User blog comment:Koteitan/Purely mathematical definition of BMS/@comment-30754445-20181123092422/@comment-30754445-20181126203827

The "constraints" I'm refering to are the ways both of our definitions for pair-sequences differ from BM1.

Both our definition take BM1's basic rule for finding the bad part, and add an additional condition for it actually being the bad part.

Your additional condition is: (a) the bad root must be a P0-ancestor of X.

My additional condition is: (b) there are no pairs after the bad root whose 0-cordinate is smaller than the bad root.

Other than that, both our definitions are identical to BM1 (and to one another). Therefore, in order to prove that our definitions are equivalent, it is sufficient to prove that (a) and (b) are equivalent.

And yes, I'm talking only about pair-sequences here. As I've already stated on my blog post, my only goal was to create a working system for pair-sequences. And I gotta say: I love that notation. I think that due to the 3-row BMS craze, the people here are grossly underestimating the beauty and power of PSS. It's simple. It's elegant. And it creates huge numbers even by googologist standards.

(I must also say that I believe the quest for a working 3-row version of BMS to be futile, at least in it's current form)