S³ geometry · 2026
Ground-State Spin and Parity from Torus Topology: Why knots are spin-½ fermions and links are pseudoscalar mesons
R. G. Measey
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Abstract
We show that the ground-state spin-parity J^P of a confined-photon state can be read directly off its topology. The confined photon's transverse polarisation is a director — a headless, ℤ_2 line field. Carried once around a single closed loop, it acquires a Möbius half-twist, making the wavefunction double-valued: spin-½, yielding spin-½ fermions for single-line knots (gcd(p,q)=1) like the electron and proton. Links with gcd(p,q)>1 are multiple loops combining to integer spin (spin-0 bosons), such as pseudoscalar mesons (P=-1). This reproduces every ground-state anchor (electron, proton, neutron, pion, neutrino) with zero parameters. Excited states are a stated GAP.
spinparitytopologytorus knotMöbius twistfermionbosonneutral link
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