You don’t make a bagel by first baking a bialy and then punching out the center. No—you roll out a snake of dough and join the ends together to form the bagel. If you denied that a bagel has a hole, you’d be laughed out of New York City, Montreal, and any self-respecting deli worldwide. I consider this final.
Not exactly a QED sort of proof, but I’ll take it as an axiom. 🙂