The Golden Mirror Between Quark and Lepton Mixing

The large mixing among leptons and the small mixing among quarks have no explanation in the Standard Model, where both are measured and put in by hand. On the C60 geometry they are two faces of one structure. The lepton anchor and the quark anchor are exact Galois conjugates under φ going to 1−φ, and the two anchors sum to one by an exact algebraic identity, 1/(2+φ) + 1/(3−φ) = 1. The large value, 1/(2+φ), is the lepton anchor; the small value, 1/(3−φ), is the quark anchor. This is the deepest statement available for why CKM differs from PMNS, forced by the representation structure and not fitted: the difference between the two mixing matrices is one Galois conjugation acting on a single structure, and the identity itself is exact and cannot be measured away. The paper also states plainly where the sector's numerical predictions stand. The bare lepton anchor, read directly as the solar mixing angle, missed when the first test came in. The coupled prediction that takes the measured reactor angle as its input, carrying the solar angle to 0.321 and the atmospheric angle to 0.570, is the one now on the line.