User blog comment:Cookiefonster/My informal proposal of BEAF from limit of tetrational arrays up to SVO/@comment-5150073-20140920170843/@comment-2033667-20140927014140

Iko, why do you believe that X^^(X+1) & n must have n^^(n+1) entries? Every valid extension I've seen violates that condition past e0. It's only a coincidence that it works for e0, actually, due to the way cantor normal form works