Dark Energy as Vacuum Mode Saturation: The Zero-Parameter Derivation Ω_Λ = 11/16 − α/π

We derive the dark energy fraction Ω_Λ from the Recognition Composition Law (RCL) and the combinatorial geometry of the three-dimensional cube Q₃, with zero adjustable parameters. The derivation proceeds in three stages. First, the Q₃ mode budget establishes the geometric base Ω_Λ⁽⁰⁾ = 11/16, arising from the ratio of passive to total vacuum recognition modes. Second, the electromagnetic coupling α enters via the U(1) parity layer of the automorphism group Aut(Q₃), yielding a radiative correction α/π that lowers the base value to Ω_Λ = 11/16 − α/π ≈ 0.6852. Third, the Equilibrium Bridge Theorem proves that the mode fraction is identical to the vacuum energy fraction: the translation symmetry of the discrete lattice forces uniform energy density per mode, so counting modes is counting energy. This third step upgrades the central result from a hypothesis to a theorem and dissolves the cosmological constant problem. The prediction agrees with Planck 2018 (Ω_Λ = 0.6847 ± 0.0073), DESI BAO DR1 2024 (Ω_Λ = 0.685 ± 0.013), and DESI DR2 2025 at well below 1σ. The equation of state w = −1 and spatial flatness Ω_Λ + Ω_m = 1 both follow as corollaries. Beyond the core derivation, we prove three new results. (i) Non-abelian gauge corrections (SU(2), SU(3)) are exponentially suppressed by the mass gap, making α/π the complete leading-order correction. (ii) The deceleration–acceleration transition redshift is z_T = (2Ω_Λ/Ω_m)^(1/3) − 1 ≈ 0.633, consistent with observation (z_T = 0.67 ± 0.10). (iii) The Perpetual Complexity Theorem: the combination of Ω_Λ > 0 with the coprimality gcd(8, 45) = 1 (forced by D = 3) guarantees that the universe generates local complexity at every epoch—thermal death is impossible. The standard QFT prediction of M⁴_Pl for the vacuum energy is shown to be the answer to a categorically different question.