Golden-Ratio Coherence Tax in Quantum Measurements: Theoretical Prediction and Trapped-Ion Evidence

We derive from first principles that quantum systems at measurement-limited coherence boundaries should exhibit a normalized coherence proxy η = φ⁻¹ ≈ 0.618, where φ = (1+√5)/2 is the golden ratio. This prediction emerges from Energetic First Principles (E1P), a mathematical framework describing coherent process dynamics through compositional energy ratios. Reanalyzing published trapped-ion data from Dumitrescu et al. (2022), we find that an independently-defined signal-resolution boundary yields η = 0.6075 ± 0.021—within 1.7% of the prediction and satisfying a preregistered ±0.03 tolerance. The same φ-scaling has been independently validated in debris disk astronomy (n=1,047 systems), Wolfram Physics Project rule dynamics, and Navier-Stokes turbulence, suggesting universal organizing principles.