Relative Field Localization: Three-Field Q-Ball Configurations and Preliminary Stability Analysis

This paper reports a post-publication development of the Relative Field Localization (RFL) programme: a repaired three-field candidate model, its flat-space stationary Q-ball branch, and a set of preliminary linear and nonlinear stability tests. The candidate introduces two massive real fields, a and chi, with a conformal factor A(chi) = exp(alpha chi), a stabilizing quartic term for a, and a bounded-from-below sufficient parameter condition. For the reference solution at omega/m=0.8, the numerical boundary-value problem returns Q=145.2731711, E=138.3719930, and E/(Qm)=0.9524952. A coupled four-real-variable linear spectrum was examined in angular sectors ell=0,...,4; no positive real growth rate was reported. A spherical nonlinear evolution with a 5% perturbation remained bounded through t=30 m^-1, with maximum relative charge drift below 2.0 x 10^-9 and energy drift below 2.7 x 10^-5. The full source code and numerical data are supplied in the accompanying package.