Closure on 60-Regular Numbers: The Structural Core of Old Babylonian Arithmetic — E8 Intelligence Research

FINDING: Old Babylonian sexagesimal arithmetic is closed under multiplication/division only on the sub-monoid of 60-regular numbers; this closure property is the structural core of OB number theory and the generative engine behind Plimpton 322 and Si.427. MATH: - Base: 60 = 2² · 3 · 5. Prime factorization {2,3,5}. - Regular numbers (OB "reciprocal-friendly"): n = 2^a · 3^b · 5^c, a,b,c ∈ ℤ≥0. These are exactly the integers whose reciprocal 1/n has a finite sexagesimal expansion. - Closure: if m,n regular, then m·n and m/n (n≠0) are regular. The set R = {2^a 3^b 5^c} is a multiplicative lattice (free abelian monoid on 3 generators), closed under multiplication and — restricted to divisibility — under division. - Reciprocals: 1/2 = 0;30, 1/3 = 0;20, 1/5 = 0;12, 1/8 = 0;7,30, etc. — all terminating. - Plimpton 322: 15 rows of Pythagorean triples (a, b, c) with c² = a² + b², parameterized by OB reciprocal pairs (x, 1/x). Columns give b/c and (b/c)² = 1 − (a/c)². Standard parameterization: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com