A lot of those moves are not accurate. like Black should never play move 20 there (in the second variation), it’s filling in Black’s own liberties, basically self-atari. Rather than correcting each move in the variations one by one, it’s better to consult KataGo for questions like these.
White lost because he played too passively for most of the game, and then misread at move 124 during his invasion, losing 18 points in one move. A 7 dan would be sharper and slightly less defensive.
very peaceful game
https://online-go.com/game/81926962
and another one
I didn’t kill any group. Just center is enough to win against corners
haha that’s both insightful and funny.
The first one is clear, playing at A (S7) is more urgent – it’s called “double sente” by Japanese players, which means if the opponent plays there first, then you are forced to respond anyway, but if YOU play there first, then the opponent needs to respond. In this case, playing at A (S7) threatens to capture the black stone at S6, so Black would need to play an extra move to fix it. You also can later cut at S5 and then extend at S4 to cause trouble (usually just ko threats) in the corner. That’s why S7 is such a valuable move at this moment.
The second one surprised me. Usually AI highly values 3-3 invasion at all times, but upon looking more closely I understand why playing at A (K11) is urgent here too. It’s not “double sente” but it’s close to it. It’s a very valuable move for both players. If Black plays there, White’s 4 stones will ALL become disconnected and brittle while Black’s group is strong and very hard to capture. If White plays there, all 4 stones are connected and 99.9% alive for the rest of the game. There is a related go proverb that says a “ponnuki” is worth 30 points in the early game, and it applies here. Playing at K11 is worth about 30 points for both players.
I don’t even understand what S7 in the first diagram is good for. What if White S7 is followed by Black R7, White Q7, Black S8? What was this exchange good for?
These kind of “double sente” moves where BOTH players gain if they are played are always urgent. To understand this better, realize that responding to an atari is usually like a double sente.
More squares achieved… 
So far, so good. Now all we need to find out is how exactly I will totally mess things up and lose 
So far, so good I guess… I made some significant blunders in the direction of play in general, but that fight went ok, I guess, and I am back on track.
Wait that’s not a square… that’s a parallelogram!
It may not be a square, but it’s still an Anti-Ladder Influence-Erasing Negation Structure, or A.L.I.E.N.S. for short 
Oh I found the proverb I referenced in my explanation of square fuseki:
To explain further, the idea is that Black must use his first move advantage to focus on developing outwards influence because White has extra points from komi, meaning if Black and White take turns claiming territory, i.e. third-line moves, White will automatically win in the end. Of course this isn’t exactly true – KataGo proves proverbs like this aren’t true a lot of the time. But I think one of the goals of playing square fuseki is to rebel against AI moves (at least AI joseki) anyway. And I don’t see AI generating clever and funny proverbs like these.
What happens if the opponent instead of the goban’s corners, plays in one of the corners of the squares?
then i just take a nearby 3-3 point. Any approaches towards my corner, I can sandwich (pincer) it with my tengen stone(s).
@square.defender has his own ways of dealing with it, different from mine: Square Fuseki ▪ Square Opening - #23 by center.square
Maybe in the future i’ll think of a more artistic solution, but if I want to win, that’s what I’ll do.
…
This is assuming black only plays one move in your corner, black can easily also take another corner of this square, and likely play the outside before you.
Okay, I’ve come up with countermeasures.
Method 1: Change target from 3x3 symmetrical center square to 4x4 asymmetrical square:
Method 2: If they’re foolish enough to challenge even the 2nd square, it’s their loss, White will have a superior position:
I don’t deserve to be credited with trying this – I verified with AI first that 4x4 center square is actually better in handicap games than in even games. It loses less points in handicap games of ANY size. More handicap stones = less points lost by playing square. I haven’t tried it with more than 7 handicap stones though.
If KataGo didn’t exist, I would not dare to play this in a handicap game.
