Plimpton 322 as a Secant/Cosecant Table from Reciprocal-Pair Lattice — E8 Intelligence Research

FINDING: Plimpton 322 encodes a sexagesimal table of regular-number pairs (leg, hypotenuse) generated by a multiplicative lattice of reciprocal pairs, functioning as a secant/cosecant table rather than a Pythagorean triple list. | MATH: Column entries are of the form (d²−n², d²+n²) or equivalently (1−t², 1+t²) where t = n/d is a rational "ratio" parameter; the tablet lists 15 rows with hypotenuse values including 169 (=13²), 185, 229, 241, 289, 305, 319, 325, 337, 361, 373, 397, 409, 439, 481. The pair (1 19, 169) corresponds to 79 and 169 in decimal; 169 = 13², and 79 is prime. The generating parameter is the reciprocal pair (x, 1/x) in base-60, where x is a "regular" number (only primes 2, 3, 5 divide it), ensuring finite sexagesimal expansion. | CONNECTION: Base-60 regular numbers form a multiplicative lattice closed under multiplication and division — the set {2^a · 3^b · 5^c}. This lattice is isomorphic to a Z³ root lattice (cubic lattice) in logarithmic coordinates. The secant va Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com