Conclusion

The electroweak gauge group is derived from Axiom S.

The break ε carries an internal two-component state encoding its relationship to the two sectors: ℋ_EW ≅ ℂ² (Lemma 1). Local basis invariance forces a gauge connection with structure group U(2) (Lemma 2). The algebraic decomposition U(2) ≅ SU(2) × U(1)_Y identifies weak isospin and hypercharge (Proposition 1).

The chiral coupling pattern is structurally identified through Axiom R’s arrow of time and the CPT identification (Proposition 2, structural, principal debt).

The Standard Model’s gauge structure SU(3) × SU(2) × U(1) is now derived: AP15 (U(1) from phase freedom), AP19 (SU(3) from orientation freedom), AP27 (SU(2) × U(1)_Y from sector-relationship freedom). Three gauge groups from three structural freedoms of ε.