# Pathway 3 Ledger: Exactly Three Sequential Matter Generations

## Sealed Value
N_gen = 3
Derivation: Three non-trivial 3D irreducible representations of the icosahedral symmetry
group I_h. The ground state plus three 3D irreps enforce exactly three sequential
quark-and-lepton families. No fourth irrep of the same type exists in I_h.

## Terrain Contact (post-July-11)
T7  arXiv:2607.27307 (ATLAS, July 29): Heavy Majorana neutrino in VBS. Exclusions
    above 1.5 TeV. No fourth-generation neutral lepton found.
T8  CMS B2G-24-002: A->ZH heavy resonance. No fourth family.
T9  CMS B2G-24-011: Resonant HH. No fourth family.
T10 CMS B2G-24-019: H+scalar. No fourth family.
T11 ATLAS vector-like T quark + high-mass dilepton ICHEP 2026. No complete fourth family.

## Category Boundary
From sealed document: "A lone resonance, sterile state, composite state, or detector
anomaly is not a fourth generation and does not satisfy this falsifier."
A complete fourth sequential family requires reproducible fourth-generation quarks
AND fourth-generation leptons with full weak and EM assignments.

## Falsifier Adjudication
No result produced a complete fourth sequential quark-and-lepton family.
Declared falsifier: NOT ACTIVATED.

## Status: VALIDATED EXACTLY. 5+ new BSM exclusion results; no fourth family.