Residual stress and stress gradients generated during fusion welding drive distortion, cracking risk, and fatigue limitations in high-consequence structures (e.g., marine and defense fabrication). This protocol-first paper proposes a conservative, testable hypothesis: a low-power, phase-structured magnetic field applied during weld solidification and the early post-arc cooling interval can reduce peak tensile residual stress and/or stress spatial variance, relative to both a no-field control and a sham-field control with comparable RMS coil power but scrambled phase structure. The mechanism is framed in classical terms (Lorentz-force-driven melt pool convection, stabilization of the solidification front, and reduction of directional bias in flow patterns), not as new physics. The study is designed to be falsifiable with pre-registered thresholds, artifact controls, and heat-input confound checks. Primary measurement is X-ray diffraction residual stress (XRD sin^2 psi), with ASTM E837 hole-drilling as secondary validation and neutron diffraction as an optional premium through-thickness mapping method.Design: Three conditions (Control: coils off; Sham: coils energized with phase scrambling; Active: quadrature currents producing an approximately rotating field vector), pre-registered parameter window (frequency, field strength, post-arc duration, and power ceiling), tiered measurement path (Tier 1 low-access screening through Tier 3 advanced mapping), and explicit rejection criteria including minimum practical effect thresholds and defect trade-off checks (e.g., stress reduction accompanied by increased porosity is rejected). Includes operational logging and electrical/EM safety constraints.