Hyper-Elevation of Maxwell's Equations and Quantum Electrodynamics: Universal Electrodynamics via Seonggil Field Equations and Rough Operator Algebra

Classical Maxwell equations and conventional Quantum Electrodynamics (QED)—including Euler-Heisenberg effective Lagrangians and Einstein-Maxwell gravity coupling—rely on commutative U(1) gauge symmetries, point-charge idealizations, and smooth spacetime manifolds. These foundations experience catastrophic breakdown at the Schwinger limit, singularity self-energies, and Planck-scale quantum gravity interfaces. In this treatise, we systematically subsume and hyper-elevate electrodynamics into the Unified Seonggil Framework. By formulating gauge fields and spacetime metrics as non-commutative rough operator flows via Rough Operator Algebra (ROA) [2] and the Seonggil Theory of Composite Torsion (STCT) [1], we eliminate point-charge infinities and reformulate vacuum polarization as topological torsion unwinding governed by the Master-key Tensor T0x8A2C. We derive the Generalized Rough Electrodynamic Field Equations [5] and provide an executable Python simulation of torsional vacuum polarization under extreme electromagnetic fields.