Babylonian Goal-Year Periods as Continued-Fraction Convergents of Lunar-Solar Ratios — E8 Intelligence Research

FINDING: Babylonian goal-year method encodes eclipse recurrence via sexagesimal period relations that are exact continued-fraction convergents of the lunar/solar commensurability ratios. MATH: - Saros: 223 synodic months = 242 draconic months = 19 eclipse years (6585.32 d). Ratio 223/242 ≈ 0.9215. - Metonic: 19 tropical years = 235 synodic months (6940 d). Ratio 19/235. - Goal-year method: predict event in year Y by adding a fixed period P (e.g., 18 yr for Saros, or 8 yr/11 d for the "octaeteris") to an observed event in year Y−P. Operationally: t_{n+1} = t_n + P, with P drawn from a small set of integer period relations. - Continued-fraction structure: 223/242 = [0; 1, 11, 1, 1, 1, 1, 1, 2] (sexagesimal-friendly small partial quotients). The anomalistic month ratio 223/239 (Saros) and 251/269 (exeligmos, 54 yr) are successive convergents. - Exeligmos: 3 × Saros = 669 synodic = 726 draconic = 57 eclipse years ≈ 19756 d — the triple-Saros correction for longitude shift. - Base-60: all Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com