Search Results Fail to Link Babylonian Regular Numbers to Z³, A₃, or Tetrahedral Symmetry — E8 Intelligence Research

FINDING: Search results are predominantly low-quality video tutorials on Babylonian base-60 numeration; no source in this set establishes a connection between Babylonian regular numbers, the lattice Z³, root system A₃, or tetrahedral symmetry. | MATH: Babylonian system: positional sexagesimal, base b=60=2²·3·5. Regular numbers (S-regular, 60-regular) = {2^a·3^b·5^c : a,b,c ∈ ℤ}. These form a multiplicative monoid isomorphic to the additive lattice ℤ³ via (a,b,c) ↦ 2^a3^b5^c. Reciprocals terminate in base 60 iff the number is 60-regular. | CONNECTION: The ℤ³ structure of 60-regular numbers is real and well-documented (Neugebauer, Friberg, Robson). However, ℤ³ here is the exponent lattice of the prime factorization, NOT the A₃ root lattice. A₃ root system lives in the hyperplane {x₁+x₂+x₃+x₄=0} ⊂ ℝ⁴, has 12 roots, Weyl group S₄ of order 24, and its weight lattice is the FCC lattice (A₃ ≅ D₃). The claim "Babylonian regular numbers lattice Z³ = A₃" is not supported: Z³ is the root lattice Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com