(quotes from that text will be in blue, formatting is done by me)

In a position, a string of a player is two-eye-alive if the opponent cannot force no intersection of the string with a two-eye-formation on.

This is the reason for your "independently alive" of Black's 4-stone chain in example #1.
"for all" would result in "can force at least one intersection of the string with no two-eye-formation on."

J2003-alive is defined like in J2003 as either uncapturable, capturable-1, or capturable-2.

This is the reason for your "independently alive" of White's single stone in example #1.

In a position, a string is WAGC-alive-in-seki if it is J2003-alive and not two-eye-alive.
In a position, a string is WAGC-alive if it is either two-eye-alive or WAGC-alive-in-seki.
In a position, a string is WAGC-dead unless it is WAGC-alive.
...
Chris Dams has proven:
WAGC-alive equals J2003-alive.

Sorry, Robert, but that's trivial, isn't it ?

J2003-alive = uncapturable OR capturable-1 OR capturable-2
uncapturable = uncapturable-two-eyed OR uncapturable-Seki
capturable-1 = capturable-1-two-eyed OR capturable-1-Seki
capturable-2 = capturable-2-two-eyed OR capturable-2-Seki
two-eye-alive = uncapturable-two-eyed OR capturable-1-two-eyed OR capturable-2-two-eyed
WAGC-alive-in-Seki = J2003-alive AND NOT two-eye-alive
WAGC-alive-in-Seki = uncapturable-Seki OR capturable-1-Seki OR capturable-2-Seki

WAGC-alive = two-eye-alive OR WAGC-alive-in-Seki
WAGC-alive = (uncapturable-two-eyed OR capturable-1-two-eyed OR capturable-2-two-eyed) OR (uncapturable-Seki OR capturable-1-Seki OR capturable-2-Seki)
WAGC-alive = (uncapturable-two-eyed OR uncapturable-Seki) OR (capturable-1-two-eyed OR capturable-1-Seki) OR (capturable-2-two-eyed OR capturable-2-Seki)
WAGC-alive = uncapturable OR capturable-1 OR capturable-2
WAGC-alive = J2003-alive

Excel would complain about a circular reference.



Perhaps you should care about "marketing", too ?


I suppose the approach we prefer is very different.
There is no problem with "state-of-the-art has changed over time" or "a non-Japanese had found inconsistencies within the rules text or its application".
When I read your sentences then arises an implicit feeling like "There is someone (may be non-Japanese) who decides what to include and what not to include to get the final result he wants." If this is not your intention, you should think about better "marketing", as written above.

My "marketing-friendly" suggestion would be the other way round.

1) Develop a rule set that is well-defined and consistent. (You have done already.)

2) Apply this rule set on the "known" examples (e.g. your #0000, Nihon Kiin Life & Death (You have done already.)). The results will be well-defined and consistent, because the rule set is. As a matter of course some of the results may not be identical to those provided with another rule set (e.g. Nihon Kiin) that has been identified as not well-defined or inconsistent or even both.

3) Develop an idea where the different results come from (we can exclude inconsistent application of the rules themselves here) and try to shape your ideas into a kind of "classes" (some elements of what I mean can be found in the "motivation" parts of your texts). This will make discussion easier, because you can discuss about principles to apply (or may be not) and have no need to worry about single "mysterious" board positions. And what is important also: Discussion about "principles" will not be mixed up with discussion about inconsistent rules' application.

The result of 3) could be something like the following:


The answers can be only "Yes" / "No", never "Right" / "Wrong".

Questions like "What kind of principle do you like more ?" should be absolutely preferred, questions like "What result in this special position do you like more ?" should be avoided in this context.

When these "principles" are identified, it will be possible to "transform" one rule set into the other. You will know which rules how to change or which precedence to include.

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

Cassandra, your discussion on #1:

As far as my personal opinion is concernced, I do not care for #1. I would happily accept one of the following: 1) both alive, 2) both dead, 3) Black alive, White dead, 4) White alive, Black dead. The #1 shape is locally non-terminal anyway.

Since the Japanese professionals chose (1) as their latest judgement, that is what I realize in J2003.

If one does not care for the judgement of Japanese professionals, then one is pretty free to choose (1), (2), (3) or (4). In that case, one might try to go for some sort of relative simplicity. (I do not think though that your general approach is simple.)

