Λ: Ground Mode of the Cosmic Boundary

The cosmological constant Λ is the largest unexplained hierarchy in physics: Λ·ℓ²_P ≈ 10⁻¹²². We derive the coefficient that determines this value from a single topological postulate. A Möbius surface embedded in S³ (∂S³ = ∅) selects anti-periodic boundary conditions; the ground-mode eigenvalue on this surface, sampled at the antinode, yields Λ_top·ℓ²_P = 2 Ω⁻¹_Λ, where Ω_Λ = (R_Λ/ℓ_P)² ≈ 10¹²² is the de Sitter–to–Planck hierarchy. The Gauss–Codazzi equations convert intrinsic 2D curvature to observed 3D spatial curvature under minimal embedding and isotropy, producing a factor of 3/2. The topology locks the coefficient: Λ_obs = 3/R², where the 3 is antinode intensity (2) times the Gauss–Codazzi interface (3/2). Λ is the ground mode of a bounded geometry. Latest derivation of this paper can be found at github.com/cosmological-constant