User blog comment:B1mb0w/Strong D Function/@comment-5529393-20150805054856/@comment-5529393-20150805085236

No, I'm afraid that we are still not on the same page. Your calculations for n=3 are not correct, because to evaluate them correctly you will have to evaluate the fast-growing hierarchy for much larger values of n than 3. Let's start with your rule L1. What makes you think that this is the case? Like I said in my last post, to evaluate $$f_{\phi+1}(3)$$ you need to be able to evaluate $$f_\phi(n)$$ for extremely large values of n. If you admit that you haven't examined how to do this yet, you can't possibly evaluate $$f_{\phi+1}(3)$$. So for example your claim that $$D(4,0,1) >> f_{\omega \cdot 2 + 1}(3)$$ is unsupported, as you need to be able to determine D(4,0,1) = D(3,D(4,0,0),D(4,0,0)) = D(3,D(3,1,1),D(3,1,1)) (is this correct? Your Strong D definition doesn't currently say what to do with zeroes.), so you need to be able to determine D(3,m,n) for very large values of m and n - yet you have not made any attempt to do this.