I’m sorry, I made a mistake!
376 should be green
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I’ll provide a new red koan as a form of repentance
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I don’t know what is going on here. Capturing 2 stones is okay, but 16 is disallowed? Let’s see what happens with moderate amounts of capturing.
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Both are red.
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How about these two?
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I have no idea 
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(a combination of “How sparse can it get while staying red?”
with the idea from earlier that this could be about the 1-1 points)
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Here’s a rule hypothesis:
The empty intersections can be colored so that at least
one pair of opposite corners are in the same chain.
equivalently
There is a path between at least one pair of opposite
corners that goes through at most one stone-color.
Due to 357 and 376, one can’t add “nothing gets captured” to the former phrasing,
although one could potentially add “after captures, the resulting position is legal” ,
which is why I submitted this post’s koan.
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Nice find! I’d like to test this by adding one black stone to a green koan (355)
If your rule hypothesis is correct, this should turn it red 
For comparison:
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How is 362 green then?
in 362, the upper-left can be connected to the lower-right by a path that avoids white.
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Oh yeah, this is very promising.
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Regardless of how the previous two are colored, I’m curious about this (to either further confirm the current theory, or explore other possibilities)
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