Dear Thomas,
A small (?) modification of the position above leads to a far more interesting position : firstly a cycle is difficult to define clearly and secondly in this position black has advantageaous loop => all white stones are dead.

Click Here To Show Diagram Code

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

There will be neither cycles nor looping any more! It will no longer be necessary to be afraid of large numbers!

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | X X X X X X X X X |
$$ | O O X X O O X O O |
$$ | . O O O X O O O . |
$$ | O O X X X X X O O |
$$ | O Q Q X X X Q Q O |
$$ | O O X X X X X O O |
$$ | O Q T X . X Y T O |
$$ +-------------------+[/go]

After Honte said the safety-first version of his magic DOUBLE-ko spell...

"Dame ari dame nashi" ==> Three liberties vs. two liberties ==> Black wins any semeai for sure.

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

Dear Thomas,

Is it a good understanding that, due to the Honte's magic DOUBLE-ko spell, you now stopped the analysis of loops, cycles and length of cycle?

What you have to clarify is the context for applying Honte's magic DOUBLE-ko spell.
I understand it has to be used in a confirmation phase but which one? I guess it could not be J89 or J2003 because in these rules the loops are already breaked with pass-for-ko or ko-pass.
I assume it is a confirmation phase you have in mind but without knowing it in detail I do not know how building interesting examples for challenging the concept.

In addition a double ko has to be defined without ambiguity:
Are two-stage ko allowed?
Are external liberties allowed?
Are extern ko allowed (as my exemple above with four ko)?
A ko must involve only one black group and one white group or could it involve more than two groups?
...

That the reason I said I have to avoid being impatient:
1) what is the exact defintion of what you call a double ko?
2) what is the confirmation phase used (pass-ko? group of stones status approach? loops wihout double ko ...)

Click Here To Show Diagram Code

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

I saw also that you handled the marked ko above as double ko though white as made the last capture in both ko. Is it really your idea?

YES. This position contains TWO connected double-ko. Thus, even if Black is ataried in one of these, he still has the ("external") liberty in the other double-ko (not to forget the liberty in his eye).
I am very sure that Black would have played a capture of his own, if his group lacked the eye that is has here.

Please stop letting problems with positions resonate implicitly in your questions, which in reality will never reach the status confirmation in their already partially exhaled life. I just don't like it when people play genius for constructing positions and run around a short time later with an IQ of 80 asking stupid questions.

Further reasoning is below...

Click Here To Show Diagram Code

[go]$$B Genuine triple-ko cycles
$$ +-------------------------------+
$$ | ? ? ? . . . . . . . . . ? ? ? |
$$ | ? O ? B . X . X . W . O ? O ? |
$$ | ? O ? O . O . B . X . X ? W ? |
$$ | ? X ? X . W . O . O . B ? X ? |
$$ | ? ? ? . . . . . . . . . ? ? ? |
$$ +-------------------------------+
$$ | ? ? ? . . . . . . . . . ? ? ? |
$$ | ? O ? O . O . B . X . X ? W ? |
$$ | ? O ? B . X . X . W . O ? O ? |
$$ | ? X ? X . W . O . O . B ? X ? |
$$ | ? ? ? . . . . . . . . . ? ? ? |
$$ +-------------------------------+[/go]

All positions in the cycle are of the type "2 : 1".

If Black captured the other White stone in the very beginning (lower cycle), ...

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------------------+
$$ | . . . . . . . . . . . . . . . |
$$ | . O . X . X . X . O . O . O . |
$$ | . O . O . O . X . X . X . O . |
$$ | . X . X . O . O . O . X . X . |
$$ | . . . . . . . . . . . . . . . |
$$ +-------------------------------+
$$ | . . . . . . . . . . . . . . . |
$$ | . O . O . O . X . X . X . O . |
$$ | . O . X . X . X . O . O . O . |
$$ | . X . X . O . O . O . X . X . |
$$ | . . . . . . . . . . . . . . . |
$$ +-------------------------------+
$$ {AR B7 O7}
$$ {AR O5 B5}[/go]

... the cycle would change its direction.

