Capsid Geometry: T-Number Theory and Electrostatic Assembly — E8 Intelligence Research

FINDING: Viral capsid geometry is governed by the Caspar–Klug quasi-equivalence theory, where T-number (T = h² + hk + k²) classifies icosahedral lattices, and assembly around electrostatic cores follows equilibrium/kinetic theories with charge-dependent free-energy minimization. | MATH: T = h² + hk + k² (h,k non-negative integers, not both zero); capsid radius R ∝ √T; number of capsid proteins N = 60T; icosahedral point group I (order 60); for T=1: N=60, T=3: N=180, T=4: N=240, T=7: N=420. The arxiv paper (0808.2204) models protein–core interaction via screened Coulomb potential V(r) ∝ (e−κr)/r with core charge Z, and free energy F = F_elastic + F_electrostatic, yielding critical assembly conditions dependent on κ (Debye length) and Z. | CONNECTION: The T-number formula is a norm form on the hexagonal lattice A₂ (root system of SU(3)); T = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 49, 52, 57, 63, 64, 67, 73, 75, 76, 79, 81, 84, 91, 93, 97, 100, 103, 108, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com