Golden Ratio Organization in Gravitational Wave Signals: Evidence from 68 Binary Mergers

This paper presents the first systematic analysis of golden ratio (φ ≈ 1.618) organization in gravitational wave signals from compact binary mergers. Using a novel Harmonic Unification Framework (HUF) pipeline, we analyzed 68 events from the LIGO catalogs (O1-O4a) and found statistically significant evidence that black hole mergers organize toward φ during coalescence. The primary finding—a negative correlation between φ-distance and harmonic power (r = -0.309, p = 0.012)—indicates that events with frequency ratios closer to the golden ratio exhibit stronger harmonic coherence. Additionally, 97% of events show φ-lattice organization, and systematic convergence toward φ occurs during the late inspiral phase (mean φ-distance decreasing from 10.9% to 8.9%). Cross-detector validation using both LIGO instruments (Hanford and Livingston) confirms these patterns are astrophysical rather than instrumental. These findings suggest spacetime dynamics during binary coalescence may be governed by geometric optimization principles, with implications for general relativity and fundamental physics.