------------------------------------

Click Here To Show Diagram Code

[go]$$B Quadruple-ko positions
$$ +---------------------------+
$$ | . . . . . . . . . . . . . |
$$ | . X . X . X . O . O . O . |
$$ | . X . O . O . X . X . O . |
$$ | . O . X . O . X . O . X . |
$$ | . O . O . X . O . X . X . |
$$ | . . . . . . . . . . . . . |
$$ +---------------------------+
$$ | . . . . . . . . . . . . . |
$$ | . X . X . X . O . . . . . |
$$ | . X . X . O . X . . . . . |
$$ | . X . O . X . X . . . . . |
$$ | . O . X . X . X . . . . . |
$$ | . . . . . . . . . . . . . |
$$ +---------------------------+
$$ | . . . . . . . . . . . . . |
$$ | . O . O . O . X . . . . . |
$$ | . O . O . X . O . . . . . |
$$ | . O . X . O . O . . . . . |
$$ | . X . O . O . O . . . . . |
$$ | . . . . . . . . . . . . . |
$$ +----------------------------+[/go]

There are six positions of the type "2 : 2", and two times four positions of the type "3 : 1" -- with reversed colours.

If the starting position is "2 : 2", either side can start the cycle.
If the starting position is "3 : 1", the player with only one stone must start the cycle.

Click Here To Show Diagram Code

[go]$$B Genuine quadruple-ko cycle
$$ +-------------------------------------------+
$$ | . . ? ? ? . . . . . . . . . . . . . ? ? ? |
$$ | . O ? O ? O . B . X . X . X . X . W ? O ? |
$$ | . X ? X ? W . O . O . B . X . X . X ? X ? |
$$ | . O ? B ? X . X . W . O . O . B . X ? B ? |
$$ | . X ? X ? X . X . X . X . W . O . O ? X ? |
$$ | . . ? ? ? . . . . . . . . . . . . . ? ? ? |
$$ +-------------------------------------------+
$$ {AR U1 Q1}[/go]

You will realise that the cycle will never reach its "2 : 2" starting position.

Click Here To Show Diagram Code

[go]$$B Genuine quadruple-ko cycle
$$ +-------------------+
$$ | . . ? ? ? . . . . |
$$ | . O ? O ? O . B . |
$$ | . X ? X ? X . X . |
$$ | . O ? B ? X . X . |
$$ | . X ? X ? W . O . |
$$ | . . ? ? ? . . . . |
$$ +-------------------+[/go]

If White captured the other Black stone (possible everywhere in the cycle), the cycle would change its direction (see the arrow in the previous diagram).

Click Here To Show Diagram Code

[go]$$B Genuine quadruple-ko cycle
$$ +-------------------------------+
$$ | ? ? ? . . . . . . . . . ? ? ? |
$$ | ? X ? X . W . O . O . B ? X ? |
$$ | ? O ? B . X . X . W . O ? O ? |
$$ | ? O ? O . O . B . X . X ? W ? |
$$ | ? O ? O . O . O . O . O ? O ? |
$$ | ? ? ? . . . . . . . . . ? ? ? |
$$ +-------------------------------+
$$ | . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . O . O . |
$$ | . . . . . . . . . . . O . O . |
$$ | . . . . . . . . . . . X . W . |
$$ | . . . . . . . . . . . B . X . |
$$ | . . . . . . . . . . . . . . . |
$$ +-------------------------------+[/go]

If the cycle is started with a "3 : 1" position, it will be possible to reach its starting point.

If Black captured the other White stone, she would continue the cycle with mirrored positions.

------------------------------------

You will realise that if a "4 : 0" starting position was possible as in your example (let's forget for a moment that this would never be part of the final position of the game), the cycle would be as enforced as with a genuine triple-ko.

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

One posting is still to be done that shows the effect of Honte's magic DOUBLE-ko spell on the ASMYMMETRICAL triple-ko cycles.


As can be seen by my respective posting about the "critical" J89 L&D-examples, there will be no loopings any more after the double-ko shape has been transformed.

"Pass-for-ko" and "ko-pass" are not required for the remaining SIMPLE-ko shapes. It should be evident that these alone cannot create any looping.


It doesn't matter which one. See above.


Sensei's Library's definition seems to be sufficient.
I am sure that you will be able to apply it on your own.
Just forget about "As can be seen for granted...". Will help you a lot.

