Plimpton 322 Decoded: A Sexagesimal-Optimized Table of Squared Secants — E8 Intelligence Research

FINDING: Plimpton 322 is not a random list of Pythagorean triples but a systematic, sexagesimal-optimized table of exact squared-secant (or cotangent) values generated by a regular-number algorithm, with Bruins' reconstruction corrected to reveal a natural "missing pairs" structure. MATH: - Core generation: For regular numbers \(p, q\) (sexagesimal reciprocals), set \(b = p^2 - q^2\), \(d = p^2 + q^2\), \(a = 2pq\) (or variant with \(b = M Q_M\)). - Bruins' scheme: \(d^2/b^2 = 1 + (a/b)^2\) → table lists \( (d/b)^2 \) values as sexagesimal reciprocals of regular numbers. - New correction (arXiv:1109.3814): Missing pairs correspond to \(p,q\) where \(p/q\) yields ratios outside the tablet's chosen interval \(1 < d/b < 1.5\) (or equivalent), giving a complete, gap-free sequence under a single rule. - Factor-12 algorithm (arXiv:2001.11141): \(b = M Q_M\) with \(Q_M\) derived from \(M\)'s sexagesimal factorization; generates all 15 rows exactly. - Trigonometric function value Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com