Goldstone Sources, Induced Gravity, and the Newtonian Coupling: A unified scalar-field analysis under the Supreme Regularity Constraint

We investigate whether the conserved charge of a localized complex scalar configuration can source a regular long-range field, whether such a field can reproduce a universal Newtonian interaction, and whether the asymptotic gravitational scale can arise from the scalar-field vacuum rather than from a bare Einstein-Hilbert coefficient. The analysis distinguishes the exact U(1) phase of the complex RFL field, an independent axion-like scalar coupled to the invariant density s = |ψ|², and a real scalar Φ with a finite nonzero vacuum value. For a regular static spherical configuration with nonzero central modulus, the phase first integral forces its monopole integration constant to vanish; any nonzero value gives divergent central gradient energy and a nonzero radial flux through arbitrarily small spheres. An independent scalar source preserves the U(1) charge and yields q_θ = κQ/(2ω). The supplied thin-wall data give a variation of approximately 6.31 in q_θ/E, excluding universal mass proportionality on the sampled branch. The finite-core field and its on-shell energy are derived with one consistent sign convention, giving an attractive interaction for like source strengths. The original ψ sector cannot supply a nonzero asymptotic tensor coefficient when s → 0 and no bare gravitational term is present. The scalar-tensor extension ξ_Φ Φ² R / 2 instead gives G_* = (8π ξ_Φ v_Φ²)^(-1). Its Einstein-frame coupling and conditional post-Newtonian constraint are derived. We also examine the relationship of this extension to the existing RFL/QGT actions and distinguish algebraic checks from nonlinear numerical results. Smooth extended sources and finite-core configurations are used throughout; local scalar regularity is not treated as proof of global boundedness of every curvature invariant.