SMEFT C2 Operator Ratios as a Test of Quantum State-Manifold Nonlinearity

If the quantum state manifold of gauge fields is a nonlinear homogeneous space M ∼= G/H, the Reference-Frame Self-Consistency (RCC) condition forces the appearance of a fibre-phase connection κµ that kinetically mixes with the Standard Model hypercharge boson. We show that this single geometric mechanism generates correlated, falsifiable predictions in the SMEFT X2 operator class. Kinetic mixing between the fibre-phase connection κµ and the SM hypercharge boson Bµ yields the dimensionless parameter ϵ = k∇ϑk 2/Λ 2 . Dynkin-index analysis fixes η2B : η2W : η2G = 1 : 2 : 3, giving Cˆ 2G : Cˆ 2W : Cˆ 2B = 1 : 1 : 1 whenever ϵ = 0. In the Kähler limit ϵ = 0, the ratios collapse to 1 : 1 : 1, recovering the linear RCC null hypothesis of the Kähler (linear) limit. Current bounds (ϵ ≲ 10−3 , |C2W | ≲ 2 × 10−4 TeV−2 ) place the linear baseline Cˆ 2 lin X = 1/12 at the HL-LHC threshold, while FCC-ee would decisively distinguish the linear and nonlinear regimes.