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

About Honte's magic spells (contd)


##### ASYMMETRICAL triple-ko cycles #1 #####

Click Here To Show Diagram Code

[go]$$B
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? X X X X X X X S ? ?
$$ ? ? X O X O X c X X ? ?
$$ ? ? O a O b O X O ? ? ?
$$ ? ? O O O O O O O ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?[/go]

--------------------------

Click Here To Show Diagram Code

[go]$$B Status assessment for BLACK groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | . . . , . . . ? . . X ? . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . |
$$ | . ? O . . ? . . . . . . . ? . O . ? . |
$$ | . ? . X B ? . M M M M M . ? B . X ? . |
$$ | . ? ? ? ? ? . M . . . M . ? ? ? ? ? . |
$$ | . . . . . . . M X X X M . . . . . . . |
$$ | . . . , . . . M M M M M . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? W . O ? . . . Q . . . ? . O W ? . |
$$ | . ? . X . ? . . . . . . . ? X . . ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . . ? X B . ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR E12 J8}
$$ {AR K5 K7}
$$ {AR P12 L8}
$$ {AR E11 F10}
$$ {AR F12 G11}
$$ {AR J5 J6}
$$ {AR L5 L6}
$$ {AR O12 N11}
$$ {AR P11 O10}
$$ {AR K9 K10}[/go]

Let's apply Honte's magic DOUBLE-ko spell to the outer ko-shapes...

Click Here To Show Diagram Code

[go]$$B Status assessment for BLACK groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q . T ? . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T ? . M M M M M . ? Q . T ? . |
$$ | . ? ? ? ? ? . M T . Y M . ? ? ? ? ? . |
$$ | . . . . . . . M Q X T M . . . . . . . |
$$ | . . . , . . . M M M M M . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T . Y ? . . . Q . . . ? T O Y ? . |
$$ | . ? Q X T ? . . . . . . . ? Q . T ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR E12 J8}
$$ {AR K5 K7}
$$ {AR P12 L8}
$$ {AR E11 F10}
$$ {AR F12 G11}
$$ {AR J5 J6}
$$ {AR L5 L6}
$$ {AR O12 N11}
$$ {AR P11 O10}
$$ {AR K9 K10}[/go]

Nothing happens to the left and right INSIDE the cycle. This means that the cycle will be left there.

Click Here To Show Diagram Code

[go]$$B Status assessment for BLACK groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q . T ? . . . , . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . M M M M S . . . . . . . |
$$ | . . . . . . . M T B Y M . . . Y . . . |
$$ | . . . . . . . M Q X T M . . . . . . . |
$$ | . . . , . . . M M M M M . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Y . . . . . Q . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . Q . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q13}
$$ {AR Q11 Q8}
$$ {AR R8 R11}
$$ {AR Q6 M3}
$$ {AR K5 K7}
$$ {AR J5 J6}
$$ {AR L5 L6}
$$ {AR M16 P13}
$$ {AR M15 P12}
$$ {AR K9 K10}
$$ {AR J8 E8}
$$ {AR C9 H17}
$$ {AR D9 H16}
$$ {AR E9 H15}
$$ {AR E7 J7}[/go]

extis the cycle.
can to nothing more but to also play outside the cycle. Both sides played one move each outside the cycle, what they could have done anyway.

Therafter, Black has to options:
UP:
He plays another move outside the cycle.
Status confirmation will continue elsewhere.
DOWN:
He captures into the double-ko, so re-entering the cycle.
White must exit the cycle again.

Therafter, Black has to options:
++ UP:
He fills the remaining ko-shape.
Status confirmation will continue elsewhere.
++ LEFT:
He plays another move outside the cycle.

Therafter, White has to options:
** UP:
She captures into the remaining ko-shape, so re-entering the cycle. Both side simulated the SIMPLE-ko cycle without breaking the rules.
** RIGHT:
She plays another move outside the cycle.


