Rule guess: When a White chain touches a Black chain, they must have the same number of liberties.
Do you allow positions that have an unequal number of White stones and Black stones? I guess it would be hard to prove that they cannot occur in a go game, since there could have been captures.
Good guess, but here are (additional) counter-examples:
Yes, I just require that all chains have at least one liberty.
With passes allowed, I believe all such positions can be reached in a normal go game, even without captures. With passes not allowed, that could be an interesting question. But a question for another thread 
Symmetry broken?
Differences I can spot:
Black/White reversed
Rotated 90ā
4 stone chain starting on 4,3 vs 5,2
None of which I can tie into the other koans we have seen
Iād try to undo some of those changes to create another red koan, we still havenāt produced one on our own.
Hypothesis: White is always in the minority when touching black chains.
More precisely: if you count the stones in a white chain and the stones in all black chains touching this white chain, then either you have counted more black stones than white stones, or the white chain is not touching any black stones at all.
Sounds like 14 and 25 should be of the same color, but they arenāt?
Not sure if it is the same, but allow me to rephrase it in a simpler manner:
āIf you eliminate all the black and white chains that touch each other, there are more (or equal) white stones left than black stonesā
Alternatively, I think this is what @ArsenLapin1 meant:
āThere are more (or equal) black stones in chains touching white, than white stones in chains touching blackā
Anyway, Iāll submit another guess
Can I ask for a counterexample?
alright, here are counter examples:
I suspect you use Katago to count the liberties, and so the count is wrong when there is a large circular group!
Here are two variations on the koans, just to see how changing a small detail affects the result:
