Babylonian Tablets Reveal Abelian Group Structure in Pythagorean Triples — E8 Intelligence Research

FINDING: Babylonian base-60 arithmetic and Plimpton 322 encode rational points on the unit circle via Pythagorean triples, forming an abelian group structure. MATH: - Base-60 (sexagesimal) positional system: place values \(60^k\) (k = …, -1, 0, 1, 2, …). - Pythagorean triples: \(a^2 + b^2 = c^2\) → rational points on unit circle: \((a/c, b/c)\). - Parametrization: \(x = \frac{2t}{1+t^2}, \ y = \frac{1-t^2}{1+t^2}\) for rational \(t\). - Abelian group: rational points on unit circle under complex multiplication \((x_1+iy_1)(x_2+iy_2)\) — group isomorphic to \(\mathbb{Q}/\mathbb{Z} \times \bigoplus_{p} \mathbb{Z}\) (per arXiv:2101.12166). - Plimpton 322: 15 rows of sexagesimal triples — likely generated by reciprocal pairs \((p/q, q/p)\) with \(p,q\) regular sexagesimal integers (i.e., \(p,q\) have only prime factors 2,3,5). CONNECTION: - Base-60 naturally yields regular numbers (2,3,5-smooth) — these generate dense rational points on the unit circle, mirroring lattice-li Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com