The Colour Embedding of a Generation in G2: 16 = 2(3) + 2(3) + 4(1) and Why the Electroweak Sector Does Not Fit

We examine how one generation of Standard Model fermions embeds in the G2 structure of the framework, and report a result with a clean success and a sharp boundary. Using the standard subgroup chain G2 ⊃ SU(3) — under which the seven-dimensional representation branches as 7 → 3 + 3̄ + 1 — with this SU(3) identified as colour, and using the standard spinor branching 16 → 8s + 8c of SO(10) → SO(8) × U(1), the colour content of one generation is reproduced exactly: 16 = 2(3) + 2(3̄) + 4(1). The sixteen Weyl fermions of a generation fill (7+1) + (7+1) under G2 with the correct colour multiplicities and nothing left over. This resolves the apparent counting obstruction (one generation has sixteen fermions, not eight) and grounds, structurally, the quark–neutrino mixing distinction reported earlier: colour-charged fermions occupy the φ-carrying parts of the seven and are therefore subject to the mixing-suppression selection rule, while colour-singlet fermions — the leptons, including the neutrinos — occupy G2 singlets and are not. The boundary: the electroweak group SU(2)_L × U(1)_Y does not fit inside SO(8) commuting with G2-as-colour — the centraliser of G2 in SO(8) is too small. We conclude that the electroweak sector cannot arise as a commuting subgroup alongside colour, and must instead emerge from the framework's symmetry-breaking sectors or affine extension. We state this boundary plainly as the central open structural problem.