Registry · Definition
IV.D347
established
formalized
IV.D347 — Three Primitive Winding Classes on T²
The three primitive winding classes on T² = (R·S¹)×(ι_τR·S¹) are (1,0), (0,1), (1,1), defined as the three lowest-eigenvalue primitive (gcd=1) modes of the T² Laplacian. Eigenvalues in units of 1/R²: λ_(1,0)=1, λ_(0,1)=ι_τ⁻²≈8.585, λ_(1,1)=1+ι_τ⁻²≈9.585. The non-primitive (2,0) mode has λ=4 (gcd=2, excluded). All higher primitive modes have λ≥4+ι_τ⁻²≈12.58, creating a clear spectral separation that isolates exactly three light generations.