User blog comment:Wythagoras/A far better bound for TREE(3)/@comment-11227630-20140622124913

I think that we know too little about the weak tree function - how can it grow as fast as f_SVO(n)?

If we don't understand how it work, we just know ([]) at SVO and (([])) at SVO+1, but we don't know how (([][])) can be at SVO*2 instead of SVO+ε(0), let alone ((([]))) and ([]).

However, to find "how can tree(n) grow as fast as f_SVO(n)" we don't need the winning sequence, just need a set of sequence whose length grow at the level of f_SVO(n).