The integer-parity kernel of the internal-U(1) mixing obstruction

In the six-dimensional SU(4) gauge-Higgs unification model, a symmetric-tensor doublet zero mode requires an even index n₃, while the hypercharge equation at the nontrivial internally mixed angle requires 3 n₃ − 2 n₄ = 1. The two integer conditions are incompatible. The physics that produces them (orbifold zero-mode parity and the hypercharge equation) is an input, not formalized here.

Main results

• even_index_hypercharge_obstruction: Even n₃ and 3 n₃ − 2 n₄ = 1 are incompatible.

theorem GaugeHiggsUnification.InternalU1MixingNoGo.even_index_hypercharge_obstruction (n₃ n₄ : ℤ) (h_even : Even n₃) (h_charge : 3 * n₃ - 2 * n₄ = 1) : False

An even n₃ and the hypercharge equation 3 n₃ − 2 n₄ = 1 are incompatible.