--------------------------------------------

Click Here To Show Diagram Code

[go]$$B Status assessment for WHITE groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | M M M M . . . ? . . X ? . . . M M M M |
$$ | M ? ? ? ? S M ? ? ? ? ? M ? ? ? ? S M |
$$ | M ? O . . ? M . . . . . M ? . O . ? M |
$$ | M ? . X B ? M . . Y . . M ? B . X ? M |
$$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M |
$$ | M M M . M M . ? ? ? ? S . M M . M M M |
$$ | . . . , . . . ? T O Y ? . . . , . . . |
$$ | . ? ? ? ? S . ? Q . T ? . ? ? ? ? S . |
$$ | . ? W . O ? . ? ? ? ? ? . ? . O W ? . |
$$ | . ? . X . ? . c o n t d . ? X . . ? . |
$$ | . ? ? ? ? ? . M M M M M . ? ? ? ? ? . |
$$ | . . . . . . M ? ? ? ? S M . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . M ? X B . ? M . . . . . . |
$$ | . . . . . . M ? ? ? ? ? M . . . . . . |
$$ | . . . . . . . M M M M M . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR J15 J14}
$$ {AR K15 K14}
$$ {AR L15 L14}
$$ {AR K12 K11}[/go]

Let's apply Honte's magic DOUBLE-ko spell to the outer ko-shapes...

Click Here To Show Diagram Code

[go]$$B Status assessment for WHITE groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | M M M M . . . ? Q . T ? . . . M M M M |
$$ | M ? ? ? ? S M ? ? ? ? ? M ? ? ? ? S M |
$$ | M ? T . Y ? M . . . . . M ? T O Y ? M |
$$ | M ? Q X T ? M . . Y . . M ? Q . T ? M |
$$ | M ? ? ? ? ? M . . . . . M ? ? ? ? ? M |
$$ | M M M . M M . ? ? ? ? S . M M . M M M |
$$ | . . . , . . . ? T O Y ? . . . , . . . |
$$ | . ? ? ? ? S . ? Q . T ? . ? ? ? ? S . |
$$ | . ? T . Y ? . ? ? ? ? ? . ? T O Y ? . |
$$ | . ? Q X T ? . c o n t d . ? Q . T ? . |
$$ | . ? ? ? ? ? . M M M M M . ? ? ? ? ? . |
$$ | . . . . . . M ? ? ? ? S M . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . M ? Q B T ? M . . . . . . |
$$ | . . . . . . M ? ? ? ? ? M . . . . . . |
$$ | . . . . . . . M M M M M . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR Q6 M3}
$$ {AR H3 D6}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR J15 J14}
$$ {AR K15 K14}
$$ {AR L15 L14}
$$ {AR K12 K11}[/go]

Nothing happens to the left and right INSIDE the cycle. This means that the cycle will be left there.

Click Here To Show Diagram Code

[go]$$B Status assessment for WHITE groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q , T ? . . . , . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . Y . . . . . . . . . |
$$ | . . . . . . . . . . . . . . s y m m . |
$$ | . . . . . . . ? ? ? ? S . ? ? ? ? W . |
$$ | . . . , . . . ? . . . ? . ? T , Y ? . |
$$ | . . . . . . . ? . . . ? . ? Q X T ? . |
$$ | . . . . . . . ? ? ? ? ? . ? ? ? ? ? . |
$$ | . . . Q . . . c o n t d . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T ? . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR J15 J14}
$$ {AR K15 K14}
$$ {AR L15 L14}
$$ {AR K12 K11}
$$ {AR H4 E7}
$$ {AR H3 E6}
$$ {AR H2 D6}
$$ {AR M4 P8}
$$ {AR M3 Q8}
$$ {AR M2 R8}
$$ {AR D8 H10}[/go]

Black's exit has already been the exemplary case.

We added White's exit (to the left).
White could also enter the GENUINE double-ko cycle by occupying Black's liberty (to the right).

Click Here To Show Diagram Code

[go]$$B Status assessment for WHITE groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T W Y ? . . . . . . . ? T . Y ? . |
$$ | . ? Q , T ? . . . , . . . ? Q B T ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Y . . . . . . . . . . . Q . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . Q . . . . . . . . . . . Y . . . |
$$ | . . . . . . . M M M M S . . . . . . . |
$$ | . . . , . . . M T B Y M . . . , . . . |
$$ | . . . . . . . M Q X T M . . . . . . . |
$$ | . . . . . . . M M M M M . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR C15 C14}
$$ {AR D15 D14}
$$ {AR E15 E14}
$$ {AR P15 P14}
$$ {AR Q15 Q14}
$$ {AR R15 R14}
$$ {AR D12 D7}
$$ {AR C7 C12}
$$ {AR D7 O18}
$$ {AR E7 O17}
$$ {AR E6 O16}
$$ {AR Q7 F18}
$$ {AR P7 F17}
$$ {AR P6 F16}
$$ {AR R7 R12}
$$ {AR Q12 Q7}
$$ {AR P12 K5}[/go]

BLACK plays outside the cycle (left).
-- White can do nothing else but to also play a move outside the cycle.
Both sides played one move each outside the cycle, what they could have done anyway.

