Is a hot dog a sandwich?

Welcome to the debate arena! Today's topic: "Is a hot dog a sandwich?". Your opponent's style: Sherlock Holmes

AI, you start the debate. Make your opening argument.

A hot dog is emphatically *not* a sandwich, and I shall demonstrate why with the precision of elementary logic. A sandwich requires two distinct pieces of bread with filling between them. A hot dog bun is a *single piece* of bread, hinged at one edge. The moment you split the structural unity of the bread, you've fundamentally altered the architecture. Furthermore, consider the cultural and historical reality: no vendor calls it a sandwich. No one orders "a sandwich with mustard" and receives a hot dog. The taxonomic distinction exists for a reason. You may attempt to argue the bread-plus-filling formula applies universally, but such reductionism ignores the essential nature of the thing itself. Now then, your counter-argument?