Derivation of the Standard Model Gauge Group SU(3)C × SU(2)L × U(1)Y from the R12 Rendering Algebra

Abstract
We derive the complete Standard Model gauge group SU(3)C ×SU(2)L×U(1)Y , its chiral fermion content, and the electric charge assignments from the R12 rendering algebra with zero free parameters. The derivation proceeds in six levels.

First, the 12-axis budget nmax = ⌊220/(γ1 + 4π/3)⌋ = 12 forces Z12 as the discrete symmetry group, whose unique non-trivial coprime factorisation Z12 ∼= Z3 × Z4 yields 3 generations × 4 types per generation.