Emergent Born-Infeld Electrodynamics from Hexagonal Twistor Networks: UV Completion in Twistor-EBIKK-β Theory

We present a rigorous derivation of nonlinear Born-Infeld (BI) electrodynamics from d = 6 twistornetworks, demonstrating: (1) exact matching of the BI Lagrangian to all orders, (2) automatic UV regularization via graph spectral geometry, and (3) testable predictions for γγ scattering at 28 TeV (FCC) and gravitational wave dispersion (LISA). The theory requires no ad hoc BI terms – all parameters derive from the fundamental length scale ℓ = κ 1/2 ≈ 10−18 m.