sense to claim that f_phi(w+1,0)(n) grows like solutions of expandal arrays since f_w+1(n) itself has expandal growth rate.