Maxwell Electrodynamics from Completion Curvature in the Residual Completion Framework V1.0

This preprint presents a theoretical derivation of the Maxwell sector within the Residual Completion Framework (RCF). The construction identifies classical electromagnetism with the SO(2)_{PR} reduced compatibility-curvature sector of a projected/residual internal frame. The electromagnetic potential arises as the P/R connection component induced by residual loading and orthogonalization, while electric source strength is associated with gauge-invariant closed P/R winding. The work derives the Maxwell equations from the corresponding curvature action and winding-source coupling, and states explicitly the limitations and validation requirements for future numerical loop studies.P. S. Arwell is a pseudonym used for this theoretical preprint. No institutional affiliation is claimed.