Ok Here we go. This rule is invariant to rotation and mirroring.
Confirmed Structural Properties (Spoiler)
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There is no red Koan without black stones.
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The rule uses the concepts of chains and liberties.
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The rule could be applied to arbitrary graphs and is independent on the drawing of the graph.
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The rule does not refer to shared liberties.
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The rule cares about the number of stones in some way.
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If a green Koan has at least one black stone, adding or removing a white stone always changes its color to red.
Koans that know Buddha-Nature:
Koans that don’t know Buddha-Nature:
Solution (solved by le_4TC)
Every black chain needs to have the same number of liberties as the total number of white stones.