User blog comment:PsiCubed2/My own version of BMS/@comment-35470197-20181120231600

> I believe (though I haven't yet proven) that in this version, the pair sequences work exactly as Buchholz Hydras (with my additional rule making sure that we don't mix-up nodes with different parents).

Then what have you precisely done? I remember that you wrote that you had your own work containing "Some proofs regarding BMS (in short: there's a way to make pair sequences work and prove that it works)".