Spectral Zeta Function of the Three-Sphere: Closed Forms and Applications to Gauge Coupling Constants

Closed-form evaluation of the unweighted spectral zeta function of the scalar Laplacian on the three-sphere S^3, with applications to gauge coupling constants in the Vacuum Mechanics framework. Perturbative expansion structure and comparison with experimental determinations are presented. Supersedes v1 (10.5281/zenodo.19247293). Developed with AI assistance (Claude by Anthropic for computation and manuscript drafting). All physical reasoning and formula identification are the author's responsibility.