Very interesting observations! How did you stumble on this? :-)
IIUC (based on one of your blog comments), you typically need one “immediate” neighborhood and one “ring-like” neighborhood further away. The latter seems like it might likely require non-locality in a fundamental sense (which typically leads to both philosophical and practical problems, like how do you keep the non-locality in check to maintain approximate locality). Any thoughts on that?
IIUC (based on one of your blog comments), you typically need one “immediate” neighborhood and one “ring-like” neighborhood further away. The latter seems like it might likely require non-locality in a fundamental sense (which typically leads to both philosophical and practical problems, like how do you keep the non-locality in check to maintain approximate locality). Any thoughts on that?