From Vortex Rings to the Top Quark: Dynamical Derivations in the Null Worldtube Framework

We model the electron as a quantized vortex ring in a superfluid vacuum, described by the Gross-Pitaevskii equation. The torus knot of the Null Worldtube (NWT) framework is identified with the vortex ring's topology. Starting from the GPE Lagrangian and Macken's spacetime impedance Z_s = c^3/G, we derive: (i) the torus tube radius r/R = 1/pi^2 (2.5% accuracy); (ii) quark confinement from the incommensurability condition gcd(n,q)=1; (iii) the pion mass m_pi = 2m_e/alpha = 140.05 MeV (0.34%); (iv) the 1/alpha energy ladder generating nuclear, heavy-quark, and electroweak scales; and (v) the top quark mass m_t = 2k^2 m_e/alpha^2 = 172,730 MeV (0.02% accuracy). All results follow from one measured mass (m_e), one coupling (alpha), and two topological integers (p=2, k=3).