Solving the Wheel Problem: A Conservative Extension of ℝ with Invertible Division by Zero

We construct a layered algebra extending the real numbers in which division by zero becomes invertible while preserving commutativity, associativity, and distributivity. Distinct quantities divided by zero remain distinguishable, avoiding the collapse present in classical wheel structures. The construction is based on finitely supported convolution algebras and admits a natural projection homomorphism onto an extended real structure.