User blog comment:Ecl1psed276/BM2 Analysis - A Summary/@comment-30754445-20180709051740/@comment-35870936-20180709195456

>> Have you proven that the ruleset you've found is correct? No, but it works for every case I could throw at it, so it's probably correct. It might not be correct, but that doesn't seem likely as of now. Nish independently figured out a ruleset for BM2, and then he looked at mine and said he thinks they are the same. And Nish knows a lot more about BMS than I do.

>> Let's assume for the moment that the ruleset is correct. Do you have any reason to assume it always terminates? Yes, based on lots of testing, my best guess is that it does always terminate. Nish/Alemagno said in discord that he is working on a proof of this at the moment.

>> Do you have any reason to assume that the given ordinals are correct? Yes. As far as I know, there have been very few detailed analyses of BM2 that go past psi(psi_I(0)). I am a member of the googology discord and there have been lots of BM2 analysis going on in there recently. The ordinals in this table are the community's current opinion on the strength of the BM2.

And lastly, Alemagno/Nish did the majority of the analysis here, and I'm 99% sure he knows how compacts work. Also, this blog post was done using UNOCF, and compacts in UNOCF are slightly weaker than compacts in normal OCF's. For example, psi(e(K+1)) in UNOCF is only psi(e(xi[2]+1)) in normal OCF's. It's not just "wishful thinking", it's the current opinion of the community at the moment. There are 2 main reasons I used UNOCF instead of Deedlit's OCF's: the main reason is that it is much stronger. The limit of UNOCF is believed to be (0,0,0)(1,1,1)(2,2,1)(3,2,0) in BMS, while Deedlit's might only get to (0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,0)(5,2,0). The second reason is that UNOCF is much simpler and easier to understand.

You should probably join discord so you are in the loop about all of this analysis.