6 The n=2 Fermion: Leptons

The n=2 sector is the simplest non-trivial fermion: a two-site equal superposition with ∥F∥ = ∥B∥ = 1∕.

6.1 Charged lepton (m = 1)

For ψ = (e₀ + ie₁)∕ (winding m=1), the compression residual B is purely antisymmetric with eigenvalues ±1∕2 and the universal −π∕2 phase of Paper VII. The fermion has a self-contained antisymmetric residual and propagates freely. This is the charged lepton.

What Standard Model language calls a “photon” is the name given to the correlation between two such fermion events: when one charged lepton recoils, another does so in a correlated way. The codec encodes this correlation in the off-diagonal of ρ. No photon particle is required; the fermion’s complexity class already contains the full correlation structure.

6.2 Neutral fermion (m = 0)

For ψ = (e₀ + e₁)∕ (winding m=0), the residual B is purely symmetric with eigenvalues ±1∕2 and zero net phase winding. The fermion has zero electromagnetic phase structure: it is electrically neutral. This is the neutrino.

Within the n=2 sector, the winding number acts as the charge selector:

• m = 0: zero phase winding ⇒ neutral fermion (neutrino).
• m = 1: one phase winding ⇒ charged fermion (electron, muon, or tau, depending on complexity level).

Electric charge is the U(1) winding number within the n=2 sector. No additional postulate is required.