Saros Eclipse Cycles (沙羅週期)

THE SAROS — the Chaldean eclipse cycle: 223 synodic months (6,585.32 days — 18 years, 11 days, 8 hours), after which Sun, Moon, node AND lunar distance return together and an eclipse repeats. The cycle that let Babylonian astronomers predict lunar eclipses centuries before geometry could say why, and the reason every modern eclipse carries a SAROS SERIES NUMBER. THE WHOLE NUMBERING FROM ONE ANCHOR: eclipses one lunation apart sit 38 series apart (mod 223), so one published anchor per kind (Solar 139 = the 2024 Great American Eclipse; Lunar 123 = 14 March 2025) determines every number — checked at load against SEVEN published canon assignments across both kinds, including the famous 1999/2017 pair proven to share Solar Saros 145 exactly 223 lunations apart, PLUS the physics law: the 2042 return of the 2024 eclipse must be FOUND by the engine within hours of peak + 6,585.32 days and land in the same series. Serves upcoming eclipses with series numbers, each one's previous and next series member, and the exeligmos (three saroi, 54y 33d — the return to your own longitude). The near-commensurability that makes it work (223 synodic ≈ 242 draconic ≈ 239 anomalistic, within 0.11 days) asserted as arithmetic; member indices deferred by name rather than fabricated; Halley's 1691 'saros' misnomer served as the story it is. Mesopotamian becomes two systems. Pure compute, no LLM.

Cost: 2 TIAN Points per call. tRPC procedure saros.cycles.