Black has two options thereafter:
++ LEFT:
He continues with another move outside the cycle.
Status confirmation will take place elsewhere.
++ RIGHT:
He captures into the double ko, so re-entering the cycle.
However, this does not make any sense, as the position is seki anyway.


White plays outside the cycle (right).
-- Black has two options thereafter:
LEFT:
He fills the remaining ko-shape, so terminating the cycle.
Status confirmation will continues elsewhere.
RIGHT:
He also plays a move outside the cycle.
Both sides played one move each outside the cycle, what they could have done anyway.

White has two options thereafter:
++ LEFT:
She captures into the double ko, so re-entering the cycle.
However, this does not make any sense, as the position is seki anyway.
++ RIGHT:
He continues with another move outside the cycle.
Status confirmation will continue elsewhere.



+++++++++++++++++++++++++++++++++++++++++++

##### ASYMMETRICAL triple-ko cycles #2 #####

Click Here To Show Diagram Code

[go]$$B
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? X X X X X X X S ? ?
$$ ? ? X O X O X c X X ? ?
$$ ? ? O a O b O X O C ? ?
$$ ? ? O O O O O O O ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?
$$ ? ? ? ? ? ? ? ? ? ? ? ?[/go]

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? O W . ? . . . . . . . |
$$ | . . . , . . . ? . . X C . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . |
$$ | . ? O . . ? . . . . . . . ? . O . ? . |
$$ | . ? . X B C . . . . . . . ? B . X C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . : . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? W . O ? . . . . . . . ? . O W ? . |
$$ | . ? . X . C . . . . . . . ? X . . C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? . . O ? . . . , . . . |
$$ | . . . . . . . ? X B . C . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR Q6 M3}
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}
$$ {AR H3 D6}[/go]

Let's apply Honte's magic DOUBLE-ko spell to the outer ko-shapes...

Click Here To Show Diagram Code

[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . . . . . ? T W Y ? . . . . . . . |
$$ | . . . , . . . ? Q . T C . . . , . . . |
$$ | . ? ? ? ? S . ? ? ? ? ? . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q . T C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . : . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q . T C . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . ? ? ? ? S . . . . . . . |
$$ | . . . , . . . ? T . Y ? . . . , . . . |
$$ | . . . . . . . ? Q B T C . . . . . . . |
$$ | . . . . . . . ? ? ? ? ? . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR M17 Q15}
$$ {AR Q12 Q9}
$$ {AR D9 D12}
$$ {AR D15 H17}
$$ {AR Q6 M3}
$$ {AR J2 J1}
$$ {AR K2 K1}
$$ {AR L2 L1}
$$ {AR J15 J14}
$$ {AR K15 K14}
$$ {AR L15 L14}
$$ {AR H3 D6}[/go]

Nothing happens to the left and right INSIDE the cycle. This means that the cycle will be left there.

--------------------------------------------

Click Here To Show Diagram Code

[go]$$B Status assessment for BLACK groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . Q . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . ? ? ? ? S . |
$$ | . M M M M M . . . . . . . ? T . Y ? . |
$$ | . M e n d M . . . . . . . ? Q X T B . |
$$ | . M M M M M . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . Y . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T B Y ? . . . . . . . ? T . Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q X T ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . a s y m m . |
$$ | . . . , . . . . . , . . . . o n e . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR K16 F8}
$$ {AR D9 D12}
$$ {AR J19 J18}
$$ {AR K19 K18}
$$ {AR P12 P9}
$$ {AR Q12 Q9}
$$ {AR R12 R9}
$$ {AR L19 L18}
$$ {AR K16 O14}
$$ {AR K16 K11}
$$ {AR J11 J17}[/go]

White plays outside the cycle. Black has three options now.

