Version 3.0 presents a substantially revised and expanded manuscript submitted to Frontiers in Astronomy and Space Sciences, archived here as the definitive preprint. This version supersedes v2.0 and refines both the presentation and the mathematical exposition of the Silver-Ratio Harmonic Framework (SRHF). The manuscript has been restructured for greater clarity, with improved separation between empirical results, comparative analysis, and speculative connections. The SRHF geometric construction figure has been updated to show the full Celtic Cross geometry with the harmonic constants (A, B, C, D) explicitly labelled, directly linking the geometric foundation to the algebraic framework. All quantitative results are unchanged: MAPE ≈ 0.72%, RMSE ≈ 0.11 AU across all planetary orbits from Mercury to Pluto. The model continues to outperform classical Keplerian and Titius–Bode formulations by over an order of magnitude, and the falsifiable prediction of a harmonic node near 2.14 AU — the Harmonia position — remains the central observational test of the framework.
Salah-Eddin Gherbi (Fri,) studied this question.