Derivation of Yukawa Coupling from Spiral Geometry in the Helix–Light–Vortex Framework

Within a speculative geometric ansatz inspired by the Helix–Light–Vortex (HLV) framework, we derive the effective Yukawa coupling constant gχ of a scalar mediator. The approach relates electron and nucleon interaction scales to their embedding in a Fibonacci–dodecahedral lattice and requires no free parameters, involving only the fine-structure constant α and the golden ratio φ. This purely geometric derivation predicts g2 χ ≈ 1.06 × 10−6 and a mediator mass mχ ≈ 16.5MeV/c2, matching recent King-plot spectroscopy data. The observed frequency nonlinearity (δνobs ≈ 0.162Hz) is interpreted as a statistical expectation shift induced by spiral vacuum modulation—a direct falsification channel (T4) of the HLV theory. This work strengthens the predictive and falsifiable character of the HLV framework and establishes a geometric basis for Yukawa-type interactions beyond the Standard Model.