Electromagnetism as an Emergent U(1) Sector of KN-Stabilized Yang-Mills Dynamics

This work presents a consolidated and internally complete treatment of electromagnetism within the framework of Symbolic Modular Field Theory (SMFT). Rather than postulating electromagnetism as an independent fundamental interaction, the paper demonstrates that classical Maxwell theory emerges dynamically as the infrared U(1) sector of a KN-stabilized Yang–Mills gauge action. The analysis shows that restricting the unified gauge sector of SMFT to its abelian subgroup yields a gauge-invariant electromagnetic action whose equations of motion reduce exactly to Maxwell’s equations in the low-entropy, low-curvature regime. The associated electromagnetic stress–energy tensor is derived and shown to couple consistently to the stabilized gravitational equations used in Symbolic Modular Gravity (SMG). Numerical lattice simulations support the analytic results by identifying a robust Maxwell window—a low-amplitude dynamical regime characterized by linear dispersion, propagating flux modes, and oscillatory gauge energy. Within this window, the KN stabilization mechanism preserves linear electromagnetic behavior while suppressing unphysical runaway dynamics outside the Maxwell regime. This document is intended as a canonical internal reference within the SMFT program. It consolidates prior work on KN stabilization, symbolic thermodynamics, and modular gravity into a single coherent treatment of electromagnetism. No modification of experimentally verified electromagnetic physics is claimed. Deviations from Maxwell behavior arise only outside the low-entropy basin and are governed by symbolic coherence dynamics rather than symmetry breaking.