The Standard Model Gauge Group from Vortex Knot Topology

We propose that the gauge group SU(3) × SU(2) × U(1) of the Standard Model can be identified with the crossing exchange algebra of the two simplest vortex topologies in a superfluid vacuum: the trefoil knot and the Hopf link. Three self-crossings of the trefoil generate su(3) through continuous strand exchange. Two perpendicular inter-crossings of the Hopf link generate su(2), while the linking phase provides u(1). The Gross-Pitaevskii nonlinearity at the Hopf crossings provides the Higgs potential, with electroweak symmetry breaking arising from crossing condensate dynamics. Coupling constants, the Weinberg angle, and mass ratios emerge as consequences of the crossing geometry on a torus with aspect ratio κ = π². Paper 8 in the Null Worldtube series.