User blog comment:Alemagno12/BM2 has a problem/@comment-30754445-20180724073311

"except that the problems start at quad sequences, which still makes the notation insanely strong (if it terminates)"

Nope.

We have absolutely no idea what-so-ever how strong BM2 is, even if it terminates. All we have are wild guesses at this point. In fact, all we have are guesses of the sort that was proved wrong a dozen times over with previous versions of BMS.

The truth of the matter is, that we don't even know whether BM2 reaches the BHO. If you asked me a few weeks ago, I would say yes, but after the spectacular failure of BM1 pair-sequences to do the job, I'll hesitate to say even this much.

You know what would be nice? If one of the proponents of BMS actually took the time to write down a careful analysis of which sequence corresponds to which ordinal. You can start small: the first step is to show, beyond all doubt, that (0,0)(1,1)(2,2) terminates and corresponds to the BHO.

And no, creating another table with a list of ordinals does not constitute proof or even evidence. What you need to do, is to show a 1-to-1 correspondence between the rules of BM2 and an existing BHO-level notation. Yes, it is difficult, but until you've done this, you have nothing.