White to play a kosumi.
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Is hane at the head of two stones still technically a kosumi? I’m not sure if the proximity of the black stones changes it…
Otherwise I guess maybe G7? 
None of your two suggestions is the game move.
Hint: don’t answer locally.
M7, move out and threaten to cut?
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J11 (to defend the group K10)?
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Correct.
Game: XLIII Italian Go Championship - Final - 2nd game
Commentary: Twitch: European Go Federation, XLIII Italian Championship
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Davide Bernardis is young and strong (among Italian players). I met him at a tournament when he was a nice boy with long elegant fingers. He was already very strong.
He then grew up and now is a very tall young man even stronger.
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This one seems difficult
Summary
Q17?
Guess
J5 maybe?
Though F17 looks nice.
I think that’s probably something that could do with being established.
Since otherwise it’s completely arbitrary
what one might “call” a kosumi. Just in that each person looking to post a puzzle might have different ideas about what counts.
So more generally should a kosumi be a “free-standing” kosumi, or if it’s part of another shape should it no longer count as a kosumi?
Edit: for the rules of the game I mean, to make guessing simpler, and more people can jump in easily. Outside of the game it doesn’t matter really.
“Shape” is a bit too general to completely forbid a kosumi which is part of a larger shape. For instance, a kosumitsuke is still a kosumi.
But at the very least, I would always require that the two points adjacent to both of the kosumi’s two stones should be empty.
Otherwise, it’s not a kosumi, but rather an empty triangle or a hane (or atari).
Kosumi
Not a kosumi
Not a kosumi
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To construct practical/useful puzzles, one might want to accept as an answer all of several good kosumis, not just the one that a pro ended up playing.
Which probably means AI analysis could help with puzzle construction: either to help select pro kosumi moves for which there wasn’t another reasonable kosumi option, or to actually have the AI provide the multiple move options.
I’m in favour of using human pro moves for puzzles rather than AI moves, which means I vote for using AI to eliminate puzzles for which the pro move isn’t the only good kosumi.
Or you could rewrite the text of the puzzle as: “In this situation, Black played a kosumi. The AI preferred another kosumi instead. Find both the kosumi that was played, and the kosumi recommended by the AI”
Guess
P17 N18
P.S. In one of my games, the position was similar:
Shapes to remember (SDK level) • Life In 19x19
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