User blog comment:B1mb0w/The Alpha Function/@comment-27173506-20160129134940/@comment-27173506-20160201135452

The TREE(3) function (you misspelled function by the way) does not exist. There is TREE(3) the value, and TREE(n) the function.

Even so, tree(3) (weak tree(n) function), may be bigger than the value you have stated (although someone may have found an upper bound, that I'm not aware of). A lower bound does not necessarily imply a value in that range.