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I don't know anything about identifying trees, really. And though I do know how to use Google and Wikipedia, I'm finding a hard time IDing this thing!
I live in northeast Massachusetts, about 40min outside of Boston and an hour from the ocean, and this tree grew up in my back yard without my noticing.. and suddenly, it's bearing fruit! I picked one of the fruit and it smells bittersweet, and not very pleasant. I doubt the fruit are ripe yet, but I don't know. They're hard and lime-like on the outside, and on the inside they have these little white lung-like sacs of juice which I imagine with time might turn into harder seeds of some sort. After cutting it open the color rapidly turned an orangey brown. Here's a picture of that:
I think you're right, those little sacs in the cut-open shell are shaped like walnuts even if they have nothing in them. I guess I just have to wait until fall and see if I can crack one open!