Eisenstein Integers Quantize Viral Capsid T-Numbers — E8 Intelligence Research

FINDING: Viral capsid triangulation numbers (T-numbers) are quantized by the Eisenstein integer lattice (hexagonal tiling), yielding only specific allowed values T = h² + hk + k², directly encoding icosahedral symmetry. | MATH: T = h² + hk + k² (h,k non-negative integers, not both zero); equivalently T = a² + ab + b² in the Eisenstein integers ℤ[ω], ω = e^{2πi/3} = −1/2 + i√3/2. Norm form: N(h + kω) = h² + hk + k². Allowed T: 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 49, 52, 57, 61, 63, 64, 67, 73, 75, 76, 79, 81, 84, 91, 93, 97, 100, ... (OEIS A003136). Icosahedral group order 60; capsid has 60T subunits. | CONNECTION: The hexagonal lattice is the root lattice A₂, with 6-fold symmetry; its dual is itself (self-dual). The ratio of nearest-neighbor distance to lattice spacing gives √3 ≈ 1.732, and the golden ratio φ = 1.618 appears in the icosahedron's geometry (edge/radius ratios). The allowed T-numbers are precisely those integers representable by the norm Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com