I don't understand an AI decision in 9x9 game

I wrote the question below based on what I saw at the end of the game. But going back to the game, I now see a different AI analysis that makes better sense. Or does it? Am I going crazy?

In game Partie amicale, the AI analysis says that white made a mistake at white’s move J2 (I can’t read the move number from the tiny move chart). It says that white should have moved to H7 instead, continuing with black H8, w J4, which secures life for the w group.

But it looks to me that after those moves, b H3 would kill the group for sure. How would w respond to b H3 to save the group for w?

White would just extend to J2.

Sure, but that doesn’t work for w. W at J4 fails, doesn’t it?

White would have one eye at H3 and one at J5.

When b plays at H3, b can capture, no?

Not if white extends to J2

No. J4 is very useful here, it means black can’t atari from j3 due to liberty shortage. This hanging connection on 1st line shape is a common eye building tesuji. Like j2 it defends h2, but indirectly and with fewer points but crucially more eyeshape.

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Note white’s liberty at F4.

Note white’s lack of liberty at H2. When b plays H3 it is atari.

Yes, so white extends to J2. White’s previous move at J4 ensures black has no follow-up to kill.

Edit: I added a variation to the game.

What? The point is that if you follow what the AI suggests for w, it looks like w dies, as I said in the original post.

I’m going to bed. I’ll check this thread tomorrow.

The AI suggest to make the H7-H8 exchange before playing the vital point of J4, as a small score improvement. I don’t see an AI suggestion to let white die.

You can zoom on a mobile phone by using your 2 fingers.

I added the key line with your likely misread that 6 is self atari.

Thank you for showing me the move w J2. For some reason I repeatedly failed to see it. I now understand that the AI was correct.