Gearing the Heavens: Antikythera's Saros and Exeligmos Eclipse Cycles — E8 Intelligence Research

FINDING: The Antikythera Mechanism encodes the Saros (223 synodic months) and Exeligmos (669 synodic months) eclipse cycles via a gear train whose tooth counts embody rational approximations of lunar and draconic periods; the Saros spiral's 223 cells map to a 254-tooth gear (draconic month ratio) with measurable gearing errors affecting pointer position. MATH: - Saros cycle: 223 synodic months ≈ 242 draconic months ≈ 239 anomalistic months ≈ 18.03 tropical years. - Exeligmos: 3 × Saros = 669 synodic months ≈ 726 draconic months ≈ 716 anomalistic months. - Key gear ratios (from known reconstruction): - 64:38 (crown gear) → 1.6842 - 48:24, 32:16, 32:16 (differential) → 2:1 each - 53:96 (draconic gearing) → 0.552083 (≈ 242/438.3) - 50:53 (anomalistic) → 0.943396 (≈ 239/253.3) - 223 cells on Saros spiral → 223 = prime, 223/235 (Metonic) = 0.948936 - Draconic month / synodic month ≈ 242/223 = 1.08520 (exact ratio from cycle). - Gear error analysis (arXiv:2208. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com