Derivation of the Proton Magnetic Moment from Topological Density Functional Theory: μₚ = Nc exp(−απ²) ≈ 2.7915 μN

We derive the proton magnetic moment μp as a leading-order theorem of the Universal Confinement Law within the Topological Density Functional Theory (T-DFT) programme. Adopting five explicitly stated assumptions (A1) holographic reduction of the T-DFT vacuum to a three-sphere boundary ∂M ≅ S3; (A2) the Schur confinement fractions fG ∈ {1/4, 1/9, 1/64} established by the Peter–Weyl theorem; (A3) the vacuum elastic constant σG = α/2 from the QED one-loop functional determinant; (A4) the proton identified as the B = 1 Skyrmion with ideal moment μpideal = Nc = 3 μN; and (A5) the real photon coupling to the conserved U(1)em current at Q2 = 0 with Schur fraction fG = 1 we prove, without any new free parameter, that μpT-DFT = Nc exp(−σGΩ3) = 3 exp(−απ2) ≈ 2.7915 μN, in agreement with the experimental value 2.79285 μN (CODATA 2022) to within 0.047%, approximately sixty times more precise than current Lattice QCD. The algebraic identity is machine-verified in Lean 4 with no unresolved proof obligations in the algebraic core and without axioms beyond standard Mathlib foundations. The same suppression factor applied to the neutron ideal moment μnideal = −2 μN yields the exact SU(6) ratio μp/μn = −3/2, also formally verified. Five falsifiable predictions are derived for future experimental tests.