User blog comment:Edwin Shade/My Googological Goals For The Year Of 2018/@comment-32697988-20180101223205/@comment-30754445-20180103215048

Obviously, since BM1 is the only system which is known to actually work.

BM1 pair-sequences is a robust (and quite powerful) notation. It has been analyzed by several people, and it's growth rate of ψ(Ωω) was demonstrated in many ways.

BM2, right now, is an unconfirmed proposal. But even if we assumed that it works properly, the whole point of BM2 was to fix a problem with triplet-sequences (sequences that start with (0,0,0)(1,1,1)...) while leaving the pair-sequence level untouched. IOW BM2 was designed to be backwards-compatible(*) with BM1, so it shouldn't matter at all which version choose.

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(*)To be more precise: BM2 should give the exact same results as BM1 for any sequence that can be arrived from (0,0)(1,1)(2,2)...