What question did this study set out to answer?

This research aims to derive the proton magnetic moment using topological density functional theory (T-DFT).

May 16, 2026Open Access

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

Key Points

This research aims to derive the proton magnetic moment using topological density functional theory (T-DFT).
Five assumptions were adopted, including holographic reduction and the identification of the proton as a Skyrmion.
The derived formula for μp was machine-verified without using new parameters beyond standard foundations.
The predictions for neutron magnetism were also formally verified, supporting the established SU(6) ratios.
The derived proton magnetic moment is μp ≈ 2.7915 μN, matching experimental values to within 0.047% accuracy.
The approach is approximately sixty times more precise than previous Lattice QCD results.
Five predictions for future tests are derived and await experimental verification.

Abstract

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.

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