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

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.