Dark Energy from Frozen Quantum Fluctuations: A One-Parameter Model with Numerical Consistency Check

We present a one-parameter phenomenological model of dark energy where the initial condition x_i is hypothesized to originate from quantum fluctuations of a scalar field in de Sitter space. The model employs a canonical scalar field Σ (the "memory field") with mass m_Σ = H, and a fluctuation field φ with postulated mass m_φ = H/2. The equation of motion x'' + 3x' + α²(N)x = 0 with α₀ = 1 follows from de Sitter thermodynamics. Fitting to BAO DESI DR2 and Pantheon+ data (N = 1603) yields x_i = 0.168721. The Bunch–Davies amplitude for m_φ = H/2 gives δφ/H = 0.168973, differing by 0.15%. This coincidence is a consequence of the mass postulate, not an independent prediction. We test for spatial variations using spherical harmonics in Pantheon+ residuals; no significant signal is found, placing an upper bound δΩ_DE/Ω_DE ≲ 0.1 on scales ≳ 100 Mpc. The mass hierarchy m_Σ² + m_φ² = 5H²/4 is postulated as a phenomenological input; twelve derivation mechanisms from first principles were tested, none yielding an exact result.