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