That certainly looks like the proper shape for a Beechnut. I thought they were slightly fuzzy, but that might be before they fall. The dark freckles could have been were the fuzz stuck out when they grew. I often try to find the tree that they fell from to help identify. A Beech should have smooth gray bark with an oval shaped leaf. I would open the nut up. It should be two sort of triangle shaped nuts if Beech. While you are studying diet of Squirrel you are also doing so for deer. They share many of the same foods, with deer having more variety. I have a Hickory in the back yard and Black Walnut in the front and a healthy squirrel population. If I was not in a subdivision, I would be doing much better in my hunting. 
I can't understand how the chipmunks around here stand them. pignuts do make good reactive targets for .17 mach 2 practice. beech nuts look like tiny chestnuts. and the deer and the squirrels luv 'em. 
lol