LEFT:
fills the remaining ko-shape.
This end status confirmation. The final position is "me ari me nashi".
This option is the ADVISABLE one.
RIGHT:
occupies the SHARED liberty.
This exits to ASYMMETRICAL triple-ko cycles #1.
MIDDLE:
is also played outside the triple-ko.
White has no other choice but to play another move outside the cycle.
Status confirmation continues elsewhere.

--------------------------------------------

Click Here To Show Diagram Code

[go]$$B Status assessment for WHITE groups
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . b l a c k . . . Y . . . . . . . . . |
$$ | . g r o u p . . . , . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q X T C . . . . . . . ? Q . T B . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . Q . . . . . , . . . |
$$ | . ? ? ? ? S . . . . . . . ? ? ? ? S . |
$$ | . ? T . Y ? . . . . . . . ? T O Y ? . |
$$ | . ? Q B T C . . . . . . . ? Q . T ? . |
$$ | . ? ? ? ? ? . . . . . . . ? ? ? ? ? . |
$$ | . . . . . . . . . . . . . a s y m m . |
$$ | . . . , . . . . . , . . . . o n e . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
$$ {AR K9 F8}
$$ {AR D9 D12}
$$ {AR J19 J18}
$$ {AR K19 K18}
$$ {AR P12 P9}
$$ {AR Q12 Q9}
$$ {AR R12 R9}
$$ {AR L19 L18}
$$ {AR L10 O14}
$$ {AR K16 K11}
$$ {AR J11 J17}
$$ {AR C9 C12}
$$ {AR E9 E12}[/go]

Black plays outside the cycle.
White can do nothing else but to play a move outside the circle, too.
Black has three options thereafter:.

LEFT:
captures into the remaining ko-shape.
This exits to the status assessment for Black groups above.
RIGHT:
occupies the SHARED liberty.
This exits to ASYMMETRICAL triple-ko cycle #1.
MIDDLE:
is played outside the triple-ko for another time.
White has no other choice but to also play another move outside the cycle.
It is likely that status confirmation will take place elsewhere.

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

OK let's try to analyse the following position using two double ko you now perfectly know.

Click Here To Show Diagram Code

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

If I analyse (maybe I am wrong?) the position with J89, J2003 ot GT territory rule then the result is seki (or no territory OC).

If now I try to use magic DOUBLE-ko spell the result is a black territory (for J89 and J2003 all white stones become dead and all black stones alive).
I do not know if DOUBLE-ko spell can be used with a different confirmation phase (to reach the correct result) but with the three rules above I see difficulties.
Surely DOUBLE-ko spell gives in a very simple way a good feelling of the result but a strict application may fail in (rare) situations (here two double ko for assuring black group two liberties). IOW, even in the confirmation phase, a liberty between two groups is not exactly the same if it is a liberty in a double ko or it it is a "simple" shared liberty.

GENUINE double-ko at left???

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O T Y X O . O X |
$$ | O O O X X X O O X |
$$ | . O Q T X . X O . |
$$ +-------------------+[/go]

Safety-first version step #1.

Click Here To Show Diagram Code

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

Safety-first version step #2.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X W W X O O X X |
$$ | W W W X X X O O X |
$$ | W W X X X O 3 O X |
$$ | W W W X X X O O X |
$$ | . W W . X 2 X O 1 |
$$ +-------------------+[/go]

cannot be captured => It IS!

------------------------

Additional GENUINE double-ko at right???

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X X X Y T O X |
$$ | O O O X X X O O X |
$$ | . O O . X T Q O . |
$$ +-------------------+[/go]

Safety-first version step #1.

Click Here To Show Diagram Code

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

Safety-first version step #2.

Click Here To Show Diagram Code

[go]$$B pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X P P X X . |
$$ | X X O O X P P X X |
$$ | O O O X X X P P X |
$$ | O O X X X X X P X |
$$ | O O O X X X P P X |
$$ | . O O . X 3 P P 1 |
$$ +-------------------+[/go]

can be captured => It is NOT!

------------------------

This procedure has ALREADY been explained to you, by the way!!!

As a matter of course, the safety-first version of Honte's magic DOUBLE-ko spell is a ONE-pass issue.
I divided it into TWO passes above to make you understand that your misunderstanding comes from the two-ko-formation at right. Where a DAME is!!!

