Recently Toshiyasu Arai submitted ["An ordinal analysis of $\Pi_{N}$-Collection"](https://arxiv.org/abs/2311.12459) and Henry Towsner submitted ["Proofs that Modify Proofs"](https://arxiv.org/abs/2403.17922), both of which claim ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:
* https://mathoverflow.net/questions/159749/consistency-of-analysis-second-order-arithmetic 
* https://mathoverflow.net/questions/144041/proof-theoretic-ordinal-of-zfc-or-consistent-zfc-extensions 

The consensus seemed to be that we were a long way away from proving anything like this. For such a big result, I am struggling to find much information on it. I think the two most obvious questions for a lay-person is:

1. What is claimed to be proof-theoretic ordinal of $Z_2$?
2. What does this mean for the ordinal analysis of $ZFC$?

Additionally what are the wider implications Proof Theory and Reverse Mathematics?