I just now happened to look out my upstairs window and saw a squirrel, moving at an eye-catchingly-slow pace along the top of our front fence (a bounding squirrel wouldn't have made me think twice). I watched him as he stopped and- these are really the only correct words for it- carefully and precisely placed this walnut on the backside of our fence. He even sat back on his haunches as if to admire the effect. Satisfied, he scampered off to his next errand.
So now I know: we have a squirrel with all the nut-hiding prowess of a three-year-old at Easter.
(at least I don't have to worry about any walnut trees springing up)