Can you please explain how general your statement "chose 'not alive', because this is the choice that has NO side effect on neighbouring chains, never" is? Is it meant to hold for ALL examples in ALL positions? If so, prove your statement!

Your attempt to repeat Chris Dams's proof: You make a mistake already in the first line. It must be:

J2003-alive = uncapturable XOR capturable-1 XOR capturable-2

I have not read the rest of your proof yet. Please check first whether your mistake has impacts on the rest.

I do not consider Chris proof trivial. (That you start with a mistake shows that it is not indeed ;) )

Marketing? Nah, I have done enough of that for my rulesets:)

"There is someone [...] who decides what to include and what not to include to get the final result he wants.": The initial intention had been to include also #16-#18 exactly as the official commentary suggested. But when I realized that that did not make sense, then 1) somebody - and the somebody had to be me since I was doing the study - had to make a related decision and 2) I modified the intention as slightly as apparently possible and necessary to create J2003 as an otherwise general model. It is not like "I chose what I wanted" but rather like "I chose what makes the greatest sense within the given context".

More or less I used your step 1-3 approach for creating J2003, except that I had to iterate about 35 - 50 versions as likely candidates for a step 1 ruleset.

You are right to ask for the step 3 principles. I cannot provide them fully so far because they are too deeply hidden in my research files. So at the moment, for #16-18, I can tell you only from my memory part of those principles:

- "collapse of the seki" in the official commentary has to be criticised as not providing explanation because that concept is not a concept of J1989.
- A pure text interpretation of J1989 should be tried if anyhow possible while consistent with also all other examples. [I found out though that such a pure text interpretation is inconsistent over the set of all known (relevant) examples.]
- As far as possible, the officially stated statuses should be recreated with a consistent method that works also for all other known (relevant) examples and that approaches a pure text interpretation of J1989 as closely as otherwise reasonably possible. [I would have to look up my files to check what is recreated. No time for that now.]

Your sample set of principles is insufficient because it ignores professional judgement entirely.

There is no mistake, Robert.

XOR is unnecessary, OR is fully enough, because the "variables" have nothing in common. They are "exclusive" in themselves.

XOR would be necessary if a chain would be possible, which is uncapturable AND capturable-1, for example, and in this case would NOT be J2003-alive. I think you know that this will not happen.

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

Robert, I will answer to your previous 2 postings tomorrow in the evening.

I just had an extensive posting ready, clicked on "Submit" and was taken by surprise by "You have to login to ...".

As a matter of course the written text had disappeared.

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

Just a short reply for now.

I think, our approaches do not differ that much, as far as the concluding results are concerned. The resulting "gap" can be "transformed", because it seems to be clear where it comes from.

I'm with you that a pure interpretation of the texts available will not end in a consistent view over all.

"Collapse of the Seki" indeed seems to be the biggest obstacle to reach consistency.

I'm afraid that there will remain the need for some precendences to simulate 1989 Nihon Kiin rules examples inconsistent concluding results with a consistent rule set.

I suppose that these inconsistent concluding results have grown over time (i.e. one result after another, each driven by a very special occasion), what is an understandable consequence of Japanese culture. Finding a satisfying conclusion of an occasion-driven discussion (not to say dispute) is more important than securing the consistency with previous ones.

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

Since this forum lack the most essential Save feature, you should a) write in a text editor, then copy and paste, then Submit, b) write here, then copy, paste, save in a text editor, then Submit or c) pray that browser does not crash and use its Go Back command the see your painfully typed text again BEFORE you kill your browser's window / process.

***

So you wanted to write:

J2003-alive = uncapturable XOR capturable-1 XOR capturable-2
<==> [by definitions]
J2003-alive = uncapturable OR capturable-1 OR capturable-2

and then proceed. I see. Don't know though when I will have time to read your second proof (attempt).

I do not like your 3) and 4). But OK, a score of 3 points for Black or 7 points for White would be an even stronger motivation than "Seki" to play out the position.


I assess the concluding result "Seki" to be far more important.

May be at least as simple as J2003


I have written "never" and I mean "never".

To explain:

I suppose you will agree to the precondition that "not alive" chains inside opposing "alive" ones will become prisoners.

"Not alive" is a passive characteristic of a chain. It has an effect on the chain under evaluation only. None of the opposing chains in its neighbourhood will be affected. Remember that "will be taken off the board" is something that is done to the chain, the chain itself remains passive.

