Recently Toshiyasu Arai submitted "An ordinal analysis of $\Pi_{N}$-Collection" and Henry Towsner submitted "Proofs that Modify Proofs", both of which claims ordinal analysis of full second-order arithmetic. There has been discussion before on MO about this, see:

• Consistency of Analysis (second order arithmetic)
• 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?