What is the status of the corner shown below?

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[go]$$Wc White to Play
$$ ------------------
$$ | . O . O . . . . .
$$ | X X X O X . . . .
$$ | . X O O X . . . .
$$ | O O O X . X . . .
$$ | . X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

My first instinct is that white is dead.

B can kill by filling in the outside liberties, then playing A17. If W captures at that point, B plays B18 and it's a dead shape.

Here I will explain it in more detail.

White is dead:
White can only play these 3 moves (a, b or c). But Black will ignore them all. Even if white plays all 3 white is still dead.

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[go]$$Wc White's moves
$$ ------------------
$$ | b O a O . . . . .
$$ | X X X O X . . . .
$$ | c X O O X . . . .
$$ | O O O X . X . . .
$$ | . X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Let's say white played all of the above moves and black answered by filling in the outside libertys:

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[go]$$Wc White captures with 5
$$ ------------------
$$ | 3 O 1 O 2 . . . .
$$ | X X X O X . . . .
$$ | 5 X O O X . . . .
$$ | O O O X . X . . .
$$ | 4 X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Then this is the result:

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[go]$$Bc Since white captured with the marked stone it is black's move
$$ ------------------
$$ | O O O O X . . . .
$$ | . 1 . O X . . . .
$$ | W . O O X . . . .
$$ | O O O X . X . . .
$$ | X X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Black now plays at and White is dead.

Obviously, if White captures Black White dies. So is it seki, or can White make it seki?

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[go]$$Wc Seki?
$$ ------------------
$$ | . O W O B . . . .
$$ | X X X O X . . . .
$$ | . X O O X . . . .
$$ | O O O X . X . . .
$$ | B X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

This, then, is the critical position. It is the only one with two shared liberties where the outside liberties are filled.

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[go]$$Bc Dead shape
$$ ------------------
$$ | . O O O X . . . .
$$ | X B X O X . . . .
$$ | 1 X O O X . . . .
$$ | O O O X . X . . .
$$ | X X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

almost fills the White eye. If White captures the Black stones Black has an inside play at to kill. White is dead.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

@Bill Spight: You also need to add that black does not need to play at 'a' after white played the marked stone.
Even with outside liberties, Black does not need to play 'a'. But the fact that you can later play 'a' is the reason why it is not seki.

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[go]$$Bc Dead shape
$$ ------------------
$$ | . O O O . . . . .
$$ | X X X O X . . . .
$$ | a X O O X . . . .
$$ | O O O X . X . . .
$$ | . X X . . . . . .
$$ | . . . X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]