User blog comment:B1mb0w/J Function Sandpit J 4/@comment-5529393-20151014104445/@comment-1605058-20151014131814

Veblen hierarchy is in general defined using fixed points of certain functions. It doesn't provide any system of fundamental sequences by itself. These can only be later described like Deedlit did in his comment, but, as you see, it doesn't provide any "canonical choice".