Closed-form evaluation of the unweighted spectral zeta function of the scalar Laplacian on the three-sphere S³, 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.
Luqman Omar Mahmood (Sat,) studied this question.