FOX Theory (Branch E): The Proton Magnetic Moment from Collective Rotation

We derive the proton magnetic moment μ_p within FOX Theory by applying the collective rotation quantization of Adkins, Nappi, and Witten (ANW) to the coupled scalar-gauge soliton of Branch C. Four principal results are established. (i) The kinetic scalar contribution to the moment of inertia vanishes exactly: Λ_φ = 0. (ii) Postulate P5 (winding 4π) and π₁(SO(3)) ≅ ℤ₂ force the soliton spin to J = 1/2, giving the ANW prefactor (3/2) independently of the gauge profile. (iii) The ratio μ_p/μ_n = −3/2 is exact by Wigner-Eckart, independently of the moment of inertia. (iv) Under hypothesis H6 (K(r*) = 1, neutron Dirichlet), the moment of inertia Λ_rot diverges because K(∞) = 0 forces (1 − K²) → 1 in the integrand. The proton moment of inertia gives Λ_p = 0.04648 MeV⁻¹, yielding μ_p = 14.3 μ_N. The factor 5.12 excess over the experimental value 2.793 μ_N is identified as a structural consequence of K(∞) = 0 (scale gap L_scale, consistent with Branches C–D). The isoscalar contribution μ_IS = 0 by SU(2) symmetry. The neutron interior moment of inertia Λ_nU(1) = 0.00992 MeV⁻¹ is reported as a Column B result. The ratio μ_p/μ_n = −3/2 is independent of the scale gap.