If I'm not mistaken, if your neighbor has a tree that has limbs growing over the fence into your yard, you are allowed to trim them back to the fence line. So I would think the same would be true being that he doesn't own the sidewalk so technically it's not his property that the tree is hanging over. I say go for it and have a few pears as a reward.
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IDK, my dad told me that people can sue if you cut their tree that is growing over into your yard. I need to do more research