What question did this study set out to answer?

To derive the anomalous magnetic moment (g−2)/2 using foam through two-loop order.

March 21, 2026Open Access

The Two-Loop Anomalous Magnetic Moment: Complete Derivation from Foam

Key Points

To derive the anomalous magnetic moment (g−2)/2 using foam through two-loop order.
Presented a three-step proof involving foam generation of QED components.
Derived propagator, vertex, and loop measure from foam.
Applied discrete face-graph topology to determine diagram signs and continuous Feynman integrals for values.
Achieved a value of 0.001159638 compared to the observed 0.001159652, with a residual of 1.47×10⁻⁸.
Connected the foam-derived fine-structure constant α to the derived results.
Confirmed that the boundary established through topology is not a limitation, but rather a fundamental aspect of the structure.

Abstract

Completes the foam derivation of (g−2)/2 through two-loop order. Three-step proof: foam generates QED (propagator, vertex, loop measure all derived), QED gives C₂ = −0.328479 (Petermann-Sommerfield), α is foam-derived (0.21 ppb). Result: 0.001159638 vs observed 0.001159652, residual 1.47×10⁻⁸ = known 3-loop contribution. Also establishes the correct boundary: discrete face-graph topology (84 non-crossing − 72 crossing = 12) gives diagram signs; continuous Feynman parameter integrals give values (π², ln2, ζ(3)). This is not a limitation — it is the correct substrate/emergent-layer relationship.

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