Cut at N3 is not preparing for the ko threat, have you seen my variation? it’s a strait ko locally, I’ve already shown the follow up in previous reply after your move 4. Look carefully.
There are other variations as well, but it’s not weakening the white groups but weaken the black stones in the corner. And white don’t need to hane if black don’t respond, just extend (and the corner four black stones is ko to live, or if black save it white can turn and break the black lower side moyo)
Another suggestion for black’s next move: Q8, theatening O7. And if white responds at O7, a knight move to M8 and perhaps create some momentum to threaten white’s moyo in the process:
I am curious though, does white have to answer Q8? Borrowing @NinjaKitty’s idea if white just connect O12, can black cover at O8 or hane at O7 really kill the white group?
I am really not sure, start from S9 I’ve tried many variations, and some ended up in a ko, some semeai, I’ve been wondering about this for a while ever since I started to doubt if it is 100% alive and how to kill the LR. Q8 does change some of the variations I tried before.
After investigating about half of them start from S9, I’d say white at least have ways to make it a ko to live (or escape), or opt for a trade and some sacrifice if needed to be.
Another way to look at this is considering if black uses O7 as a ko threat and white ignores it and takes the ko, will black’s next move following up O7 be Q8? I’d follow up with P7, so maybe P7 is also a good candidate? Intuitively a peep did look like a possible threat for the LR white group.
So I will change my vote to B7 or B8.
B7 may be the safe move, taking some profit in sente.
But B8 is also very attractive, though it depends on how many 20+ points ko threats black has.
This depends partly on how many ko threats black has in the center. But for that we also have to consider that black already secured his upper left group, so white’s E12 cutting stone and D13 stones are fairly light (not that important anymore). Only the F13 stone is still important to white.
For example, white could respond like this when black cuts at F12 as a ko threat:
(3 and 6 are ko captures)
White loses 15-20 points around D13, but white gains more or less the same in the lower left (perhaps even more).
So black may not gain from this ko fight, unless there are many threats around L17.
I’d answer white’s O7 with black O9. I just don’t see where white is running to, at least not if white strengthens black’s center stones by giving up on E12. But maybe that’s just me wanting B8 to work.