Particles
EstablishedThe Electron
The electron is T(1,1): the simplest torus knot. Its mass, charge, spin, and magnetic moment all follow from the T(1,1) geometry. It is the fundamental unit of the particle spectrum.
T(1,1) — the trefoil precursor: winds once in each direction on the Clifford torus, gcd(1,1)=1 ✓
Properties from topology
- Charge: winding number → charge = (elementary charge unit).
- Spin: self-link=1 → FR phase −1 → spin-½.
- Mass: confined photon at frequency → mass = 0.511 MeV/c².
The electron magnetic moment
from the T(1,1) topology (the doubled winding gives factor 2).
Why there is no simpler particle
T(1,1) is the minimal non-trivial torus knot with gcd=1. T(1,0) and T(0,1) are not knots — they are circles (the photon).
The photon as T(0,∞) or T(∞,0)
An unconfined photon has no torus confinement → no rest mass → travels at .
Electron stability
T(1,1) is topologically stable — it cannot be continuously deformed to the unknot without breaking the S³ topology constraint.
The muon and tau
Appear to be excited states of T(1,1) with higher confined-photon frequency — same topological class, different energy level. Mass hierarchy [O].
Key numbers
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