_________________
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]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X . X . X O X |
$$ | O O O X X X O O X |
$$ | . O . O X O . O a |
$$ +-------------------+[/go]

What is finally your conclusion when you use magic DOUBLE-ko spell to this specific position?
IOW, has black to add a move in normal play at "a" in order to prove all white stones are dead?

Such seemingly different result after the application of Honte's magic DOUBLE-ko spell on two-ko-formations (i.e. being NO GENUINE DOUBLE-ko), as you did it, is a clear sign that Black should have invested another move (or however much) for occupying all DAME before the game stopped, in order to get rid of that FAKE double-ko at the right under J89 etc.

What Black would have done under J89 etc. for sure anyway , even if he has never heard of labradors, as his fencing group would be neighboured to a DAME, destroying all his potential territory beyond.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X . X . X O X |
$$ | O O O X X X O O X |
$$ | . O . O X O . O 1 |
$$ +-------------------+[/go]

Said and done!

Click Here To Show Diagram Code

[go]$$B pass; pass
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X . X . X O X |
$$ | O O O X X X O O X |
$$ | . O . O X O . O X |
$$ +-------------------+[/go]

As you will easily see, all of White's stones are dead after Black's additional move in status confirmation.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X . X 2 X O X |
$$ | O O O X X X O O X |
$$ | . O . O X O 3 O X |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X 4 X O 5 O X |
$$ | O O O X X X O O X |
$$ | . O . O X . X O X |
$$ +-------------------+[/go]

This is also true during "play"!!!

++++++++++++++++++++++++

Sooner or later, you will realise that it is completely nonsensical to turn the analysis of UNFINISHED positions into a hobby.

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

Just returned from walking the labrador...

C O R R E C T I O N


Status analysis for White's groups in the "uncapturable" world.

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X . X 2 X O X |
$$ | O O O X X X O O X |
$$ | . O . O X O 3 O 1 |
$$ +-------------------+[/go]

Click Here To Show Diagram Code

[go]$$B pass-for-ko
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . X X X X . . |
$$ | . X X X O O X X . |
$$ | X X O O X O O X X |
$$ | O O O X X X O O X |
$$ | O O X . X O 5 O X |
$$ | O O O X X X O O X |
$$ | . O . O X . X O X |
$$ +-------------------+[/go]

White's stones are all dead.


++++++++++++++++++++++++

Conclusion:

Teire is needed in the world of "two-eye-formations".
In the "uncapturable" world, the position can remain as it is.

Nothing to worry about, because this is the "usual" difference of one point / one move between both worlds.

++++++++++++++++++++++++

That was the very last time that I painted the diagrams for you!!!
Your claims are without substance and therefore not credible.

In future, please provide evidence that contains sufficiently detailed move sequences.

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

Sorry Thomas I was very sure you were able to give very easily the result either in J89 (=> black should add a move) and OC in your world of "two-eye-formations"(=> black do not need to add a move).

To be forgiven I can propose a still easier (I hope it is!) position:

Click Here To Show Diagram Code

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

Looking at the white group in the corner do you agree it is a double ko according to SL defintion:
Double ko refers to any situation in which a group has two kos, and these determine its status
Here if black takes a ko it is sente and white only defense is to take the other ko.

In J89 do you agree that the game is finished? Do you agree that the result is that all black stones are dead?

In your world of "two-eye-formations" do you agree that white stones In the corner are dead => anti seki?

One detailed sequence in J89:

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . O . X O 3 O . |
$$ | . . O . X X O O O |
$$ | . . O O X 1 X O O |
$$ | . . . O X X O O O |
$$ | . . . O O O X X X |
$$ | . . . . . O O 2 4 |
$$ | . . . . . . O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

Do not hesitate if you need other detailed move sequences.

You learned absolutely nothing!!!

You just don't want to believe what other people have written. Instead, you continue fooling them.

Simply apply the safety-first version of Honte's magic DOUBLE-ko spell before doing anything else, and hopefully it will be revealed to you that the formation you like so much is only a "two-ko-formation".

First, internalize what a GENUINE DOUBLE-ko is and in the meantime, stop annoying other people.
I would have expected someone living in the ruleset world to be able to understand basic CONCEPTS and PRINCIPLES with ease.

