Thanks guys!
When I had googed them that is what I thought but my neighbor said he thought it looked similar to the Kaki (

) one BUT these ones have a "double butt" lol, on the bottom.
I hate to cut it open and waste if it's not ripe enough.
I guess I just need to knock on the door of that house to say "Hi, I'm vabeachgirlNYC and I was wondering what those fruit trees were because I stole one and don't know what to do with it" Haha!
Here's a pic of the bottom.