"Not alive" does not preemt any evaluation of neighbouring opposing chains (to achieve an intended concluding result). If at least one of these opposing chains ends as "not alive", too, our chain will remain on the board. If all of these opposing chains end as "alive", our chain will be taken off the board. What is done to our chain depends on the evaluation results of the neighbouring opposing chains only.

"Alive" is an active characteristic of a chain. It potentially affects all neighbouring opposing chains, because it says: "Be aware to become 'alive', else I might take you off the board." "To take something off the board" is actively done to others.

I do not worry about the "alive"-"alive" coexistence of uncapturable chains that are situated in a concluding Seki. Nor about really capturable "dead" stones, which are Nakade inside opposing chains.

The problem arises with opposing capturable chains that are positioned to become a concluding Seki, as in example #1.

If Black's 4-stone chain is evaluated as "alive", it will be become mandatory to have "alive" for White's single stone, too. Else there will be no Seki. The result of the evaluation of one chain determines the (so far unknown) result of the evaluation of another one.

So first there is the (desired) status of White's single stone. Second comes the desperate search for a procedure to achive this (desired) result. There is no independence between procedure and result any more.

And what is even more dangerous: Once you have decided on this very special procedure, it might have side-effects on positions you probably do not want it to have. Had we (uncertain as we were) chosen "not alive", the concluding result would have been the same, and nothing else on the board would be pre-empted.






May be the attached diagram will help you with the topic.

Or in short:
Let C = A - B
Let D = C + B
It follows D = (A - B) + B = A
I wouldn't call this "proof", but "circular reference".


"I modified the intention" is the kind of "marketing" I would suggest you to avoid

Taking your last sentence, try to start from the end for what I meant with "better marketing".

1) There is the given context.
2) This is the developed rule set.
3) Here are the results of the "new" rule set.
4) Here is which results differ from the "old" one (respectively which are better defined).
5) This is why they differ (respectively ...).
6) Suggested principles to heal (most of) the differences.
7) This is why these principles make sense.

Did you read any "I chose" within 1) to 7) ?



Yes, this "concept" makes it difficult to find consistency within the rules.

I thought a lot about the corresponding examples yesterday.

Your "Hypothetical Ko-Pass" is a brilliant idea to simulate "collapse of a Seki" during evaluation. How long had you thought about it ? Despite the 1989 Nihon Kiin results are achieved with its help, be aware that your procedure provides a very one-sided discrimination of the defender.

All of the corresponding examples contain a chain with a Double-Ko (-Seki temporarily) on one side and capturable opponent's stones on the other. Due to the necessary Ko-Passes of the defender (the attacker does not need to make any, I suppose), the Double-Ko remains open until the attacker had been able to capture everyting what he could capture on the other side. This indeed "resolves" the Seki and the Double-Ko as well. (Might be a more "marketing-oriented" description than many more or less crypical coded move sequences. )

The resulting effect is the same as with a model, I visualised for me, which does not have a special Ko rule for evaluation. And which by far is not as elegant as your solution.

"If the status of a chain cannot be decided, because the evaluation sequence runs into a cycle, try a second time after taking all dead stones (as found within all the non-cycle evaluations) of the board."



I agree. With the text alone, there is not consistent application on the examples possible that matches the "official" results.


You are true, if the aim is the replacement of the Nihon Kiin rules set (as of 1989, taken together with the 1989's intention) with a consistent one, mirroring the 1989's intention.


These principles enlighten the scene from a different point of view. This could open the chance to discuss "Does the 2010's intention match the 1989's intention ?" based on a broader foundation of arguments.

Think about "collapse of the Seki", for example.

"Method A within model a (may be the "old" one) gives the same (may be desired) result(s) as
Method B within model b (may be the best consistent one, based on solid research) as
Method C within model c (may be another consistent one, just another point of view) as
Method D within model d (may be another consistent one, not found yet).

Does whatever happens within methods A to D to get the result match the 2010's intention ?"

If the answer is "Yes", we will choose Model b.

It goes without saying that the models' "principles" must be acceptable. Something like "The result could be achieved within my model, if one side plays two moves in a row during evaluation." will be a show-stopper.

