This paper demonstrates that the fine structure constant α and the cosmological constant Λ are not independent — they are two aspects of the same algebraic structure in ℚ(√5). The bridge between them runs through the class number of ℚ(√5) (which equals 1, giving unique factorisation) and the discriminant. The formula log₁₀(ρ_Λ) = −(α⁻¹ × 2/√5 + φ⁻²) = −122.951 connects the 10¹²³ hierarchy of Λ to the fine structure constant through the factor 2/√5, which is the height-to-diagonal ratio of a regular pentagon. The cosmological constant hierarchy is not a problem. It is a theorem.