Introduction to the fast-growing hierarchy

Hello googology wiki. Recently there's been the extremely concerning incident regarding username5243 no longer wanting to talk about the DNA ORDINAL with me. This had led to frustrating, as this is something very important that needs to be discussed. You fag gots need to get your shit together and analyze my ordinal before I unload a can of 100% premium ass whooping on you. In fact, a prominent and influential figure in the googology community has just given me 100 accounts which I will use to destroy this site with my bots if you do not tell me the value of the DNA ordinal... in the name of GOD I'm not messing around here. I am dead serious.

The ordinal
To see the ordinal please check out this video.

Recently I am writing a book about making a bound for my DNA ordinal. I am almost finished with the book (which currently has over 9000 words), but I need some serious help regarding set theory for making the bound and a following proof. My best result to this point is that my DNA ordinal is between PTO(Pi^1_3-CA0) and PTO(Pi^1_3-CA+BI), which is on the realm of 2-stable ordinals. Noted that I generally like to refer to SLCON (see here ) as a side tool to help me to determine the size of DNA ordinal.

Here's some important results from SLCON, as in the page, plus some minor modifications based on some chat and some professional study of ordinal hierarchies: 1st ω-ple 2-stable ordinal; limit of first n 2-nonprojectables = S[SS_ω[σσ_ω]]

(Noted that the SLCON page is actually wrong here for technical reasons because 2-nonprojectables and ω-ple 2-stables are not exactly the same conditions. The former one is actually a stronger condition than the former one. More precisely, the supremum of the first n ω-ple 2-stable ordinals is the first nonprojectable ordinal)

1st (ω+1)-ple 2-stable ordinal; 1st 2-nonprojectable and (+1)-2-stable: S[SS_ω[σσ_ω+1]]

'''I had done some works to refine the hierarchy on papers. More specifically, to make the hierarchy of fine structures between the two ordinals.'''

Your job
Get to analyzing it, bitches. No more mr. nice guy. I'll SWAT you atheist pricks if you tempt me.

This is a message to the discord too. I will end you all!!