"Does anyone know what this might be for? This is mounted on the stairwell side of our basement door frame. The arms can be pushed up to expand the gap at the bottom and pushed down to close it. 1920s Midwest bungalow."
It's obviously a gravity-based implement holder, but the question is, what's the implement? One reader theorized it's to hold a wet mop, allowing it to dry; but the OP responds that there isn't much room there for a mop, not to mention the object is mounted directly on the other side of this door:
So I'd say mop is out. Any ideas? World's most elaborate scarf holder for, er, people who put on scarves to enter their basement?