Geometric Standard Model: Part III. Topological Heuristics and the Derivation of Fundamental Constants

This paper investigates the geometric origins of fundamental physical constants within a constrained 3+1+2 multitemporal spacetime manifold. By modeling elementary fermions as energy-minimizing developable Möbius knots and gauge interactions as topological reconnections, we heuristically derive the scales of four fundamental constants from first principles without empirical parameters. Utilizing spatial-to-temporal dimensional ratios and the Wunderlich aspect ratio limit for isometric embeddings, we analytically project the fine-structure constant (\alpha \approx 1/137), the muon-to-electron mass ratio (m_\mu/m_e \approx 205.1), the electroweak mixing angle (\sin^2\theta_W \approx 0.222), and the anomalous magnetic moment (a_e \approx \alpha/2\pi). The remarkable convergence of these geometric derivations with experimental data provides a strong proof-of-concept that the phenomenological parameters of the Standard Model are deterministic macroscopic manifestations of underlying topological constraints.