Registry · Theorem IV.T171 tau-effective formalized

IV.T171 — Fourth Generation Excluded (Topological)

|fermion generations| = 3 from π₁(τ³). Three independent proofs: (1) H₁(τ³;ℤ) ≅ ℤ³ (rank = 3); (2) exactly 3 primitive winding classes (1,0), (0,1), (1,1) on T² below spectral gap to (2,1); (3) L = S¹∨S¹ has exactly 3 topologically distinct regions (lobe₁, lobe₂, crossing). Result is topological (energy-independent).

Book IV Part 5 Ch. 35

Dependency Graph

Depends on (4)

Depended on by (9)

Lean Formalization

Module: TauLib.BookIV.Particles.ThreeGenerations

Symbol: Tau.BookIV.Particles.fourth_gen_excluded_topological