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

Your long discussion of "not alive" versus "alive": Letting there be "not alive" in #1 together with some careless definition of it can also have undesired side effects on other examples. I guess one could also define "not alive" so that it becomes more active although so far, AFA I recall, "alive" has indeed been the (more) active of the two types.

Thx for your attempts to teach marketing;) The best marketing does not alter the contents of the context of professional games and examples though. J2003 must fit that context, whatever the marketing. And J2003 does.

Later research (like Dams's proof) revealed further reasons why J2003 has a very good life model. Had I anticipated that, I might have set another initial principle: to unify the life concepts of J1949/WAGC and J1989.

How long I had thought to find the J2003-ko-pass rule? It is hard to say. Something like having worked on J2003 for ca. 5 +- 3 months already, then looking for the right hypothetical ko ruleset for 2 +- 3 months. Bill's unrelated suggestion then suddenly gave me the idea "in a flash" (I think I had it when awaking the next day); so I needed to test it against my ca. 100 J1989/J2003 ko examples, which may have taken a day or several days. This is like research goes: For months little progress, then sudden insight when having a hint about the "missing link".

Discrimination of the defender? Yes, J2003 assumes the worst case for him: that the attacker moves first. Whether the ko-pass rule favours the attacker or the defender, I am not sure; move-sequences are not always straightforward!

"You are true": Is it correct that I exist?:)

The 1989 intention? "Struggling to get a ruleset that we can sell for some years as explaining Japanese rules while pretending not to use precedents.":)

I am not worried about 2010 intentions.

Your diagram picture is not a mathematical proof. For the proof, see the other thread.

Robert, I suppose you didn't realize that there is nothing to prove.

Let me quote again

In a position, a string is WAGC-alive-in-seki if it is J2003-alive and not two-eye-alive.
In a position, a string is WAGC-alive if it is either two-eye-alive or WAGC-alive-in-seki.

The circular reference can be found in clause 1.

It says:

Property C (WAGC-alive-in-seki) equals a subset of property A (J2003-alive).
Property B (two-eye-alive) is that what is excluded.

Clause 2 then defines:

Property D (WAGC-alive) is the aggregation of property B and property C.

Herewith property B, which has been excluded from property A in clause 1, is included again. As a result, nothing is excluded any more.

The two rule sets use different groupings of one and only one basic set only. One rule set groups "horizontally", the other one "vertically". Thats what my diagram should make evident. What you call a "proof" can be done with any two rule sets using the quoted clauses.

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

Never is there nothing to prove. Even if proving is trivial, that trivial proof has to be done.

The proof is trivial for WAGC-alive-in-seki. The proof is not trivial when WAGC-alive is not WAGC-alive-in-seki.

Concerning your funny diagram, after you have found for 3 of 6 intersections of digram rectangles that the proof is trivial, you still need to prove it for the other 3 cases. Either on a case-by-case basis or for all cases together.

Now, let me say it for the third time, READ CHRIS DAMS'S PROOF!

viewtopic.php?p=12388#p12388

You wrote:
"two-eye-alive = uncapturable-two-eyed OR capturable-1-two-eyed OR capturable-2-two-eyed"

Let me write down it more correctly; 1) equivalence, not an equation(!), 2) XOR, 3) no "2-eyed" in the terms:

two-eye-alive <==> uncapturable XOR capturable-1 XOR capturable-2

This is what had to be proven!!! Just writing down the equivalence does not self-fulfil the necessity to actually do the proof. Chris Dams has proven it though.

Robert, for the third time, it makes no sense to "prove" that your construction uses a circular reference. May be that using dozens of lines in Chris' "proof" makes it very difficult to realise this fact by laying a smoke screen.

Within your WAGCmod there are no further clauses available than those, which I quoted.

Topic is "life" and "life" only.

Fully independent of the definition of "uncapturable", "capturable-1", and "capturable-2" there are only two distinct "classes" chains of these statuses can be devided into, following your text.

• The chain has two eyes.
• The chain is part of a Seki.

Generally speaking, these classes are independent from there definition, too. Important is only that the two classes are distinct and exaustive. What they are indeed in your text.

As you can see in my diagram, there are 6 resulting classes.

J2003 and WAGC use mere different clustering of them, that's all.

As I wrote above, the reason for this result is that your construction is grounded on a circular reference, so it is grounded on sand.

Perhaps you understand the nature of your construction better with an example, which is non Go related:

• A cat without a tail is a rabbit.
• A rabbit with a tail is a dog.
• So a cat is a dog.

