What question did this study set out to answer?

The aim is to derive the two-loop g−2 coefficient C₂ from foam topology without relying on QED.

March 21, 2026Open Access

C₂ from Axiom Zero: A Complete Independent Derivation of the Two-Loop Anomalous Magnetic Moment

Key Points

The aim is to derive the two-loop g−2 coefficient C₂ from foam topology without relying on QED.
Direct derivation from foam topology
Inclusion of terms from the Petermann-Sommerfield formula
Analysis of wavefunction renormalization and face graph counting
Normalization by gauge parameters in D-mode loop phases
Utilization of T₂g winding harmonics and coefficients.
C₂ coefficient calculated as −0.328478966
Agreement of findings at 3×10⁻¹⁶
No free parameters used in calculations
Derived terms include wavefunction renormalization and logarithmic contributions
Apéry's constant relates without Feynman integrals.

Abstract

The two-loop g−2 coefficient C₂ = −0. 328478966 is derived directly from foam topology without QED as intermediary. All four terms of the Petermann-Sommerfield formula are derived: 197/144 from wavefunction renormalization Z₂ plus face graph counting; π²/12 from two D-mode loop phases normalised by Ngauge=12; −π²ln2/2 from the Eg threshold √ (CA+1) =2; and 3ζ (3) /4 from T₂g winding harmonics Σ1/n³=ζ (3) weighted by CA/λEg=3/4. Apéry's constant enters not from a Feynman integral but from π₁ (T₂g) =ℤ. Agreement: 3×10⁻¹⁶. Zero free parameters.

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Cite This Study

Luke Martin (Wed,) studied this question.

synapsesocial.com/papers/69be37866e48c4981c677433 https://doi.org/https://doi.org/10.5281/zenodo.19085432

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