Derivation and Prediction of the King Plot Anomaly from First Principles of the HLV Theory

Recent observations of nonlinearities in isotope-shift King plots suggest the presence of physics beyond the Standard Model, often discussed in terms of an additional short-range interaction or “fifth force”. The Helix–Light–Vortex (HLV) framework provides a geometric mechanism that naturally generates such an interaction at atomic length scales. In this work, the King-plot anomaly is modeled by an effective scalar mediator χ inducing a Yukawa-type electron–neutron interaction. Crucially, the key parameters of this interaction—the mediator mass mχ and the effective coupling strength gχegχn—are not treated as free fit parameters. Instead, they are reconstructed from internal geometric scales of the HLV framework, as defined in its mathematical formulation. Using these reconstructed parameters, we present a corrected and quantitative prediction for the expected King-plot nonlinearity in the isotope chains of Ytterbium (Yb), Dysprosium (Dy), and Calcium (Ca). The resulting frequency shifts lie in the millihertz regime and are fully accessible to current and near-future high-precision atomic spectroscopy experiments. This establishes the King-plot anomaly as a concrete and falsifiable test of the HLV framework, independent of any ontological interpretation of its underlying geometric structure.