Take something away. Add this something again. Name the result new.

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

Your foggy meta-discussion prevents you from seeing the problem. The problem stated in details is:


Proposition:

In a position, let X be an arbitrary, fixed string.

X is WAGC-alive <==> X is J2003-alive.


Start of a Proof:

"X is WAGC-alive <==> X is J2003-alive"
<==>
"X is two-eye-alive XOR X is WAGC-alive-in-seki <==> X is J2003-alive"
<==>
"X is two-eye-alive XOR (X is J2003-alive AND NOT (X is two-eye-alive) <==> X is J2003-alive"
<==>
"
Case 1: X is two-eye-alive:
X is two-eye-alive <==> X is J2003-alive
Case 2: NOT (X is two-eye-alive):
X is J2003-alive <==> X is J2003-alive
"

Up to here, Case 2 is proven. To prove all, what remains to be proven is is Case 1. This is to be done below.

"X is two-eye-alive <==> X is J2003-alive"
<==>
"X is two-eye-alive <==> X is uncapturable XOR X is capturable-1 XOR X is capturable-2"

This is still to be proven in this proof scheme. See Chris Dams's proof for that.

***

Now back to your fog:

"The chain has two eyes.": Nonsense. Being two-eye-alive does not equal "The chain has two eyes." (In the given context, "eye" is undefined anyway! And we call the thing "string" and not "chain".) but it equals "the opponent cannot force no intersection of the string with a two-eye-formation on.".

"The chain is part of a Seki.": Nonsense. In the given context, "seki" is undefined and "being part of" is undefined. We may use: "NOT (X is two-eye-alive)".

I do not study the rest of your fog.

Learn to transform correctly! Do not introduce terms or expressions out of the void but respect what is given in the context!

In WAGCmod there first you define a property "2-eye-alive" that neither equals J2003-alive nor any of its subsets uncapturable, capturable-1, capturable-2.

It follows

J2003-alive = 2-eye-alive OR (NOT 2-eye-alive)

In a position, a string is WAGC-alive-in-seki if it is J2003-alive and not two-eye-alive.

gives

WAGC-alive-in-seki = J2003-alive AND (NOT 2-eye-alive)
WAGC-alive-in-seki = (2-eye-alive OR (NOT 2-eye-alive)) AND (NOT 2-eye-alive)
WAGC-alive-in-seki = (2-eye-alive AND (NOT 2-eye-alive) OR ((NOT 2-eye-alive) AND (NOT 2-eye-alive)
WAGC-alive-in-seki = FALSE OR (NOT 2-eye-alive)
WAGC-alive-in-seki = NOT 2-eye-alive

But be aware that
WAGC-alive-in-seki is (unnecessarily, see below) introduced as a function of J2003-alive
WAGC-alive-in-seki = f(J2003-alive)
and that you have done nothing more than giving a name to what is the complement of what you defined before
and (see the last line) that WAGC-alive-in-seki is not affected by whatever J2003 may be, despite what you proposed in the first line.

In a position, a string is WAGC-alive if it is either two-eye-alive or WAGC-alive-in-seki.

is

WAGC-alive = 2-eye-alive OR WAGC-alive-in-seki
WAGC-alive = 2-eye-alive OR (NOT 2-eye-alive)

That indeed gives the same as above with J2003, but that's trivial anyway.

The application of any property to any basic set results in two subsets. subset 1 fulfils the property, its complement, subset 2, does not. May be that one of these two subsets is empty.

If we follow further what you think a "proof" is, we will probably get

J2003 = WAGC-alive

as a result. But WAGC-alive = 2-eye-alive OR WAGC-alive-in-seki, so

J2003 = 2-eye-alive OR WAGC-alive-in-Seki
J2003 = 2-eye-alive OR f(J2003)

J2003 now is defined as function of itself. What has proven the circular reference I mentioned earlier.


By the way:
Just replace "J2003" with "J1989" in your WAGCmod construction's text. The result will be equivalent, trivial as it is:
WAGC-life = J1989-life

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

Yes, except that I use a different spelling.



Immaterial, or why do you state this?



No. This does not follow. Writing it as an equation does not make any sense. Maybe you mean this?

X is J2003-alive <==> X is 2-eye-alive OR (NOT (X is 2-eye-alive))

The right side is a truth. The left side is either a truth or a falsehood, of which either is possible. Therefore your "implied" stated equivalence is a falsehood.

