Parameter-Free Resolution of the Schmidt Line Anomalies via Nuclear Vacuum Topology

For nearly 90 years, the Schmidt limits have failed to accurately predict the magnetic dipole moments of most nuclei, historically necessitating the phenomenological adjustment of effective g-factors (gs)eff. Here, we present a parameter-free, ab initio topological model — the Rodrigues Meta-Law — that derives magnetic moment attenuation strictly from the geometric elasticity of the confined nuclear vacuum. By defining the vacuum boundary via the fine-structure constant (a) and the spherical solid angle (4p), the deviation from the ideal Schmidt line is calculated using quantized topological invariants (fG) derived from the Peter-Weyl theorem for compact Lie groups. Crucially, the mapping of a nuclide to its respective symmetry group (e.g., SU(2) sphere, SO(3) rotor) is deterministically locked by independent empirical observables, such as the electric quadrupole moment (Q), prohibiting arbitrary parameter fitting. Furthermore, the framework mathematically subsumes classical single-particle theory, recovering the ideal Schmidt lines exactly in the limit of zero metric coupling (a → 0). The model successfully neutralizes parity inversion anomalies in extreme nuclei and yields highly accurate predictions for rigid SU(2) states, demonstrating that the quenching of nuclear magnetic moments is a fundamental geometric consequence of vacuum topology rather than a phenomenological many-body artifact.