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9 The Fermion Classification

Table 2 presents the fermion complexity classes. The right-hand column gives the Standard Model label for the fermion event correlations that an observer using that language would identify — not the name of a fundamental particle, but the name given to a pattern of fermion behaviour.

(n,m) ∥F∥ ∥B∥ Symmetry Fermion class SM correlation label Status
(1,0) 1 0 — Localised, no residual vacuum exact
(2,0) 1∕√2-- 1∕√2-- symmetric Neutral lepton neutrino exact
(2,1) 1∕√2-- 1∕√2-- antisymmetric Charged lepton electron/muon/tau exact
(3,0) 1∕√3-- ∘2-∕3- symmetric Colour-neutral scalar Higgs sector conjecture
(3,1) 1∕√ -- 3 ∘ ---- 2∕3 mixed Colour-charged, confined quark/gluon exact
(4,2) 1∕2 √ -- 3∕2 symmetric Spin-2 fermion class open open
Table 2: Fermion complexity classes. The “SM correlation label” column gives the Standard Model name for the correlation pattern an observer would attribute to this fermion class. These are derived labels, not fundamental particles. “Status” refers to the (n,m) norm structure of Section 3, which is exact in every row; it does not certify that all SM particles sharing a label are distinguished by the framework. In particular the three charged leptons share the single class (2,1) and are not yet distinguished by mass — see Section 10.

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