Fruit Tree Question

Fruit Tree Question

I just moved last November (I live in Massachusetts). Between settling in to the apartment and the winter season, I never really explored the yard until recently. My boyfriend and I have been raking and we've come across dozens of pits. Most of chewed open by squrriels or have rotted. They seem to be around this one tall tree. Here is one of the pits: pit Anyway, I was just curious to what fruit it may have come from. I don't see any smaller fruit trees, just this one tall tree where most of the pits seem to be. I remember seeing small round greenish fruits when I was a kid back where I grew up (still in MA) but can't remember what they were. Any clue? thank you!
Hello!

Hello!

Farmers Market

Farmers Market

well, not my room…but my apartment.

well, not my room…but my apartment.

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Contorted Filbert

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Butterflies

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The Curse of the Black Thumb