Emergent Maxwell Equations from the Universal Ψ Lagrangian - Vector Coherent Modes, Gauge Invariance, and Electromagnetic Propagation

We derive the full structure of Maxwell electrodynamics directly from the Universal Ψ Lagrangian.Vector coherent modes emerge as the unique antisymmetric excitations around thestationary solution Ψ0, and the electromagnetic field strength Fμν arises naturally from the antisymmetricsector of the second variation of the action. No fundamental gauge symmetry, noU(1) field, and no phenomenological assumptions are introduced. Gauge invariance appears as afunctional identity resulting from the null directions of the quadratic form. The wave equation,propagation speed, Poynting structure, and charge conservation all emerge purely variationally.The analysis is closed, parameter-free, and provides a complete derivation of classical electrodynamicsas an emergent phenomenon.