Fractal Coherence Restoration in the N-Body Problem: Universal Stability through Golden Ratio Modulation

I propose a novel framework for the N-body problem, extending the fractal coherence restoration model—modulated by the golden ratio (ϕ ≈ 1.618)—to systems with N ≥ 3. The approach introduces a scalar coherence field, Φ(x, t), which weakly couples to masses and biases orbital frequency ratios toward ϕ. Through this mechanism, the model achieves significant chaos suppression and enhanced orbital stability. Finite-difference time-domain (FDTD) simulations performed for N = 3, 4, and 5, including hierarchical configurations such as the Sun–Jupiter–Earth–Moon system, demonstrate: Reductions in Lyapunov exponents of up to 82%, Decreases in spectral entropy of about 38%, Stability improvements exceeding 77% in specific regimes Furthermore, the model predicts a preferential clustering of orbital frequency ratios at Fibonacci convergents (e.g., 8/5, 13/8), together with enhanced stability of Lagrange points and choreographic orbits. These findings suggest the existence of a universal principle of dynamical stability, with the potential to revolutionize celestial mechanics and provide new insights into both astrophysical systems and quantum chaos analogs. For a deeper understanding of this work, see “Gravity as a Fractal Restoration Vector Field: A Unified Model Based on Gφ-Coherence” https://doi.org/10.5281/zenodo.17049868