Observable Universe from a Functional Equation: Six Zero-Parameter Predictions from the Recognition Composition Law

From a single functional equation—the Recognition Composition Law (RCL)—and the combinatorics of the three-dimensional cube Q₃, we derive six testable cosmological predictions with zero adjustable parameters: (i) the dark energy fraction Ω_Λ = 11/16 − α/π ≈ 0.685, (ii) the Hubble tension ratio H_late/H_early = 13/12, (iii) the observable universe radius R_obs ≈ 4.32 × 10²⁶ m, (iv) the cosmic age t_age ≈ 13.4 Gyr, (v) the baryon-to-photon ratio η_B ≈ φ⁻⁴⁴ ≈ 6.4 × 10⁻¹⁰, and (vi) the dark energy equation of state w = −1 exactly. All six predictions agree with observation to within 5% or better. Every structural result in the derivation chain is machine-verified in Lean 4 with zero sorry statements and zero Recognition-Science-specific axioms. The derivation simultaneously resolves the Hubble tension, dissolves the 10¹²⁰ cosmological constant problem, and explains the Dirac large-number coincidence.