MERLIN SCIENCE — Plimpton 322 as a Sexagesimal Lattice of Rational Points on the Unit C — E8 Intelligence Research

Plimpton 322 is not a random list of Pythagorean triples but a systematic enumeration of rational points on the unit circle, generated by reciprocal pairs of regular sexagesimal numbers. For the working scientist, this touches a deeper question: did an ancient culture encode a group-theoretic structure, the arithmetic of Gaussian integers restricted to primes two, three, and five, without leaving us a proof? The tablet's fifteen rows, with diagonals that are all regular sexagesimal integers, suggest they were not merely computing but sampling a lattice. Here is the mechanism. Every rational point on the unit circle can be written as x equals two p q over p squared plus q squared, and y equals p squared minus q squared over p squared plus q squared. For p and q regular in base sixty, meaning their prime factors are only two, three, and five, these coordinates are rational and the diagonal, p squared plus q squared, is itself regular. The tablet's entries correspond to specific p o

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com