Electromagnetism from the Lattice Field Medium

This publication presents a computational demonstration that Maxwell-like electromagnetic structures emerge from scalar field dynamics without imposing electromagnetic postulates. Using the variable-mass Klein-Gordon equation with spatially varying chi(x,t), emergent electric and magnetic field analogues are defined through spatial derivatives and Helmholtz-Hodge decomposition. Across 21 validation tests, we verify all four Maxwell equation analogues to machine precision, demonstrate wave propagation with measured velocity c_num = 0.9865 +/- 0.014, confirm chi-dependent refractive-index behavior, and reproduce Poynting flux, polarization, and charge-current continuity. These results provide a complete computational example of emergent electromagnetic structure arising from a single underlying PDE. We also acknowledge Francis Procaccia for collaborative stencil-testing discussions and independent exploratory runs that helped stress-test the mixed-operator interpretation used in this release (GOV-01 propagation candidate with GOV-02 vacuum geometry).