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

FWIW I think the above IS a genuine double ko death.

Click Here To Show Diagram Code

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

Really double-ko? Or ONLY two ko-shapes?
Give Black's fencing more liberties, and so you will see...

Click Here To Show Diagram Code

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

Really double-ko? Or ONLY two ko-shapes?
Give Black's fencing less liberties, and so you will see, too...

As I already tried to explain to Gérard, a GENUINE double-ko does NOT change its L&D status with the occupation of DAME. As it does have AT THE VERY MOST ONE.
In the case BOTH groups are connected to the outside, this is true for every single of these groups. You needed at least TWO outside liberties for killing the opponent's group after having filled one of the two ko-shapes.

Click Here To Show Diagram Code

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

Probably this will become more evident with having Black's fencing group's connected. You will also recognise that NONE of the ko-captures is a valid ko-threat.

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

Sure the double ko disappears if you change the position proposed. I agree at 100%.

Click Here To Show Diagram Code

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

If it is black to play this position is obviously a two ko-shapes: black connects one ko and then fight the other ko.

Click Here To Show Diagram Code

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

Please, try to respect without any change the position I proposed.

You seem to not agree that this position is not a double ko but what harms in this position when you take SL definition?
1) the white stones in the corner are alive due to the presence of the double ko
2) if black takes one of the ko it is sente and white must take the other ko to live
3) as a consequence black has locally an unlimited number of ko threats
What do you require in addition?

OC I saw your OWN requirement (it is not in SL definition)
a GENUINE double-ko does NOT change its L&D status with the occupation of DAME. As it does have AT THE VERY MOST ONE.

In J89 finding a dame requires a rather long process in which the status of all groups of stones has to be determined carefully. BTW this process is particularly delicate in double ko situation because the status of the isolated stones that be captured in the ko is of primary importance.
Anyway, according to J89, I do not see any dame adjacent to the black groups in my position above
In this context it appears that in your requirement "a GENUINE double-ko does NOT change its L&D status with the occupation of DAME. As it does have AT THE VERY MOST ONE" both the words "double-ko" and "DAME" have another meaning that the common one.
I think it is the basic reason of the misunderstanding.
If you just define what is a "Honte's double ko" and what is a "Honte's dame" then surely all the misunderstandings will diappear.

Click Here To Show Diagram Code

[go]$$W
$$ +-------------------+
$$ | . . O . X O . O . |
$$ | . . O . X X O O O |
$$ | . . O O X . X O O |
$$ | . . . O X X O O O |
$$ | . . . O O O X X X |
$$ | . . . . . O O 1 . |
$$ | . . . . . . O O O |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ +-------------------+[/go]

The L&D status of White's group in the corner does NOT depend on the two ko-shapes, as can be easily proven.
Please be aware that Sensei's Library's definition refers primarily to "play".

The L&D status of Black's group does NOT depend on the two ko-shapes as well, as White will be able to occupy its outside liberties with ease. Black might prolong his lifetime a bit by capturing into the double-ko, but that's all.

Click Here To Show Diagram Code

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

From White's point of view, it's just a semeai with Black's three stones below. Same as in this diagram.
White has THREE liberties vs. Black's TWO, so she will win, even if Black is allowed to move first.
Count the compound of the two ko-shapes simply as an approach-move liberty.

Click Here To Show Diagram Code

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

The same applies here.

Click Here To Show Diagram Code

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

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

Seeing that the marked black group is dead I agree to say that it is double ko death.

However, I my mind, the status of this black group is irrelevant. I chose this position only to minimise the number of black stones.
I could have as well chosen the following position with the same result:

Click Here To Show Diagram Code

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

but I not very satisfied with such position because it is an unfinished one.

I could even have chosen this other unfinished position with the same result:

Click Here To Show Diagram Code

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

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

No Thomas I cannot agree on this point. In J89, when you look for the status of the white group in the corner it is BLACK to play first.


Agreed. A double ko in the confirmation phase has never been defined. If you use it with a different definition you have to give this defintion and maybe you have to use another wording to avoisd ambiguity : "Honte's double ko for confirmation phase" or whatever you want


Still agreed, contrary to white group, the status of black does not depend on the double ko