Addendum III to Model H: Connections with Fundamental Constants, Nuclear Forces, and Baryonic Mass

This addendum extends the theoretical framework of Model H, previously applied to galactic dynamics, by proposing numerical connections between the geometric tension parameter and the fundamental constants of particle physics. Using updated cosmological data (Planck/CODATA 2022), we identify relationships linking a single parameter (τ = 9.47×10⁻⁴) to the fine-structure constant, the coupling constants of nuclear forces, and the proton-to-electron mass ratio. The observed numerical correspondences, all with precision exceeding 99%, are presented as working hypotheses requiring independent verification. Furthermore, we propose a hypothesis for resolving black hole singularities: the spacetime superfluid would possess a maximum density ρ_max = δ × ρ_Planck, eliminating the infinite divergence and replacing it with a finite dense core.