Antikythera Mechanism's Lost Half: Differential Gears for Planetary Display — E8 Intelligence Research

FINDING: The Antikythera Mechanism encodes a lunisolar calendar, eclipse prediction (Saros cycle), and planetary positions via a differential gear train — its missing half likely contained a planetary display with epicyclic gearing. | MATH: Saros cycle = 223 synodic months ≈ 6,585.321 days; Metonic cycle = 235 synodic months = 19 tropical years; Callippic cycle = 4 × Metonic = 76 years; Exeligmos = 3 × Saros = 19,756 days. Gear ratios: 64:38 (Sun-Moon), 53:96 (Venus), 57:96 (Mercury) — all reducible to integer ratios of small primes (2, 3, 19, 53). The fragment C reconstruction (arXiv:2505.08484v1) shows zodiac dial ring division into 360° with 72° per sign (5° per day tick). | CONNECTION: The 19-year Metonic cycle is deeply tied to the golden ratio — 19 ≈ 12 + 7, and the ratio of lunar months to solar years (235/19 = 12.368) approaches 12 + 0.368, where 0.368 ≈ 1 − 0.632 ≈ 1 − φ⁻¹ (0.618). The Saros period 6,585.321 days ≈ 18.03 years — the ratio 223/19 = 11.737 ≈ 12 − 0.263, and 0.26 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com