User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 3/@comment-5529393-20130530121945

Good heavens, are you seriously trying to say that such a simple rule as nesting the next lower number n times reaches the TFB ordinal??? I can't believe that. You say "Quite a lot of the evaluation relies on the type-k brackets doing to   Ω  k       exactly as type-1 brackets do to omega", but what reason is there for such a strong conclusion?

Let's examine brackets of type 2.

[1(1)[_2 1]] = [1 (1) [1 (1) [1 (1)... [1 (1) 1] ...1] 1] 1].

But remember, nesting is weaker than having longer arrays, since each array of length n+1 is defined using deep nesting on arrays of length n. So the above is less than [1 (1) 1 (1) ... 1 (1) 1], and we aren't breaking into new territory here.