User:Alemagno12/Six Trials of Formal Analysis

I've been a googologist/apeirologist for 9 years now, and have made many analyses ever since. However, all of my analyses have been heuristic guesses and analysis tables; I've since learned how to do formal proofs and I've tried to make formal analyses a few times now, but I've always lost motivation pretty quickly, leaving only a draft or an unfinished proof somewhere in the Googology Discord (see e.g |this or |png).

So I'm proposing myself six analysis challenges to become more familiar with formal analyses, which will hopefully motivate me to do more of them in the future:

1. HPrSS v1 by Yukito vs HPrSS v3 by Yukito (expected correspondence: lim(HPrSSv1) = HPrSSv3(0,3,5,2,5,7,4,7,9,5), from a |2018 heuristic analysis)
2. HPrSS v2 by Yukito vs HPrSS v3 by Yukito (expected correspondence: lim(HPrSSv2) = HPrSSv3(0,3,5,8,10,4), from a |2018 heuristic analysis)
3. [TBA] vs [TBA]
4. [TBA] vs [TBA]
5. Dropping Hydra (x = 1) by Hyp cos vs BM2.3 by Bashicu and koteitan (expected correspondence: lim(Dropping Hydra) = BM2.3(0,0,0)(1,1,1)(2,2,0))
6. Dropping Hydra (full) by Hyp cos vs BM2.3 by Bashicu and koteitan (expected correspondence: lim(Dropping Hydra(x+1)) = BM2.3(0,0,0)(1,1,1)(2,2,1)^x(2,2,0))