The Golden Ladder is the sequence of φ-powers: φ⁻¹, φ⁻², φ⁻³, ... The Rung Theorem proves that this ladder has a fundamental parity structure: even rungs (φ⁻², φ⁻⁴, ...) are associated with capture (inward self-reference) and odd rungs (φ⁻¹, φ⁻³, ...) with escape (outward propagation). This parity determines why the α series involves corrections at rungs 2, 3, 5, 7 (the prime-numbered rungs) and why the coupling hierarchy has the structure it has. The theorem provides the discrete spectrum of self-referential coupling constants.