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Probably the most fundamental question, however i still don't understand how the GI resolution "Auto" mode relates to the size of the scene.

How can we know what is the GI res assigned when "Auto" is on?

Does the "Auto" mode sets the Gi resolution adaptively or does it just select the best fit GI res value for the entire scene?

Good question but not so basic I guess:)

AFAIK Kray chooses GI res size based on the scene. So it evaluates the photons in the scene and based on the density of photons it chooses appropriate GI size.

You can see what GI size it chose in kray log where it precomputes irradiances. For example:
precomputing irradiances (S=1 r=0.17) > r=0.17 is GI resolution (0.17m)