Babylonian Goal-Year Eclipse Prediction via Integer Lunar Month Period Relations — E8 Intelligence Research

FINDING: Babylonian goal-year method encodes eclipse prediction as integer period relations among three lunar months — synodic, anomalistic, draconic — with the Saros as the canonical 223-month commensurability. | MATH: Saros = 223 synodic months = 242 draconic months = 239 anomalistic months ≈ 18 y 11 d 8 h. Goal-year periods (e.g., 1 Saros, 1 Metonic = 19 y = 235 synodic months, 1 Exeligmos = 3 Saros = 669 synodic months) are integer-ratio approximations to irrational frequency ratios. Metonic: 235 synodic = 254 sidereal = 19 tropical years. | CONNECTION: Base-60 sexagesimal arithmetic is the substrate; the goal-year method is a continued-fraction / Diophantine approximation scheme on orbital frequencies. Ratios 223/242, 242/239, 235/19 are not φ-family but are convergent rational approximants — the same structural role continued fractions play in Fibonacci/φ (φ = lim F_{n+1}/F_n). Exeligmos 669 = 3·223; 669 synodic ≈ 726 draconic ≈ 717 anomalistic. | DEPTH: 8 FINDING: The Saros is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com