Cuneiform Discovery: Cuneiform mathematical astronomy goal-year texts — E8 Intelligence Research

**Discovery: The Arithmetic of Eclipse Cycles in Goal-Year Text BM 36910** The Goal-Year Texts (Akkadian *qû urru*) represent the apex of Babylonian mathematical astronomy: empirical predictive algorithms stripped of geometric models, operating purely on integer period relations in sexagesimal arithmetic. BM 36910 (Sippar, ca. 240 BCE), a canonical example, does not compute planetary positions geometrically; it tabulates the *integer differences* in years, months, and days between a "Goal Year" and prior observation years where phenomena (lunar/solar eclipses, planetary stations, first/last visibilities) recur with high fidelity. **1. Mathematical & Astronomical Knowledge: Integer Period Relations** The tablet encodes the fundamental periodicities of the Moon and planets as linear Diophantine approximations. For the Moon, the scribe exploits the **Saros** (223 synodic months ≈ 239 anomalistic months ≈ 242 draconitic months) and the **Exeligmos** (3 Saros = 669 months = 19,756 days). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com