I think that Black will often have a ko threat in the top left corner, but there are some wrinkles.
- Click Here To Show Diagram Code
[go]$$Bc Ko threat?
$$ -------------------
$$ | . . . . . O O X .
$$ | . 1 . O O O X X .
$$ | . . . O X X . . X
$$ | . 3 . O O X . . .
$$ | . . . O 2 O X . X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]
Let Black play

as a ko threat. Now if

fills the ko, Black jumps to

. This looks a lot like seki.
However . . .
- Click Here To Show Diagram Code
[go]$$Wcm4 Seki?
$$ -------------------
$$ | . 2 . . . O O X .
$$ | 6 X 1 O O O X X .
$$ | 4 3 5 O X X . . X
$$ | 9 X 8 O O X . . .
$$ | 0 7 . O O O X . X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]

secures the White eye and threatens to take away the Black eye.

-

secure the Black eye in the corner. But now

threatens to make a second eye for White.

prevents that, but now White plays a throw-in at

.
- Click Here To Show Diagram Code
[go]$$Wcm14 No Seki
$$ -------------------
$$ | . X 3 . . O O X .
$$ | X X O O O O X X .
$$ | X O O O X X . . X
$$ | 2 X X O O X . . .
$$ | X O 1 O O O X . X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]
White wins the semeai, so that line does not work for Black.
- Click Here To Show Diagram Code
[go]$$Bcm5 Seki?
$$ -------------------
$$ | 3 2 1 7 . O O X .
$$ | . X O O O O X X .
$$ | 5 4 6 O X X . . X
$$ | . X . O O X . . .
$$ | . . . O O O X . X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]
Suppose that Black tries the hane,

.

throws in and then

-

prevent an eye for Black. But then

not only takes away White’s eye, it prevents the throw-in trick because of damezumari.
- Click Here To Show Diagram Code
[go]$$Wcm12 Ko
$$ -------------------
$$ | X . X X . O O X .
$$ | . X O O O O X X .
$$ | X O O O X X . . X
$$ | 1 X 4 O O X . . .
$$ | 2 3 . O O O X . X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]

takes ko.
But White has a slightly different throw-in trick, which makes ko. And White takes the ko first, so Black still has to find a ko threat.
But wait! There’s more! White can do better.
- Click Here To Show Diagram Code
[go]$$Wcm8 Another ko
$$ -------------------
$$ | X 3 X 1 . O O X .
$$ | . X O O O O X X .
$$ | . 2 . O X X . . X
$$ | . X . O O X . . .
$$ | . . . O O O X . X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]

makes ko and an eye at the same time.

In addition . . .
- Click Here To Show Diagram Code
[go]$$Wc Ko threats
$$ -------------------
$$ | X . X O . O O X .
$$ | . X O O O O X X .
$$ | 6 X . O X X 4 . X
$$ | 5 X 2 O O X 3 . .
$$ | . 1 . O O O X a X
$$ | O O O O O X . O X
$$ | O X O X X . X O X
$$ | X X X X X X X O X
$$ | . . X O O X O X X[/go]
White has three local threats.

threatens to make a second eye,

threatens to capture three Black stones for a second eye, and

threatens to take away Black’s eye. White has a threat at “a”, but it is not large enough to make up for letting Black live in the corner.
Does Black really have a ko threat in this corner? If White fills the 1/3 point ko, he trades it for a larger ko, but not one which Black takes first, one which White takes first, instead. Furthermore, White has three local ko threats. Black needs four extra threats just to keep up!
That is true. But this is a picnic ko for Black. White has to win it, or get sufficient compensation in exchange. Otherwise White takes a loss by winning the 1/3 point ko. But Black can afford to lose the ko, as long as she gets enough in exchange. And all Black needs to get enough is enough to afford to lose the original 1/3 point ko. In effect, Black is fighting the original, small ko while White is fighting the large ko. White may have ko threats that would be effective in the original ko fight but are too small to win the large ko. Also, Black may have losing ko threats that she could not afford to play against the original, small ko, but which she can afford to play against the large ko.

So whether this is a ko threat for the 1/3 point ko is a big maybe.
