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

We derive the proton magnetic moment μₚ 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 μₚ/μₙ = −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 Λᵣot diverges because K (∞) = 0 forces (1 − K²) → 1 in the integrand. The proton moment of inertia gives Λₚ = 0. 04648 MeV⁻¹, yielding μₚ = 14. 3 μN. The factor 5. 12 excess over the experimental value 2. 793 μN is identified as a structural consequence of K (∞) = 0 (scale gap Lₛcale, consistent with Branches C–D). The isoscalar contribution μIS = 0 by SU (2) symmetry. The neutron interior moment of inertia Λₙ^U (1) = 0. 00992 MeV⁻¹ is reported as a Column B result. The ratio μₚ/μₙ = −3/2 is independent of the scale gap.