Good question

Hint 1. The problem's main diamonds are still hidden
Hint 2. The solution is much longer

What do mean by your Hint2 ? I do not get the point.

Click Here To Show Diagram Code

[go]$$B Komi = 0.5
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . Z O O O W B . O . . . . |
$$ | . . Z . O X X X O O O O . |
$$ | . . . O B X , . . X X X . |
$$ | . # . O O X . X X X . X X |
$$ | . O Y . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O . X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , . O , X X X O . . |
$$ | O . . X X O O O X X O . . |
$$ | X . O . O . X O X O O . . |
$$ | . X O X . O . . X X O . . |
$$ +---------------------------+[/go]

I do not have any idea for the right side, but for the upper left corner ...

If White's upper string got into some kind of damezumari (through something like , concrete sequence still unknown), Black might get the change to place the two stones, due to the multi-stage-ko in the lower right corner.
Thereafter, might become interesting, at least as a ko threat.
And suddenly, there might be some kind of semeai (at least the threat of a seki), as White's group does not have sooo many liberties thereafter ...

With regard to the upper left corner, we will have to remember that Black might be able to play at least two moves in a row locally, probably three.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

The current solution has 67 moves. The real solution has over 100 moves

thank you, I had somehow overlooked this comment. (Now I feel dizzy...)

Since Black wins against the strongest white defence we could find so far, that can only mean that W has an even stronger defence somewhere, right? (Unless Black is greedy and wants a better score than B+0,5. But that's hard for me to believe; the result so far and the balance of the furikawaris give a impression of perfection to me...)

Oops, does that mean it is possible for white to choose a far longer defense? It is more and more unbelivable. Could you give us another hint? Maybe where white can make another choice?

The same ko but with more ko threats

Hint 3. In the position are more ko threats. But white and also black must prepare them...beforehand

Is it a good improvment ? (I still need some more work to continue from this new idea)

Click Here To Show Diagram Code

[go]$$Wm24
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O 2 X , . X X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O 1 X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . O X X O . X |
$$ +---------------------------+[/go]

Yes, 24 and 25 prepare ko threats

Click Here To Show Diagram Code

[go]$$Wm24
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O X X , . B B B B O |
$$ | . . . O O X . B B B . B B |
$$ | . O X . O X . . . . . W . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O O X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . O X X O . X |
$$ +---------------------------+[/go]

What I have not yet discovered is how to use the white marked stone. I guess I can build a damezumari on the black marked group but it is not clear if I have to search an atari or a seki. I continue to search. In any case it is quite interesting.

Click Here To Show Diagram Code

[go]$$Bm59 Komi = 0.5; prisoners
$$ +---------------------------+
$$ | . . O X X X X X O . O . O |
$$ | . 1 O O O O X X O . X . O |
$$ | . . X a O X X X O O O O O |
$$ | . . . O X X , . X X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O Z . O X . . . . . O . |
$$ | O O O O O X O . O X X X . |
$$ | X O X X O O X X . X O X X |
$$ | X X X . X O X O . X O O O |
$$ | . . X , X O O X X X O . X |
$$ | O O O X X O O O X X O X O |
$$ | . X O X O . X O X O O O . |
$$ | O X O X O O . O X X O . O |
$$ +---------------------------+[/go]

I would like to suggest this .

Black's does not have any benefit for the ensuing sequence after the used move at A, so it is unlikely that A is the correct choice here.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------+
$$ | . . O X X X X X O X X X . |
$$ | . . O O O O X X O . X X O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O X X B W W X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O O X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . O X X O . X |
$$ +---------------------------+[/go]

Just another matter of shape:

Before the ko starts, White would like to have created another formation at the top ( ), reducing Black's string to the left to only three liberties.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O . X , . . X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O , X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . . X X O . M |
$$ +---------------------------+[/go]

Just another deep "feeling":

I can't really believe that the correct solution sequence should contain so many White passes.
Therefore, I do not "feel" that Black will play at in the lower right corner.

Additionally, I do not "feel" that White would start the ko-fight, as this measure would cost her some Black stones in her prisoners lid.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Click Here To Show Diagram Code

[go]$$Bm21 Komi = 0.5; prisoners:
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O . X , . . X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O , X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . 2 X X O . 1 |
$$ +---------------------------+[/go]

After we saw that this is losing.
What about the move below:

Click Here To Show Diagram Code

[go]$$Bm21 Komi = 0.5; prisoners:
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O . X , . 2 X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O , X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . . X X O . 1 |
$$ +---------------------------+[/go]

and now if

Click Here To Show Diagram Code

[go]$$Bm21 Komi = 0.5; prisoners:
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O . X , 3 2 X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O , X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . 4 X X O . 1 |
$$ +---------------------------+[/go]

and white has gained one point

and if

Click Here To Show Diagram Code

[go]$$Bm21 Komi = 0.5; prisoners:
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O 8 X 5 4 2 X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X , X O 9 X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O 6 X O X O O O X |
$$ | . X O X O O 7 3 X X O . 1 |
$$ +---------------------------+[/go]

black has lost one ko threat

If we want to use the white stone on the right side, how about this?



oops... not quite 100 moves, but pretty close!

In the second diagram, Black could remove the D4 ko threat before starting the ko fight, and also the indirect ko threat on G7 (assuming that W has set 28 to 29, which seems more efficient to me). This 2-point loss should be compensated by connecting G2.

interesting move

Click Here To Show Diagram Code

[go]$$Bm21 Komi = 0.5; prisoners:
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O 8 X 6 4 2 X X X O |
$$ | . . . O O X 7 X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X , . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X 9 X O 5 X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . 3 X X O . 1 |
$$ +---------------------------+[/go]

both black and white lost 4 points and 1 ko threat. so black still win

or

Click Here To Show Diagram Code

[go]$$Bm21 Komi = 0.5; prisoners:
$$ +---------------------------+
$$ | . . O X X X X . O . X X . |
$$ | . . O O O O X . O . X . O |
$$ | . . . . O X X X O O O O O |
$$ | . . . O 6 X . 5 2 X X X O |
$$ | . . . O O X . X X X . X X |
$$ | . O X . O X . . . . . O . |
$$ | O O O O O X 9 . O X X X . |
$$ | X O X X O O X . . X O X X |
$$ | X X X . X O X . . X O O O |
$$ | . . X 7 X O 4 X X X O . X |
$$ | O O O X X O O O X X O X . |
$$ | X X O X O . X O X O O O X |
$$ | . X O X O O . 3 X X O . 1 |
$$ +---------------------------+[/go]

black lost 3 points and white lost 4 points. both lost 1 ko threat. so black still win

Very convincing explanation. Thank you Dany and Jmeinh

White can reach 102 moves but by losing one point => black wins by 1.5 points in this variation: