The golden ratio φ is not just a beautiful number that appears in nature and art. It is the unique stable eigenvalue of self-reference — the only number that is its own self-referential fixed point under the operation x → 1 + 1/x. Any initial condition converges to φ under repeated application of this map. φ is stable, unique, and unavoidable for any self-referential system. This paper proves the uniqueness: among all positive reals, only φ satisfies φ = 1 + 1/φ with no external parameter. It is the attractor of all self-referential dynamics.