Wedding rings come in pair. I meant she hid Admiral's ring of the pair. She hid those before they had sex so the possibility she did that to make clarification to Kaga later is not zero. If we think she planned it all then maybe she knew Admiral probably will give the ring to Kaga first. Being serious as Kaga is, she would not accept Akagi's feelings at that point cause she think she would hurt Akagi further and cheat on Admiral ('marry' Admiral out of a sense of duty). That 'marriage' word is harmful. Since Akagi took those items, Admiral had to 'marry' her first I guess. Well, if it's not like that then I'll go with the option she keep the items to get married with Kaga later (both strengthening procedure & actual proposal).
That makes sense. Though there is no sense in hiding the certificate then. When Akagi and the Admiral 'married' I mean, cause that wouldn't be anywhere near Kaga since she's not the Secretary (I assume, since Akagi is behind him and that is typically how they're depicted when they are in the Secretary position). But yeah, I can accept that Akagi maybe asked the Admiral to 'marry' her first or something along those lines so that he didn't 'propose' to Kaga and then the whole thing you wrote out.
Edit: I'm not making any sense right now but simply put I think Akagi keeps the items from her own 'marriage' to avoid misunderstanding with Kaga (her original plan) and maybe also confiscates the items prepared for Kaga's 'marriage'. Doing so to preventing Kaga from thinking it's a real marriage and being forced to have sex with Admiral is strange since he know Kaga now has that mutation (wouldn't he be the receiving end in that situation ?). Plus Akagi already explained to Kaga the marriage is a contract to strengthen one's ability. If she did confiscate Kaga's items then she is planning to use it and sneak a marriage with her.
I got it this time xD In that scenario though, it would have probably been before Kaga had her mutation. So it would be Kaga who married first before she was sunk.
I think that her sinking and 'mutation' could be tied with Akagi 'marrying' the Admiral perhaps? Cause she assumed that Akagi doesn't love her and so became reckless and she sank and then came back with a 'mutation' because of her 'regrets'.
Still, I don't think Akagi marrying Kaga would raise her level cap though. Then again, it wasn't mentioned if it had to be the Admiral or it could be anyone else. If it could be anyone else, nothing would've stopped Akagi from propositioning Kaga in the first place, and at the same time she could've just explained it was for 'strengthening purposes' if Kaga was dubious about it for some reason.
Yeah, there are a couple of ways it could work for why it was hidden. The most logical (for me) being that Akagi hid the (new) ring and certificate so that the Admiral wouldn't 'marry' Kaga and she wouldn't be with him out of duty. She still has her vagina so.