I love this thing. My theory is that it is a folk/trench art creation modeled on Dutch and English combination lock dialed snuff boxes of the 18th and 19th century (one photo at the end as example.) Those were more refined and the dialing/locking mechanisms concealed, while here it's all revealed on the interior of the lid. I love it precisely for this homespun-ness, and of course for being shaped like a little book, and for the pleasure of turning those three rotating arrows to just the right spots to have it satisfyingly open.
2 7/8" x 2 13/16" x 1" and in very good condition, I'd guess early 20th c. It takes a little trial and error to get all three arrows lined up just right to unlock it, but that's part of the fun, and the turn them when closed to keep it locked. The seller I purchased from included a diagram of the combination, which I will send along as well.