Localized Scalar States, Constrained Vector Modes, and Radiation-Boundary Tests in an Augmented Classical Field Theory

We present a numerical study of a dimensionless classical effective field theory containing two interacting complex scalar fields and a separately postulated, Gauss-constrained massive vector field. At fixed scalar charge $Q_2=750$, three-dimensional constrained minimization produces a localized stationary scalar configuration whose energy lies below the corresponding free-charge threshold. Constrained-Hessian analysis and finite-time nonlinear evolution support restricted classical stability within the specified model. The augmented theory also supports oscillatory localized vector modes. Perturbative outgoing-wave calculations yield nonzero scalar radiation responses, and a retarded vector-backreaction calculation agrees with the corresponding outgoing energy flux to approximately 0.13% at matched spatial resolution. This agreement does not establish continuum convergence or a directly measured intrinsic lifetime. We further develop action-matched causal radiation interfaces and test their coupling to a nonlinear three-dimensional interior across 1,024 transverse Fourier modes. Numerical comparisons demonstrate short-time agreement with independent finite-domain reference calculations and consistent charge and energy accounting. However, stationary exterior-field initialization, complete nonlinear radiation closure, and numerical-dissipation separation remain unresolved. A final nonlinear one-period return calculation fails to establish an exact periodic scalar–vector excitation despite accurate conservation diagnostics. Independent microscopic scalar-only spectroscopy has likewise not established an isolated composite spin-1 particle pole. These findings support specific classical numerical results and computational methods, but do not demonstrate physical particle emergence, quantum stability, an intrinsic excitation lifetime, or the emergence of spacetime and gravity.