w₀ = -0. 729 from the asynchronous asymmetric spiral model

The Dark Energy Spectroscopic Instrument (DESI) has reported a preference for dynamical dark energy, with the present-day equation-of-state parameter w0 deviating fromthe cosmological constant value −1. We derive an exact closed-form expression for w0from a single algebraic constraint Φ2 = Φ + 1 (golden root φ) and the identification ofthe deceleration–acceleration transition with the Lucas boundary L6 = 18. The result,w0 = −1 + 1/φ2 − 2/L6 = −0.729, contains zero free parameters and agrees with DESIand compendium constraints to within 0.03σ. We give a full derivation: tree-level deviation −1 + 1/φ2from a dual-root expansion picture, and a first-order boundary correction−2/L6 from the coupling at the transition. The Chevallier–Polarski–Linder (CPL) parameterwa = −2/φ2is also fixed. We then show that the same boundary retrodicts the transitionredshift ztr = 1/φ ≈ 0.618 and the dark-energy and matter densities ΩΛ = φ3/(2 + φ3),Ωm = 2/(2 + φ3), in agreement with supernova/BAO/CMB transition estimates and Planck2018. The framework suggests that the DESI anomaly may be explained by a geometricboundary effect rather than by fine-tuned scalar fields.