User blog comment:Alemagno12/About the fanmade OCF/@comment-32697988-20180408234329/@comment-30754445-20180418001454

@CatIsFluffy

Don't you mean "stable cardinals"?

@Rpakr - "How do we know if an OCF reaches PTO(KP+Pi3 reflection)?"

The same way way we know that any notation reaches its claimed level:  By either:

(1) Providing a formally proof. This is usually done by showing that the proposed system is equivalent - ordinal-for-ordinal - to a known system already established to reach the desired strength. Another method of proof would be to somehow show that the proposed OCF cannot be proven to be well-founded in KP+Pi3 reflection (though this route is usually far more difficult).

(2) A careful analysis which was done and confirmed by a person who understands these levels really really well.

The problem regarding option #2, though, is that there are very few people who really get how the ordinals work at this level. At best, there are a handful of people here who are qualified (Deedlit and Hyp Cos are - really - the only two candidates I can think of right now). At worst, there are none.

So I really think that if we're going into all this trouble to construct an actual "standard OCF for the wiki", we should also go into the trouble of rigorously proving that it works.