I do not know why you state it nor how you would want to imply it.

Since you begin with making mistakes, I do not read the rest of your statements, except that you abuse "=" frequently there. Use "<==>" (or, if you prefer a different spelling, "<=>" or "==" or "iff"). But "=" is for algebra.

Robert, it seems that you like the text a bit longer, here it is:


In WAGCmod there first you define a property "2-eye-alive" that neither equals J2003-alive nor any of its subsets uncapturable, capturable-1, capturable-2.

It follows

c is J2003-alive == c is 2-eye-alive XOR (NOT 2-eye-alive)

In a position, a string is WAGC-alive-in-seki if it is J2003-alive and not two-eye-alive.

gives

c is WAGC-alive-in-seki == c is J2003-alive AND (NOT 2-eye-alive)
c is WAGC-alive-in-seki == c is (2-eye-alive XOR (NOT 2-eye-alive)) AND (NOT 2-eye-alive)
c is WAGC-alive-in-seki == c is (2-eye-alive AND (NOT 2-eye-alive) XOR ((NOT 2-eye-alive) AND (NOT 2-eye-alive)
c is WAGC-alive-in-seki == c is FALSE XOR (NOT 2-eye-alive)
c is WAGC-alive-in-seki == c is NOT 2-eye-alive

But be aware that
WAGC-alive-in-seki is (unnecessarily, see below) introduced as a function of J2003-alive
WAGC-alive-in-seki = f(J2003-alive)
and that you have done nothing more than giving a name to what is the complement of what you defined before
and (see the last line) that WAGC-alive-in-seki is not affected by whatever J2003 may be, despite what you proposed in the first line.

In a position, a string is WAGC-alive if it is either two-eye-alive or WAGC-alive-in-seki.

is

c is WAGC-alive == c is 2-eye-alive XOR WAGC-alive-in-seki
c is WAGC-alive == c is 2-eye-alive XOR (NOT 2-eye-alive)

That indeed gives the same as above with J2003, but that's trivial anyway.

The application of any property to any basic set results in two subsets. subset 1 fulfils the property, its complement, subset 2, does not. May be that one of these two subsets is empty.

If we follow further what you think a "proof" is, we will probably get

c is J2003-alive == c is WAGC-alive

as a result. But c is WAGC-alive == c is 2-eye-alive XOR WAGC-alive-in-seki, so

c is J2003-alive == c is 2-eye-alive XOR WAGC-alive-in-Seki
c is J2003-alive == c is 2-eye-alive XOR f(J2003-alive)

J2003-alive now is defined as function of itself. What has proven the circular reference I mentioned earlier.


By the way:
Just replace "J2003" with "J1989" in your WAGCmod construction's text. The result will be equivalent, trivial as it is:
c is WAGC-alive == c is J1989-alive

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

"It follows
J2003-alive == 2-eye-alive XOR (NOT 2-eye-alive)"

Your claimed implication is wrong. Counter-example:

Click Here To Show Diagram Code

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

The white string is not two-eye-alive. By your claimed equivalence above,

2-eye-alive XOR (NOT 2-eye-alive) ==> J2003-alive,

so by your claimed equivalence, the white string must be J2003-alive.

However, the white string is neither uncapturable, capturable-1, nor capturable-2; it is not J2003-alive. Contradiction to the assumption that your claimed equivalence would hold! Thereby your claimed equivalence is a falsehood.

Since the start of your text begins with a mistake, I do not read the rest of your text.

Please refer to


Neither J2003-alive's basic set nor WAGC-alive's basic set consists of any "dead" chains.

It's like "OR" vs. "XOR" with you. Apparently you are neglegting the environment's preconditions.

As I wrote before, "XOR" is not needed, because this means to apply an exclusive function to something that is exclusive by itself. If ever applying "XOR" would give a result that differs from the result when using "OR", then there is something wrong with the overall structure.

Something that is "NOT 2-eye-alive" as a member of a subset of "J2003-alive" cannot be "dead", because these chains are not within "J2003-alive" and therewith are not in scope.

I'd like to recommend you to have a look at my diagram.

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

If you did not split your proof attempt over several messages, I would have less difficulties to understand your intention. Below I state what currently I think YOU want to write for your proof attempt.