Sometimes, in a game of Go, we get a life where there is a false eye involved: There are two groups with a single real eye, each, but they are connected to one another via a false eye, allowing their individual eyes to join forces to ensure life. Something like this:
$$Bcm0 $$ ......... $$ .OOOOO... $$ .OXXXO... $$ .OX.XOOO. $$ .OXXaXXO. $$ .OOOX.XO. $$ ...OXXXO. $$ ...OOOOO. $$ .........
While the false eye at
a is not necessary (black could fill it and still live), it does not need to be filled either, directly providing a liberty to each of the two black chains. I wonder whether it's possible to construct a live that entirely relies on such false eyes?
In this question, I use a purely local definition of a false eye: A false eye is a free spot that is a freedom of two distinct chains. I am aware that there are other definitions of false eyes that would call the example above a living group with three eyes.